{
  "$schema": "./element-isotope-catalog.schema.json",
  "schema_version": "1.1.0",
  "title": "Element and isotope observations and construction research",
  "coverage": "Initial, non-exhaustive catalogue: hydrogen-1 and hydrogen-2 only. This is not a table of all stable isotopes.",
  "sources": [
    {"id": "storage-branch-comparison", "kind": "repository", "location": "research/voevodsky/storage-branch-comparison.md", "description": "Parallel transparent-interaction complexity audit and exact sine-packet optimization at fixed battery capacity/mean energy, with other-input and free-phase controls."},
    {"id": "storage-branch-comparison-results", "kind": "repository", "location": "research/voevodsky/results/storage_branch_comparison.json", "description": "Exact 769-term pair expansion, truncation failures and cyclotomic optimized battery fidelities; objective-dependent tradeoffs are retained."},
    {"id": "finite-work-battery-pulse", "kind": "repository", "location": "research/voevodsky/finite-work-battery-pulse.md", "description": "Unchanged error-sector hold with an explicit finite coherent work ladder; total pulse energy and joint reversal hold, while reduced logical fidelity has a finite-resource cost."},
    {"id": "finite-work-battery-pulse-results", "kind": "repository", "location": "research/voevodsky/results/finite_work_battery_pulse.json", "description": "Exact source-sector energy pairings, finite ladder boundaries and fidelity/reversal tests for five coherent work packets."},
    {"id": "error-transparent-bond-pulse", "kind": "repository", "location": "research/voevodsky/error-transparent-bond-pulse.md", "description": "Uniform recovery-frame pulse with energy conservation and single-fault transparency; the changed off-code hold law and old-energy obstruction are explicit."},
    {"id": "error-transparent-bond-pulse-results", "kind": "repository", "location": "research/voevodsky/results/error_transparent_bond_pulse.json", "description": "Exact complete error-basis and intertwining checks, 120 mid-pulse cases and a 1/2-unit energy obstruction for the unchanged old error-sector hold."},
    {"id": "bond-battery-transfer-pulse", "kind": "repository", "location": "research/voevodsky/bond-battery-transfer-pulse.md", "description": "All-time matched-sector bare-energy conservation for the direct spectral pulse, with a one-physical-fault counterexample to transferring the earlier circuit's fault guarantee."},
    {"id": "bond-battery-transfer-pulse-results", "kind": "repository", "location": "research/voevodsky/results/bond_battery_transfer_pulse.json", "description": "Exact half/full encoded pulses, energy commutator and a mid-pulse Pauli fault yielding fidelity 1/2 after correct syndrome recovery."},
    {"id": "pairwise-bond-battery-storage", "kind": "repository", "location": "research/voevodsky/pairwise-bond-battery-storage.md", "description": "Explicit battery-architecture change eliminates modular history addressing: pairwise SWAP-plus-flips retains the input in battery occupations, with an existing-code implementation."},
    {"id": "pairwise-bond-battery-storage-results", "kind": "repository", "location": "research/voevodsky/results/pairwise_bond_battery_storage.json", "description": "Exact pair energy map, encoded logical states and one-fault propagation controls; no off-sector or intermediate-pulse energy theorem."},
    {"id": "history-code-circuit", "kind": "repository", "location": "research/voevodsky/history-code-circuit.md", "description": "Explicit Clifford history encoder/decoder and syndrome-conditioned recovery; ideal controls and one-event physical-noise assumptions remain."},
    {"id": "history-code-circuit-results", "kind": "repository", "location": "research/voevodsky/results/history_code_circuit.json", "description": "Exact gate lists, full component inverse checks and complete physical-error correction table with retained syndrome phases."},
    {"id": "encoded-history-memory", "kind": "repository", "location": "research/voevodsky/encoded-history-memory.md", "description": "Prior five-qubit-code adapter for 22 history labels; single physical-qubit correction is distinct from the uncorrected logical history-phase fault."},
    {"id": "encoded-history-memory-results", "kind": "repository", "location": "research/voevodsky/results/encoded_history_memory.json", "description": "Exact history isometry, 75 nonzero physical-error syndromes, recovery identities and logical/two-fault controls with source hashes."},
    {"id": "prior-five-rail-code", "kind": "repository", "location": "research/kitaev/s3-five-rail-code-and-transversal-obstruction.md", "description": "Owning exact component code, logical operators and recovery tables; naive transversal gate assumptions fail."},
    {"id": "prior-shor-recovery", "kind": "repository", "location": "research/kitaev/s3-five-rail-shor-recovery.md", "description": "Verified-cat syndrome schedule, resource counts and separated one-error-correction boundary."},
    {"id": "seam-addressed-history-storage", "kind": "repository", "location": "research/voevodsky/seam-addressed-history-storage.md", "description": "Reversible seam-addressed filling with a finite battery, coherent-sector energy conservation, off-sector residuals and a zero-energy history phase-error control."},
    {"id": "seam-addressed-history-storage-results", "kind": "repository", "location": "research/voevodsky/results/seam_addressed_history_storage.json", "description": "38808 addressed-step cases, 21 source branches, exact native energy residuals and a history fidelity loss despite unchanged filled-bond energy."},
    {"id": "filled-bond-history-storage", "kind": "repository", "location": "research/voevodsky/filled-bond-history-storage.md", "description": "All-filled bonds retain arbitrary seam amplitudes through explicit quantum history and an energy-conserving finite-battery exchange; global control and history assumptions remain."},
    {"id": "filled-bond-history-storage-results", "kind": "repository", "location": "research/voevodsky/results/filled_bond_history_storage.json", "description": "Exact native energy-block, tensor-metric, exchange, amplitude-recovery and finite-battery conservation checks for controlled filled-bond storage."},
    {"id": "single-seam-memory-occupation", "kind": "repository", "location": "research/voevodsky/single-seam-memory-occupation-bridge.md", "description": "One actual seam connects amplitude memory to the existing occupation hold law with phase-corrected recovery and control work; the many-seam encoding is one-hot, not all-filled."},
    {"id": "single-seam-memory-occupation-results", "kind": "repository", "location": "research/voevodsky/results/single_seam_memory_occupation.json", "description": "Exact isometry, unitary write/read, invariant hold, balanced work and 21-seam code occupation bound; no autonomous or mass claim."},
    {"id": "geometric-phase-bridge", "kind": "repository", "location": "research/voevodsky/geometric-phase-energy-bridge.md", "description": "Exact native proton/belt phase and energy reconstruction with supplied adapters; electron fixed-cell restriction fails."},
    {"id": "geometric-phase-bridge-results", "kind": "repository", "location": "research/voevodsky/results/geometric_phase_energy_bridge.json", "description": "Exact mode, return, Hamiltonian, metric and seam comparisons, with electron attachment-orbit control."},
    {"id": "phase-occupation-frontier", "kind": "repository", "location": "research/voevodsky/phase-occupation-persistence-frontier.md", "description": "Persistent checkpoint and immutable source replay; constructive existence is distinct from forced occupation."},
    {"id": "phase-occupation-necessity-results", "kind": "repository", "location": "research/voevodsky/results/phase_occupation_necessity.json", "description": "Existing bond-versus-syndrome control replayed on the frozen bridged source, not a refutation of conditional occupation constructions."},
    {"id": "retained-energy-prior-recovery", "kind": "repository", "location": "research/voevodsky/prior-retained-energy-mechanism-recovery.md", "description": "Recovered memory, charging, reservoir and sector-protection mechanisms; uniform construction does not require uniqueness."},
    {"id": "prior-projection-memory", "kind": "repository", "location": "research/nima/comparison-update-dynamics-and-energy-normalization.md", "description": "Existing reversible projection-memory lift, conserved budget, record reuse and normalization boundaries."},
    {"id": "native-phase-seam-memory", "kind": "repository", "location": "research/voevodsky/native-phase-seam-reversible-memory.md", "description": "Actual belt lift with 18 phase and 21 seam amplitude records, exact recovery and back-action; not stationary storage or mass."},
    {"id": "native-phase-seam-memory-results", "kind": "repository", "location": "research/voevodsky/results/native_phase_seam_memory.json", "description": "Exact 75-dimensional recovery, 39 metric-unitary involutions, spectral generators and bare-energy nonconservation controls."},
    {"id": "common-assembly-ledger", "kind": "repository", "location": "src/ledger/20261010-4319 Common Geometric Assembly with Retained Interfaces.md", "description": "Ledger 4319: common geometric constructor, reversible centroid modes, six-hypothesis audit and subdivision counterexample, with scope and graph provenance."},
    {"id": "common-assembly-audit", "kind": "repository", "location": "research/voevodsky/common-geometric-assembly-six-hypothesis-audit.md", "description": "Six tested geometric hypotheses distinguish source-driven construction, relative interfaces, refinements and higher fillers; no intrinsic four-dimensional reset was established."},
    {"id": "common-assembly-audit-results", "kind": "repository", "location": "research/voevodsky/results/common_assembly_hypotheses.json", "description": "Fresh six-test suite and exact source-driven proton 1836-manifest regression, including obstruction tests."},
    {"id": "relative-geometric-constructor", "kind": "repository", "location": "research/voevodsky/relative-geometric-source-constructor.md", "description": "One orbit/supporting-facet/relative-boundary/cone constructor from explicit seed points, metrics, affine isometries and attachment roles; no target cell lists in the constructor."},
    {"id": "relative-geometric-results", "kind": "repository", "location": "research/voevodsky/results/relative_geometry_sources.json", "description": "Exact independent comparisons of distances, facets, subdivisions, centers and attachment marks, plus source deletion and parameter controls."},
    {"id": "geometric-mode-selection", "kind": "repository", "location": "research/voevodsky/relative-geometric-complex-mode-selection.md", "description": "Nontrivial centroid-mode support replaces explicit neutron cap exclusions at maximal supporting-facet resolution; complex-plane projection alone does not erase caps."},
    {"id": "geometric-mode-selection-results", "kind": "repository", "location": "research/voevodsky/results/relative_geometry_mode_selection.json", "description": "Exact four/six/five facet selection, affine-frame covariance, complex-mode interpretation and non-erasure control."},
    {"id": "geometric-mode-motion", "kind": "repository", "location": "research/voevodsky/relative-geometric-reversible-mode-motion.md", "description": "Exact encode/phase-advance/decode motion on facet centroids, retaining fixed channels; source-scheduled periods are not physical particle periods."},
    {"id": "geometric-mode-motion-results", "kind": "repository", "location": "research/voevodsky/results/relative_geometry_mode_motion.json", "description": "Exact forward and stepwise reverse histories, metric-energy conservation, target matching and fixed-mode loss controls; neutron input has no explicit rim protection."},
    {"id": "centroid-refinement-counterexample", "kind": "repository", "location": "research/voevodsky/centroid-admission-refinement-counterexample.md", "description": "Unrestricted cellwise centroid admission fails subdivision invariance: neutron caps return after refinement. Geometric supporting-plane regrouping restores the narrower facet-level result."},
    {"id": "centroid-refinement-results", "kind": "repository", "location": "research/voevodsky/results/centroid_admission_refinement.json", "description": "Exact 18-versus-24 neutron triangle counterexample and parent-label-independent supporting-plane regrouping control."},
    {"id": "spinor-interacting-construction", "kind": "repository", "location": "research/voevodsky/spinor-interacting-construction.md", "description": "Classical fixed-lead state space, Hamiltonian dynamics, source symmetry, tangent stability and finite-amplitude checks for the four-ray ground orbit."},
    {"id": "spinor-interacting-results", "kind": "repository", "location": "research/voevodsky/results/spinor_interacting_construction.json", "description": "Fresh nine-stage construction verification with retained upstream receipt hashes; not quantization or repository-wide closure."},
    {"id": "spinor-ground-orbit", "kind": "repository", "location": "research/voevodsky/spinor-ground-orbit.md", "description": "Critical-family exhaustion proves the global hard-flux pure-state minimum and identifies four source-covariant minimizing rays with retained binary rotation phases."},
    {"id": "spinor-ground-orbit-results", "kind": "repository", "location": "research/voevodsky/results/spinor_ground_orbit.json", "description": "Symbolic cofactor/purity identities, exact critical-energy intervals, 24 binary rotations and 576 group compositions."},
    {"id": "spinor-fixed-flux-relaxation", "kind": "repository", "location": "research/voevodsky/spinor-fixed-flux-relaxation.md", "description": "Joint charged-density/electric minimization retaining source flux, with exact global pure-state energy bounds and feasible source-derived deformation."},
    {"id": "spinor-fixed-flux-results", "kind": "repository", "location": "research/voevodsky/results/spinor_fixed_flux_relaxation.json", "description": "Exact Gauss lead flux, four-address trial identities and symmetric two-copy positive-operator lower certificate."},
    {"id": "spinor-face-magnetic-action", "kind": "repository", "location": "research/voevodsky/spinor-face-magnetic-action.md", "description": "Complete magnetic feedback on source dual-face loops, finite-stiffness current obstruction and exact source-flux constraint multiplier."},
    {"id": "spinor-face-magnetic-results", "kind": "repository", "location": "research/voevodsky/results/spinor_face_magnetic_action.json", "description": "Exact loop incidence, Gauss/power balance, coherent circulation and reversible numerical magnetic feedback."},
    {"id": "spinor-matter-link-adapter", "kind": "repository", "location": "research/voevodsky/spinor-matter-link-adapter.md", "description": "Exact actual-spinor kinetic/current adapter retains curved face-link phases and exposes the electric-only holonomy cancellation."},
    {"id": "spinor-matter-link-results", "kind": "repository", "location": "research/voevodsky/results/spinor_matter_link_adapter.json", "description": "Exact source intertwiner, signed current/Gauss/gauge identities, face-loop phases and common three-species exterior graph."},
    {"id": "common-charging-mass-closure", "kind": "repository", "location": "research/voevodsky/common-charging-mass-closure.md", "description": "Recovered common charging law closes the absolute baselines and yields an all-coupling bound excluding simultaneous proton/electron and neutron-proton mass agreement."},
    {"id": "common-charging-mass-results", "kind": "repository", "location": "research/voevodsky/results/common_charging_mass_closure.json", "description": "Exact occupied-channel minima, absolute readout and scale-free mass-inequality controls."},
    {"id": "interacting-elementary-reference", "kind": "repository", "location": "research/voevodsky/interacting-elementary-reference.md", "description": "The actual four-face spinor has a full-doublet all-face field contact and exact common-field rest energy 3/4 clock unit; dressed normalization still fails the mass comparison."},
    {"id": "interacting-elementary-results", "kind": "repository", "location": "research/voevodsky/results/interacting_elementary_reference.json", "description": "Exact stored-spinor contact reconstruction, kinetic eigenspaces, finite-pool dressed ratios and held-out numerical comparison."},
    {"id": "finite-record-mediator", "kind": "repository", "location": "research/voevodsky/finite-record-mediator-constructor.md", "description": "Source-addressed signed controlled gates construct a finite neutral-record vertex and oscillator limit; direct electron-gap mass comparison fails."},
    {"id": "finite-record-mediator-results", "kind": "repository", "location": "research/voevodsky/results/finite_record_mediator_constructor.json", "description": "Exact signed-gate identities, finite-pool ground brackets, non-symmetric-sector bounds and held-out mass-scale comparison."},
    {"id": "neutral-mediator-mass-bridge", "kind": "repository", "location": "research/voevodsky/neutral-mediator-mass-bridge.md", "description": "Complete scalar-field dressing on all-face source profiles gives a heavier belt with shared parameters, retaining field energy and induced self-energy."},
    {"id": "neutral-mediator-mass-results", "kind": "repository", "location": "research/voevodsky/results/neutral_mediator_mass_bridge.json", "description": "Exact rational Schur-tail bounds certify the infinite-oscillator mass splitting in elementary-gap units."},
    {"id": "elementary-gap-contact-bridge", "kind": "repository", "location": "research/voevodsky/elementary-gap-contact-bridge.md", "description": "Spin-preserving one-clock contact adapter: full exchange projector leaves zero splitting; adding equal-gap auxiliary occupation reverses the local-contact ordering."},
    {"id": "elementary-gap-contact-results", "kind": "repository", "location": "research/voevodsky/results/elementary_gap_contact_bridge.json", "description": "Exact projector and matched-zero checks, source contact hash and rational ground-energy brackets for the elementary-gap adapter."},
    {"id": "prior-deuterium-binding-search", "kind": "repository", "location": "research/voevodsky/prior-deuterium-binding-search.md", "description": "Recovered binding benchmarks, connected-energy tests and completed triangle-port failures relevant to the missing deuterium interaction."},
    {"id": "hydrogen-shell-benchmark", "kind": "repository", "location": "research/voevodsky/hydrogen-attachment-candidate.md", "description": "An added attractive radial shell law gives negative energy but the twelve-site position reader fails spherical-density tests."},
    {"id": "binding-connected-energy", "kind": "repository", "location": "research/nima/binding-composition-coherence.md", "description": "Connected-energy discriminator separates interaction from constituent self-energies; route coherence does not select binding."},
    {"id": "hminus-binding-benchmark", "kind": "repository", "location": "research/nima/hminus-nested-orbitals.md", "description": "Exchange-symmetric, jointly relaxed Coulomb trial demonstrates binding below a consistently calculated breakup threshold."},
    {"id": "inner-face-response-failure", "kind": "repository", "location": "research/nima/inner-face-response-port-binding.md", "description": "The state-dependent gate needed for the proposed nonlinear triangle response is outside the existing stage algebra."},
    {"id": "deuterium-typed-breakup", "kind": "repository", "location": "research/voevodsky/deuterium-typed-rim-and-breakup-test.md", "description": "Spinor-valued rim lift, opposite-charge attachment test and exact pair-versus-breakup accounting in the common exterior model."},
    {"id": "deuterium-typed-breakup-results", "kind": "repository", "location": "research/voevodsky/results/deuterium_typed_rim_binding.json", "description": "Exact lifted maps, charge/spin controls and exterior-energy cancellation or repulsion; no nuclear binding added."},
    {"id": "deuterium-rim-response", "kind": "repository", "location": "research/voevodsky/deuterium-two-rim-response.md", "description": "Actual lower/upper rim trace, joint minimum-energy extension and binding-sign test; hydrogen readout constructor extended to separate nuclear and electronic binding inputs."},
    {"id": "deuterium-rim-results", "kind": "repository", "location": "research/voevodsky/results/deuterium_two_rim.json", "description": "Exact rim incidence, joint trace, retained residual, static stiffness and two dynamic response channels."},
    {"id": "deuterium-mass-results", "kind": "repository", "location": "research/voevodsky/results/deuterium_mass_readout.json", "description": "Source-retaining deuterium atom/deuteron readout with exact recoil and radiation accounting; supplied illustrative binding controls."},
    {"id": "open-flux-vacuum", "kind": "repository", "location": "research/voevodsky/open-flux-common-vacuum.md", "description": "One zero-background graph with explicit exterior charge and energy admits empty and occupied states; relaxed sector energies depend on boundary attachment."},
    {"id": "open-flux-results", "kind": "repository", "location": "research/voevodsky/results/open_flux_common_vacuum.json", "description": "Exact common-graph Gauss checks, minimum-energy fluxes, convex sector minima and a boundary-rule counterexample."},
    {"id": "boundary-exposure", "kind": "repository", "location": "research/voevodsky/boundary-exposure-transition.md", "description": "Continuous boundary-exposure audit quantifies the conductance at which the candidate belt-proton ordering reverses."},
    {"id": "boundary-exposure-results", "kind": "repository", "location": "research/voevodsky/results/boundary_exposure_transition.json", "description": "Exact network checks and rational brackets on global-energy sign transitions; no measured mass fit."},
    {"id": "weighted-matter-link", "kind": "repository", "location": "research/voevodsky/weighted-matter-link-adapter.md", "description": "Exact source-weighted adapter to the existing matter/link field feedback, including native alignment, current and Gauss checks."},
    {"id": "weighted-matter-link-results", "kind": "repository", "location": "research/voevodsky/results/weighted_matter_link_adapter.json", "description": "Actual graph weights, exact intertwining/current controls, reversible numerical backreaction and the common-vacuum Gauss gate."},
    {"id": "prior-gauge-feedback", "kind": "repository", "location": "research/nima/record-gauge-feedback-loop.md", "description": "Existing conditional matter/link Hamiltonian, field backreaction, Gauss law and reversible stepping reused by the weighted adapter."},
    {"id": "source-channel-closure", "kind": "repository", "location": "research/voevodsky/source-channel-closure-and-all-face-dressing.md", "description": "Source-only channel elimination, contact-dependence audit and a coherent profile over all six cross-face interfaces of each carrier."},
    {"id": "contact-source-closure-results", "kind": "repository", "location": "research/voevodsky/results/contact_source_closure.json", "description": "126 contact comparisons, exact reversals, uncertified cases and cancellation of source-only static self-energy."},
    {"id": "all-face-contact-results", "kind": "repository", "location": "research/voevodsky/results/all_face_contact.json", "description": "Actual six-interface lists and exact one-mode/two-mode coherent profile reductions under equal per-contact coupling."},
    {"id": "charge-compatible-contact", "kind": "repository", "location": "research/voevodsky/charge-compatible-internal-contact.md", "description": "Internal-channel completion preserves supplied particle charges and baryon labels; the positive common-law splitting is independent of the shared bare offset."},
    {"id": "charge-compatible-contact-results", "kind": "repository", "location": "research/voevodsky/results/charge_compatible_contact.json", "description": "Exact charge commutators, weighted Hermiticity, stable reference controls and common-offset cancellation."},
    {"id": "common-contact-dressing", "kind": "repository", "location": "research/voevodsky/common-contact-dressing-comparison.md", "description": "Matched local proton/belt contacts have an exact response ordering; an identical stable reference coupling places the dressed belt branch above the proton branch."},
    {"id": "common-contact-results", "kind": "repository", "location": "research/voevodsky/results/common_contact_dressing.json", "description": "Exact source contact weights, positive response-order certificate and common-parameter dressed pole brackets."},
    {"id": "belt-coherent-port", "kind": "repository", "location": "research/voevodsky/belt-coherent-port-and-vacuum-stability.md", "description": "Actual symmetric bridge contact, coherent overlap and conditional neutral-reference vacuum-stability test."},
    {"id": "belt-coherent-port-results", "kind": "repository", "location": "research/voevodsky/results/belt_coherent_port_vacuum.json", "description": "Exact source contact weights, resolvent, negative excitation witnesses and positive-offset stability thresholds."},
    {"id": "belt-interface-response", "kind": "repository", "location": "research/voevodsky/belt-interface-response-and-prior-audit.md", "description": "Prior-mechanism audit and source-derived three-mode bridge response, static stiffness and precise vacuum-coupling boundary."},
    {"id": "belt-interface-response-results", "kind": "repository", "location": "research/voevodsky/results/belt_interface_response.json", "description": "Exact rational resolvent, Schur reduction and minimal response realization checks, without added record factors."},
    {"id": "collective-spectrum", "kind": "repository", "location": "research/voevodsky/collective-carrier-spectrum.md", "description": "Exact collective-mode reduction and full proton/belt excitation spectra on the retained carriers, without added seam qubits."},
    {"id": "collective-spectrum-results", "kind": "repository", "location": "research/voevodsky/results/collective_carrier_spectrum.json", "description": "Invariant-sector identities, rational characteristic polynomials, exact soft-root isolation and numerical mode diagnostics."},
    {"id": "seam-mass-comparison", "kind": "repository", "location": "research/voevodsky/seam-mass-comparison.md", "description": "Held-out mass comparison rejects both direct electron-gap identifications of the fixed seam-only model; connected seam reductions do not repair them."},
    {"id": "seam-mass-results", "kind": "repository", "location": "research/voevodsky/results/seam_mass_comparison.json", "description": "Exact-enclosure mass tests against retained rounded reference data, source hashes and connected-subgraph census."},
    {"id": "single-clock-seam", "kind": "repository", "location": "research/voevodsky/single-clock-seam-record.md", "description": "One shared involution clock fixes occupation, consistency and mixing strengths, a neutral record spectrum and a positive belt increment."},
    {"id": "single-clock-seam-results", "kind": "repository", "location": "research/voevodsky/results/single_clock_seam_record.json", "description": "Exact actual-seam recording, history reversal, single-clock spectral and occupation checks."},
    {"id": "seam-occupation", "kind": "repository", "location": "research/voevodsky/persistent-seam-occupation-energy.md", "description": "Existing charged-core dressing coupled to actual belt seam projectors; a positive-operator bound preserves the carrier return and gives a positive relative occupation energy."},
    {"id": "seam-occupation-results", "kind": "repository", "location": "research/voevodsky/results/seam_occupation_energy.json", "description": "Exact seam, symmetry and two-level spectral checks for persistent interface occupations with quantum record mixing."},
    {"id": "native-energy-lift", "kind": "repository", "location": "research/voevodsky/native-operation-energy-lift.md", "description": "Uniform operation-defect energy and metric-normalized seam reflections construct the proton and belt returns from native cycles, rotations and shared-edge matching."},
    {"id": "native-energy-results", "kind": "repository", "location": "research/voevodsky/results/native_operation_energy_lift.json", "description": "Exact native-operation, kernel, shared-edge incidence and energy-intertwining checks."},
    {"id": "nima-uniform-core", "kind": "repository", "location": "research/nima/uniform-local-core-proof.md", "description": "Uniform source-derived involution dynamics in standard complex semantics; construction existence does not require source uniqueness."},
    {"id": "cost-selection", "kind": "repository", "location": "research/voevodsky/selection-alignment-cost-selection-audit.md", "description": "Recovered prior energy-selection work and exact source-interchange constraints on traversal costs, stored gaps and preparation effort."},
    {"id": "cost-selection-results", "kind": "repository", "location": "research/voevodsky/results/selection_alignment_cost_selection.json", "description": "52488 interchange tests, explicit cost-equation witnesses, symmetry and positive reservoir countermodels."},
    {"id": "local-sector-protection", "kind": "repository", "location": "research/nima/mass-local-sector-protection.md", "description": "Exact Gauss constraints and restricted tensor-factor locality protect sector transitions but permit diagonal energy shifts."},
    {"id": "source-interchange", "kind": "repository", "location": "research/nima/mass-source-interchange-coherence.md", "description": "Retained-operation squares and cubes preserve genuine traversal histories and nonzero cycle resources."},
    {"id": "constraint-energy", "kind": "repository", "location": "research/voevodsky/constraint-energy-and-retained-record-accounting.md", "description": "Common constraint Hamiltonian, reversible syndrome records, exact coordinate transport and separation of constraint energy from stored rest energy."},
    {"id": "constraint-energy-results", "kind": "repository", "location": "research/voevodsky/results/constraint_energy_accounting.json", "description": "Exact spectra, operator intertwining, local-rank comparison and reversible recoding controls."},
    {"id": "geometry-energy-bridge", "kind": "repository", "location": "research/voevodsky/geometry-comparison-energy-bridge.md", "description": "Invertible comparison-slot to proton-transfer map, contravariant belt support comparison, and exact stage-energy differences."},
    {"id": "geometry-energy-results", "kind": "repository", "location": "research/voevodsky/results/geometry_comparison_energy_bridge.json", "description": "Exact record replay, support budgets, coefficient mismatch and energy-reader controls."},
    {"id": "charged-core-dressing", "kind": "repository", "location": "research/nima/mass-comparison-charged-core-dressing.md", "description": "Constructed finite dressing Hamiltonian, energy hierarchy and parameter/mixing controls."},
    {"id": "quotient-charge", "kind": "repository", "location": "research/nima/mass-primitive-quotient-charge.md", "description": "Joint collective/elementary quotient charge action, conditional energies and sector-protection gap."},
    {"id": "rotor-actions", "kind": "repository", "location": "research/nima/mass-rotor-action-and-external-charge.md", "description": "Phase locking versus charge locking and their different energy/charge scaling."},
    {"id": "pair-coupling", "kind": "repository", "location": "research/voevodsky/electron-pairing-coupling.md", "description": "State-dependent phase attachment, neutral spinor-pair vertex and equal-mass control."},
    {"id": "hydrogen-mass", "kind": "repository", "location": "research/nima/hydrogen-mass-readout.md", "description": "Witness-retaining hydrogen mass adapter with photon recoil and exact conservation; physical inputs supplied."},
    {"id": "gram-spectrum", "kind": "repository", "location": "research/nima/mass-carrier-gram-spectrum-audit.md", "description": "Exact Gram-energy spectrum and failure to derive the 1836 excitation ratio."},
    {"id": "comparison-resource", "kind": "repository", "location": "research/nima/proton-electron-shared-state-comparison-hypothesis.md", "description": "Comparison slots, positive traversal resources and failed fractional-tail trials."},
    {"id": "locking-controller", "kind": "repository", "location": "research/nima/mass-history-retaining-locking-interaction.md", "description": "Reversible driven charge-locking preparation with retained history and explicit reservoirs."},
    {"id": "nudat", "kind": "external", "location": "https://www.nndc.bnl.gov/nudat3/", "description": "NNDC NuDat 3 nuclear-data reference for isotope identification and stability. Reference recorded, not retrieved or independently audited during catalogue creation."},
    {"id": "nist-hydrogen", "kind": "external", "location": "https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=H", "description": "NIST hydrogen isotope identification and composition reference. Reference recorded, not retrieved or independently audited during catalogue creation."},
    {"id": "proton-research", "kind": "repository", "location": "research/nima/baryonic-matter-bridge.md", "description": "Proton-like construction and the boundary between mathematical construction and physical identification."},
    {"id": "belt-geometry", "kind": "repository", "location": "research/voevodsky/coupled-six-piece-belt.md", "description": "Six-piece belt construction."},
    {"id": "belt-core", "kind": "repository", "location": "research/voevodsky/belt-three-by-twelve.md", "description": "Intrinsic three-sector, twelve-coordinate belt return, including adapter costs."},
    {"id": "electron-frontier", "kind": "repository", "location": "research/voevodsky/electron-charge-spin-frontier.md", "description": "Checked tetrahedral spinor doublet and charge, mass, and exchange limitations."},
    {"id": "isotope-attachments", "kind": "repository", "location": "research/voevodsky/electron-pentachoron-attachment.md", "description": "Proposed pentachoron geometry and hydrogen isotope attachment matches; explicitly not derived binding dynamics."},
    {"id": "spin-interfaces", "kind": "repository", "location": "research/voevodsky/pentachoron-geometric-spin-interfaces.md", "description": "Geometry-derived spin interfaces, exact-matching obstructions, and four lowest mismatch modes."},
    {"id": "spin-interface-results", "kind": "repository", "location": "research/voevodsky/results/pentachoron_spin_interfaces.json", "description": "Recorded exact finite-check results, not physical validation."},
    {"id": "interface-contract", "kind": "repository", "location": "research/voevodsky/cell-interface-assembly-contract.md", "description": "Conditional linear assembly contract and supplied flat full-spinor extension."},
    {"id": "recombination-note", "kind": "repository", "location": "research/voevodsky/edge-link-recombination-exchange-symmetry-and-polarization-correlations.md", "description": "Recorded investigation of recombination and correlation; intrinsic state-selection law unresolved."},
    {"id": "viewer-source", "kind": "repository", "location": "papers/witness-generators/proton-neutron-assembly.html", "description": "Authoritative viewer source; visual stages are explanatory proxies."},
    {"id": "viewer-checker", "kind": "repository", "location": "research/voevodsky/checkers/check_unified_assembly_page.mjs", "description": "Executable checks for geometry, attachments and UI; these do not establish physical binding or stability."}
  ],
  "mechanisms": [
    {
      "id": "retained-phase-energy-memory", "name": "Retained phase, energy bridge and reversible memory", "status": "conditional",
      "summary": "Full geometry recovers native proton/belt phase and energy operators. Reversible belt memory reaches occupation storage through a one-hot code; an explicit added quantum history then retains all amplitudes in all-filled bonds with a finite energy-balancing battery. Local autonomous storage and electron five-cell transport remain open.",
      "assumptions": ["Retain ordered corners, selected character, native metric, grouping and alignment operations. The belt frame has squared scale 8/3 relative to the geometric source.", "Use one complex amplitude memory per rank-one rejected direction with inherited metric, and a declared phase-then-seam schedule; these memories are not binary occupation registers.", "A uniform constructive witness need not be uniquely forced by the source; necessity is a separate stronger claim."],
      "results": [
        {"status": "checked", "statement": "The exact transparent pair projector has 769 physical Pauli terms: one identity, 300 weight-six, 360 weight-eight and 108 weight-ten terms. Keeping only weight-three terms in each component operator, even after normalizing its clean-code action, fails all fifteen nonzero correctable error sectors. This rules out that direct truncation, not ancillary or approximate implementations.", "source_ids": ["storage-branch-comparison", "storage-branch-comparison-results"]},
        {"status": "checked", "statement": "For the finite-work midpoint-input objective, a sine packet is optimal at fixed M with fidelity (1+cos(pi/(M+1)))/2. At M=16 it improves 0.96875 to about 0.99148655 at unchanged capacity and mean ready energy. It is not a worst-case optimum: at M=4 the other tested fault/input fidelity worsens. Exact cyclotomic pulse tests and free-phase checks at a declared commensurate schedule pass; preparation and physical clock costs remain inputs.", "source_ids": ["storage-branch-comparison", "storage-branch-comparison-results"]},
        {"status": "checked", "statement": "Keeping the old error-sector hold, finite work-ladder pairings conserve total hold/work energy at every pulse angle and retain joint reversibility. For uniform ready packets on M interior levels, a tested mid-pulse physical fault gives logical target fidelity 1-1/(2M), from 1/2 at M=1 to 31/32 at M=16. Shifted battery correlations and boundary failures remain explicit; these examples are not optimal bounds, noise thresholds or calibrated energies.", "source_ids": ["finite-work-battery-pulse", "finite-work-battery-pulse-results"]},
        {"status": "checked", "statement": "The actual reversible recovery map supplies a uniform error-sector extension whose direct pair pulse conserves its hold Hamiltonian and preserves the logical endpoint through a single correctable physical fault at any pulse time. Exact error-basis/intertwining checks and 120 mid-pulse cases pass. The new hold matches old code energies but explicitly changes off-code error energies; direct many-body implementation is assumed, not derived local hardware.", "source_ids": ["error-transparent-bond-pulse", "error-transparent-bond-pulse-results"]},
        {"status": "checked", "statement": "Under the old hold law, the same physical-error copies of logical 00 and 11 have energies 1/4 and 3/4. An error-transparent transfer between them cannot conserve that unchanged bare hold. Either the explicit new error-sector coupling or an additional energy-exchange resource is necessary; the change is not an unreported coordinate convention.", "source_ids": ["error-transparent-bond-pulse", "error-transparent-bond-pulse-results"]},
        {"status": "checked", "statement": "The direct spectral pair pulse has Q=(I+ZZ-XX+YY)/4 and commutes with the matched-sector hold energy at every pulse angle. Exact encoded half/full pulses pass. Ideal switching has zero net work when the pulse strength begins and ends at zero; controller implementation is not derived.", "source_ids": ["bond-battery-transfer-pulse", "bond-battery-transfer-pulse-results"]},
        {"status": "refuted", "statement": "The earlier physical SWAP/Pauli circuit's one-fault guarantee does not apply to the direct encoded spectral pulse. An actual single physical Z fault at half pulse leaves target fidelity 1/2 after correct syndrome recovery, despite unchanged bare energy. The direct interaction includes weight-6 and weight-10 terms; continuous energy and fault claims must hold for the same implementation.", "source_ids": ["bond-battery-transfer-pulse", "bond-battery-transfer-pulse-results"]},
        {"status": "checked", "statement": "A new explicit architecture pairs every bond with a battery bit of gap J-epsilon. The Clifford map (n,b)->(1-b,1-n) fills bonds and retains the original pattern in battery occupations, removing separate history lookup. Exact matched-sector endpoint energy remains 41/4 for the one-hot bank; this is not a coordinate change of the previous ladder or a global off-sector conservation law.", "source_ids": ["pairwise-bond-battery-storage", "pairwise-bond-battery-storage-results"]},
        {"status": "checked", "statement": "The pair map has an exact existing-code implementation using five physical SWAPs and six Pauli gates per pair: 210 encoded data qubits across all bonds and battery bits. Tests cover all four logical pair states, 30 single-input-error and 93 single-gate-fault cases per pair. With clean input one gate fault leaves at most one correctable error per affected block; simultaneous input and gate faults are not certified. Intermediate control energy and physical noise remain open.", "source_ids": ["pairwise-bond-battery-storage", "pairwise-bond-battery-storage-results"]},
        {"status": "checked", "statement": "The prior history code now has an explicit Clifford encoder/decoder and full retained-syndrome correction table. Exact Q(sqrt(2),i) checks cover all 32 component basis inverses and all single-physical-qubit Pauli/logical-input cases. Five blocks encode 22 labels in 25 physical data qubits. This bare circuit assumes ideal controls; it does not establish fault-tolerant decoding, a microscopic noise source or protected modular-address operations.", "source_ids": ["history-code-circuit", "history-code-circuit-results"]},
        {"status": "checked", "statement": "The 22 history labels embed isometrically into five logical qubits encoded with five prior [[5,1,3]] blocks: 25 physical data qubits. Exact checks give 75 distinct nonzero single-physical-qubit syndromes and preserve all history amplitudes under fault-free recovery. The reused Shor schedule consumes 240 cat/data contacts, 180 verification checks and 240 fresh cat qubits across five blocks, under its original separated 1-EC assumptions.", "source_ids": ["encoded-history-memory", "encoded-history-memory-results", "prior-five-rail-code", "prior-shor-recovery"]},
        {"status": "checked", "statement": "The original logical history-label phase fault remains in the encoded code space with zero syndrome, so encoding alone does not repair that same source-level fault. A two-physical-qubit fault control also leaves a logical error after single-error correction. Physical noise coupling and encoded control implementation remain unconstructed; no lifetime or stability follows.", "source_ids": ["encoded-history-memory", "encoded-history-memory-results"]},
        {"status": "checked", "statement": "A reversible history-addressed schedule fills all 21 bonds with twenty active seam steps per branch and a finite 21-level battery of spacing 1/4. Every reachable coherent-sector stage conserves total energy 41/4 and inverse read restores input/history/battery. Actual off-sector residuals are nonzero: this addressed replacement is not globally energy-conserving or proved microscopically local.", "source_ids": ["seam-addressed-history-storage", "seam-addressed-history-storage-results"]},
        {"status": "checked", "statement": "A phase flip on one degenerate history label leaves all 21 bonds occupied and register/battery energies unchanged, yet reduces exact recovered-state fidelity below one. Occupation gaps do not protect coherent history; an explicit noise model and protection mechanism remain necessary.", "source_ids": ["seam-addressed-history-storage", "seam-addressed-history-storage-results"]},
        {"status": "checked", "statement": "The 21 one-hot amplitudes can be reversibly encoded into all-filled bonds plus 21 orthogonal quantum-history labels. An N-controlled exchange conserves the bare carrier/register/battery Hamiltonian; a finite battery receives the five-unit difference between 41/4 and 21/4 at the existing fixture. All native energy blocks, tensor metrics and complex amplitudes are checked. This adds a ready degenerate history resource and global control; it is not an autonomous local latch or a mass result.", "source_ids": ["filled-bond-history-storage", "filled-bond-history-storage-results"]},
        {"status": "checked", "statement": "One actual seam admits a 37-dimensional memory code in the 72-dimensional carrier/bit space and a full unitary write/read. The existing g=0 occupation law preserves the written coherent carrier and occupation; phase-corrected read recovers the input. Write releases mismatch energy into an explicit work account and read consumes it. The encoding uses the full coherent vector and is not a proved local autonomous device.", "source_ids": ["single-seam-memory-occupation", "single-seam-memory-occupation-results"]},
        {"status": "checked", "statement": "The same encoding extends to a 57-dimensional one-hot code for 21 seam amplitudes, invariant under the existing zero-mixing hold law. Total occupation expectation is at most one. At the declared fixture its memory energy is 41/4 versus 21/4 for the all-filled ground. The 21-dimensional memory cannot be losslessly compressed into that rank-one ground without extra retained degrees of freedom; these are model energies, not masses.", "source_ids": ["single-seam-memory-occupation", "single-seam-memory-occupation-results"]},
        {"status": "checked", "statement": "All twelve proton and eighteen belt triangle modes, collective returns and native Hamiltonians are reconstructed exactly. All 21 native belt seam projectors are recovered; the full mesh has 24 shared edges, so native grouping remains substantive input.", "source_ids": ["geometric-phase-bridge", "geometric-phase-bridge-results"]},
        {"status": "checked", "statement": "Native constraint energy vanishes on the coherent return. Recovered seams satisfy P_e N=0 and (I-P_e)N=N, connecting to the existing conditional occupation law without fitted weights.", "source_ids": ["geometric-phase-bridge-results", "seam-occupation"]},
        {"status": "refuted", "statement": "Centroid-only data do not determine the chiral line: reversing ordered corners preserves centroids but changes the projector. Unitary centroid motion cannot be identified by isometric conjugacy with the nonunitary native local cycles.", "source_ids": ["geometric-phase-bridge", "geometric-phase-bridge-results"]},
        {"status": "checked", "statement": "The electron five-cycle visits all five attachment tetrahedra rather than preserving the single cell carrying the existing spinor. Its restriction to that old spinor cell is not a closed action.", "source_ids": ["geometric-phase-bridge-results"]},
        {"status": "checked", "statement": "On the same bridged source, the existing bond and syndrome interpretations preserve the return but give increments 21/4 and zero at the declared zero-mixing fixture. Occupation is not forced by geometric/phase data alone; this does not refute either conditional construction or require uniqueness before constructing a witness.", "source_ids": ["phase-occupation-necessity-results", "phase-occupation-frontier", "retained-energy-prior-recovery"]},
        {"status": "checked", "statement": "The actual belt's 36 complex coordinates plus 18 phase and 21 seam amplitude memories form a 75-dimensional realization. All 39 lifts are metric-unitary involutions; reverse-order recovery passes on every basis vector, including populated records. Record-frame rescaling preserves dynamics and budget.", "source_ids": ["native-phase-seam-memory", "native-phase-seam-memory-results"]},
        {"status": "checked", "statement": "For two explicit phase/seam mismatch inputs, the carrier reaches its coherent vector while removed amplitude remains in memory. Reverse execution restores the input and empties records. Forward reuse produces back-action; two forward sweeps do not undo the seam fixture. A coherent input with ready memories creates no mismatch record.", "source_ids": ["native-phase-seam-memory-results"]},
        {"status": "checked", "statement": "Every lift admits the existing positive spectral generator H_gate=pi*(I-U)/2. Each gate conserves its own spectral energy and the combined metric budget, but all 39 fail to commute with the unchanged bare carrier constraint Hamiltonian. These observables are not silently identified.", "source_ids": ["native-phase-seam-memory", "native-phase-seam-memory-results", "nima-uniform-core"]}
      ],
      "open_obligations": ["Construct compatible electron spinor, metric and energy transport across all five cells.", "The seam-addressed schedule is checked on the coherent sector; handle off-sector energy exchange and establish microscopic locality. The prior-code history adapter corrects the declared single-physical-qubit noise model; the encoder/decoder and ideal recovery controls are explicit. The pairwise battery architecture removes modular addressing with a checked encoded gate. Two conditional routes are checked: changed error-sector hold with exact logical transparency, or unchanged hold with a finite coherent work battery and residual logical/battery correlations. Physically admit and implement one coupling/resource contract; fault/recovery work, noise rates and an autonomous controller/latch remain open.", "Do not infer a stationary latch, calibrated masses, isotope binding or stability; prior mass-comparison failures remain in force."],
      "source_ids": ["storage-branch-comparison", "storage-branch-comparison-results", "finite-work-battery-pulse", "finite-work-battery-pulse-results", "error-transparent-bond-pulse", "error-transparent-bond-pulse-results", "bond-battery-transfer-pulse", "bond-battery-transfer-pulse-results", "pairwise-bond-battery-storage", "pairwise-bond-battery-storage-results", "history-code-circuit", "history-code-circuit-results", "encoded-history-memory", "encoded-history-memory-results", "prior-five-rail-code", "prior-shor-recovery", "seam-addressed-history-storage", "seam-addressed-history-storage-results", "filled-bond-history-storage", "filled-bond-history-storage-results", "single-seam-memory-occupation", "single-seam-memory-occupation-results", "geometric-phase-bridge", "geometric-phase-bridge-results", "phase-occupation-frontier", "phase-occupation-necessity-results", "retained-energy-prior-recovery", "prior-projection-memory", "native-phase-seam-memory", "native-phase-seam-memory-results", "nima-uniform-core", "seam-occupation", "seam-mass-results", "common-charging-mass-results"]
    },
    {
      "id": "common-geometric-assembly", "name": "Common geometric assembly with retained interfaces", "status": "conditional",
      "summary": "One source-parameterized orbit, supporting-facet and coning procedure reproduces the tetrahedron, six-panel belt and pentachoron. Nontrivial centroid modes select active maximal geometric facets while fixed channels remain interfaces. The unrestricted mesh-cell rule fails a subdivision test.",
      "assumptions": ["Seed points, positive-definite metrics and affine symmetry generators are supplied geometric data; dimension and the neutron gap are not derived from minimal primitive arrows.", "Admission is evaluated on maximal supporting facets, not arbitrary mesh cells. Proton/electron attachment-pole records remain supplied; the mode-based neutron source has no explicit rim exclusions.", "Complex-mode motion implements the supplied actions and declared generator schedule. Centroid channels are not the existing spinor or staged coefficient-arrow channels."],
      "results": [
        {"status": "checked", "statement": "The same constructor, without particle-name branches or target cell lists, generates four proton vertices and four facet cones, six neutron vertices and six admitted panel cones, and five electron vertices and five four-dimensional cones. Independent checks match all distances, coarse facets, centers, attachment marks and the twelve/eighteen triangle subdivisions; electron cones form a stellar subdivision of the pentachoron.", "source_ids": ["relative-geometric-constructor", "relative-geometric-results"]},
        {"status": "checked", "statement": "With explicit neutron rim exclusions removed, facet-centroid mode support retains four proton facets, six of eight neutron facets, and five electron facets. The two zero-score neutron cap centroids are retained as interface channels. Exact affine coordinate changes preserve the result.", "source_ids": ["geometric-mode-selection", "geometric-mode-selection-results", "geometric-mode-motion-results"]},
        {"status": "checked", "statement": "Exact cyclotomic encoding, phase advancement and decoding implement each source isometry reversibly, with orthogonal modes and preserved metric energy. Deleting the fixed mode breaks recovery of both neutron cap centroids. Their corners still move; stationary centroids are not erased cells.", "source_ids": ["geometric-mode-motion", "geometric-mode-motion-results"]},
        {"status": "refuted", "statement": "Unrestricted cellwise centroid admission is not invariant under geometry-preserving subdivision. Selecting neutron facets before subdivision gives eighteen triangles; subdividing first gives twenty-four because both cap centroids split into active child centroids.", "source_ids": ["centroid-refinement-counterexample", "centroid-refinement-results"]},
        {"status": "checked", "statement": "Regrouping refined cells by maximal supporting planes, without consulting parent labels, restores the eighteen-triangle neutron surface. This verifies the narrower facet-level rule on the tested sources, not a general WG derivation.", "source_ids": ["centroid-refinement-results"]},
        {"status": "checked", "statement": "The six-hypothesis audit supplies exact reconstruction and obstruction tests. No intrinsic reset after dimension four follows from coning, closure or collapse to a point. The source-driven proton regression still matches the historical 1836 typed-arrow manifest; that count is not inferred from the new centroid channels.", "source_ids": ["common-assembly-audit", "common-assembly-audit-results", "common-assembly-ledger"]}
      ],
      "open_obligations": ["Derive source metrics, generators and geometric roles from independently admitted primitive-arrow data; necessary generators within these records do not prove global minimality.", "Derive or independently discriminate the maximal-facet centroid-mode admission law from WG, retaining the subdivision counterexample.", "The proton/belt phase and energy adapter is now checked with supplied native conventions; construct the missing electron five-cell spinor/energy transport. No new neutron count follows from centroid channels.", "Derive physical charges, mass, isotope binding and stability separately; source-scheduled returns are not established particle periods."],
      "source_ids": ["common-assembly-ledger", "common-assembly-audit", "common-assembly-audit-results", "relative-geometric-constructor", "relative-geometric-results", "geometric-mode-selection", "geometric-mode-selection-results", "geometric-mode-motion", "geometric-mode-motion-results", "centroid-refinement-counterexample", "centroid-refinement-results"]
    },
    {
      "id": "deuterium-rim-response", "name": "Deuterium two-rim response and mass accounting", "status": "conditional",
      "summary": "Both actual belt rims now have a joint coefficient trace and exact minimum-energy extension. Matching is a positive compatibility penalty, not attractive binding. A separate deuterium mass readout retains nuclear and electronic binding inputs and radiation recoil.",
      "assumptions": ["Use the C3-aligned scalar belt modes with metric diag(3*n); constituent coefficient adapters are not inferred from visual face coincidence.", "The mass readout reuses the existing hydrogen one-photon threshold algebra; constituent masses and binding controls are supplied.", "The electron port remains rank-two spinorial and requires a typed adapter into the rim response."],
      "results": [
        {"status": "checked", "statement": "The declared tensor-spin lift preserves both rim components and has T_spin E_spin=I4. Same-species rim matching is rotation covariant; fixed neutral linear matching between opposite-charge proton/electron amplitudes fails. The existing weight-two link or binary singlet has the required phase type.", "source_ids": ["deuterium-typed-breakup", "deuterium-typed-breakup-results"]},
        {"status": "refuted", "statement": "The current common-exterior model does not bind proton and belt: with the same total reservoir charge the breakup difference is zero, while pooling independent unit reservoirs adds repulsion eta. A source-authorized cross-carrier interaction is missing.", "source_ids": ["deuterium-typed-breakup", "deuterium-typed-breakup-results"]},
        {"status": "checked", "statement": "Lower rim triangles are 1,7,13 and upper rim triangles 4,10,16. The joint trace has a unique minimum-energy extension and retains four residual coordinates. Its exact energy is (1499960093/591106225)*|lower-upper|^2.", "source_ids": ["deuterium-rim-results"]},
        {"status": "refuted", "statement": "Positive rim-matching energy alone does not supply attractive binding below the zero-constraint breakup baseline. Equal rims cost zero; opposite rims cost positive energy.", "source_ids": ["deuterium-rim-response", "deuterium-rim-results"]},
        {"status": "checked", "statement": "Deuteron and atom rest energies retain separate nuclear and electronic deficits. The supplied-input effective photon channel conserves exact four-momentum including recoil; its illustrative binding values are not deuterium predictions.", "source_ids": ["deuterium-mass-results"]}
      ],
      "open_obligations": ["Spinor-valued rim types are constructed by a declared lift; source the constituent-preserving charged interaction rather than a species-converting linear match.", "Calculate composite and breakup energies in the same interacting vacuum to derive binding.", "Derive nuclear and electronic binding values and the stable isotope sector."],
      "source_ids": ["deuterium-typed-breakup", "deuterium-typed-breakup-results", "deuterium-rim-response", "deuterium-rim-results", "deuterium-mass-results", "hydrogen-mass"]
    },
    {
      "id": "weighted-matter-link", "name": "Source-weighted matter/link feedback", "status": "conditional",
      "summary": "Exact source-weighted field feedback now has a conditional zero-background completion with exterior flux and energy retained. It admits a common empty reference, but the relaxed belt-proton energy ordering depends on the physical exterior attachment, which remains unselected.",
      "assumptions": ["Reuse the prior classical matter/link law on the phase-selected source amplitudes, with their inherited metric.", "Hopping weights are derived from the actual Hamiltonians; electric coefficient beta and model time remain supplied.", "Use the electric-only specialization, without inventing filled magnetic loops.", "The numerical fixture has a fixed compensating background; its conserved amplitude norm is not identified with measured electric charge."],
      "results": [
        {"status": "conditional", "statement": "The hard-internal-flux classical state space is locally CP^3 times T* T^3. The four minimizing rays carry distinct conserved exterior lead assignments; full minima are four angle tori. Fixed-lead Hamiltonian dynamics, Gauss/current reconstruction and source rotations are constructed. Numerical tangent and finite-amplitude checks pass; no inter-sector hopping is generated.", "source_ids": ["spinor-interacting-construction", "spinor-interacting-results"]},
        {"status": "checked", "statement": "For the existing beta=3/5, eta=1/5 hard-source-flux fixture, critical-point exhaustion proves the global four-line pure-state minimum 0.1798077094008586. There are four minimizing rays, one per high-density face; the competing two-pair stationary family costs 0.1799010143019994.", "source_ids": ["spinor-ground-orbit", "spinor-ground-orbit-results"]},
        {"status": "checked", "statement": "All 24 binary tetrahedral rotations transport the deformed minimizing rays with source phases retained, and all 576 compositions close. A full rotation acts as -I. The four rays span four coordinates and are nonlinear minima, not a rank-two linear ground eigenspace.", "source_ids": ["spinor-ground-orbit-results"]},
        {"status": "conditional", "statement": "With source face flux constrained and the prior beta=3/5, eta=1/5 fixture, joint pure-spinor/electric relaxation has certified global energy between 0.17940817039929 and 0.17980770940086 before its occupation offset. Electric flux is retained; a symmetric two-copy positivity certificate gives the global lower bound and feasible source-derived deformations give the upper bound.", "source_ids": ["spinor-fixed-flux-relaxation", "spinor-fixed-flux-results"]},
        {"status": "refuted", "statement": "Retaining source flux does not freeze the bare charged coherent spinor: its energy is 0.18, while four source-equivalent deformed trials cost 0.17980770940086 with dark fraction 0.0000924313. The successor critical-point audit identifies these four-address states as global minima and checks their full binary rotation transport.", "source_ids": ["spinor-fixed-flux-results"]},
        {"status": "checked", "statement": "The four geometric dual-face loops now carry the reused cosine magnetic action relative to the source spinor connection. Exact boundary, signed Gauss and total Hamiltonian power identities pass; complete numerical feedback is reversible with second-order energy errors.", "source_ids": ["spinor-face-magnetic-action", "spinor-face-magnetic-results"]},
        {"status": "refuted", "statement": "No finite cosine stiffness exactly preserves the native pure-spinor flux: its source circulating current has squared norm 1/9 while the magnetic gradient vanishes at native flux. A current-aligned infinitesimal field variation lowers energy for every finite stiffness.", "source_ids": ["spinor-face-magnetic-results"]},
        {"status": "conditional", "statement": "The exact relative face-flux constraint C*A=0 retains the native kinetic doublet up to gauge. Its coherent circulation is cancelled by the explicit reaction multiplier lambda=-q*C*J/4. Full charged-density relaxation and physical implementation of the constraint remain to be tested.", "source_ids": ["spinor-face-magnetic-action", "spinor-face-magnetic-results"]},
        {"status": "checked", "statement": "The actual four-face spinor admits a weighted four-line adapter preserving its doublet kernel. Its six normalized hopping magnitudes are 1/sqrt(3), with mandatory onsite coefficient 1-sqrt(3) and nonflat source face-loop phases +/-i. Signed current, continuity and gauge identities pass for either charge sign.", "source_ids": ["spinor-matter-link-adapter", "spinor-matter-link-results"]},
        {"status": "conditional", "statement": "The existing exterior graph extends to 35 vertices and 97 links with declared charges +1,0,-1 for proton, belt and elementary spinor. Empty and opposite-charge sectors obey one zero-background Gauss law. Pure coherent spinors have field energy 2*beta/15+eta/2 independently of logical spin direction.", "source_ids": ["spinor-matter-link-results"]},
        {"status": "refuted", "statement": "The electric-only extension does not preserve the elementary source doublet: free link phases cancel its intrinsic face holonomy and give minimum mu_e+1-sqrt(3)+beta/8+eta/2 with a rank-one fixed-field ground. Signed electric loading also gives no positive neutral-belt excess. A source-compatible face-holonomy action is required.", "source_ids": ["spinor-matter-link-adapter", "spinor-matter-link-results"]},
        {"status": "checked", "statement": "A single 31-vertex, 87-link graph with zero background admits the empty state and either unit internal norm-charge carrier sector, retaining compensating exterior charge and its energy. These are classical constrained sectors, not identified electric charges or quantum particle gaps.", "source_ids": ["open-flux-vacuum", "open-flux-results"]},
        {"status": "conditional", "statement": "With exterior leads at cross-face contact endpoints, global density relaxation leaves the belt above the proton. A common alternative rule with leads at every mode vertex reverses the ordering, so geometry alone does not select the sign.", "source_ids": ["open-flux-vacuum", "open-flux-results"]},
        {"status": "conditional", "statement": "Opening the six belt middle-mode leads continuously decreases its minimized energy. At beta=3/5, the sign changes at relative electric conductance 0.252446898910; the exterior coupling law must determine which side is physical.", "source_ids": ["boundary-exposure", "boundary-exposure-results"]},
        {"status": "checked", "statement": "Exact H V=V K identities recover the proton's 12 selected amplitudes and 24 native-alignment links, and the belt's 18 amplitudes with 21 seam plus 18 native-alignment links. Orthogonal carrier complements remain identified.", "source_ids": ["weighted-matter-link", "weighted-matter-link-results"]},
        {"status": "checked", "statement": "Exact weighted continuity, Hamiltonian current, Gauss derivative, power balance and finite gauge controls pass. Numerical feedback changes electric fields and link phases, is reversible within tolerance, and has second-order energy-error scaling.", "source_ids": ["weighted-matter-link-results"]},
        {"status": "conditional", "statement": "At fixed positive-total background, an empty matter state cannot satisfy Gauss on a closed graph. A common vacuum needs a source-supported signed-species or boundary-flux completion; the adapter does not yet calculate rest mass.", "source_ids": ["weighted-matter-link", "prior-gauge-feedback"]}
      ],
      "open_obligations": ["Identify the physical exterior coupling and its conductance metric; a conditional common empty reference exists, but its energy ordering is boundary-dependent. Derive quantum particle sectors and electric charge rather than identifying conserved norm with them.", "The classical interacting state space and fixed-lead dynamics are constructed. Specify and justify a quantization or additional boundary interaction before asserting a quantum ground doublet or inter-sector transitions. Physically implement the exact flux sector or source its finite stiffness. Identify field normalization, physical charge and time.", "Extend the field coupling to populated phase-orthogonal sectors and distinguish classical feedback from a quantum vacuum calculation."],
      "source_ids": ["open-flux-vacuum", "open-flux-results", "boundary-exposure", "boundary-exposure-results", "weighted-matter-link", "weighted-matter-link-results", "prior-gauge-feedback", "collective-spectrum", "native-energy-lift"]
    },
    {
      "id": "collective-carrier-spectrum", "name": "Collective carrier excitation modes", "status": "conditional",
      "summary": "The actual belt Hamiltonian has an exactly closed six-amplitude sector: one coherent mode and five collective excitations. Its softest excitation is antisymmetric between the paired faces. No independent seam resources are added.",
      "assumptions": ["Retain the previously declared native-operation defect Hamiltonian and its common energy unit pi*hbar/tau.", "Use the actual geometric mode norms and metric-normalized shared-edge projectors.", "These finite carrier eigenstates are not assumed to be independent oscillator factors or physical electron/neutron states."],
      "results": [
        {"status": "refuted", "statement": "Closing the shared field model with one common charging gap per retained channel cannot fit both mass ratios at any coupling. Its exact bound is splitting/electron <= (proton/electron-1836)/1835. Matching the retained proton ratio limits the splitting to 42.5153911 eV, not 1293332.72146155 eV. The source contact ordering remains valid; the combined charging/field mass interpretation fails.", "source_ids": ["common-charging-mass-closure", "common-charging-mass-results"]},
        {"status": "conditional", "statement": "The actual four-face electron spinor's normalized all-face contact is its entire rank-two return. Under the identical neutral mediator and occupation baseline one, its dressed rest energy is exactly 3/4 clock unit. The belt-proton splitting divided by this interacting reference is certified between 0.18619762532247 and 0.18619762534688.", "source_ids": ["interacting-elementary-reference", "interacting-elementary-results"]},
        {"status": "refuted", "statement": "Identifying the interacting spinor reference with the electron rest energy yields 95.146791 keV splitting, rather than the retained 1293.332721 keV. Dressing the elementary carrier improves the denominator but does not close the numerical mass comparison.", "source_ids": ["interacting-elementary-results"]},
        {"status": "checked", "statement": "Two signed source-controlled record involutions give Q_plus+Q_minus=I-P tensor X. Their full diagonal contribution is a scalar shared with the empty reference. A normalized pool of neutral records has ladder sqrt((n+1)*(1-n/M)), constructing the displacement vertex and oscillator limit without discarding a species-dependent contact term.", "source_ids": ["finite-record-mediator", "finite-record-mediator-results"]},
        {"status": "conditional", "statement": "Finite pools of 16, 64 and 256 neutral records retain heavier-belt ordering, with certified splittings approximately 0.137133116, 0.139003555 and 0.139486022 elementary-gap units. Omitted occupations and non-symmetric record sectors are included in the bounds. Admission of the signed controlled operations and collective normalization remains physical input.", "source_ids": ["finite-record-mediator-results"]},
        {"status": "refuted", "statement": "The charged occupation reference equates its sector excitation energy with the elementary gap, but directly identifying that gap with electron rest energy predicts 71.3600933 keV neutron-proton splitting rather than the retained reference 1293.3327215 keV. No common bare offset changes that difference.", "source_ids": ["finite-record-mediator", "finite-record-mediator-results"]},
        {"status": "conditional", "statement": "A complete neutral scalar-mediator law on the actual all-face profiles retains the heavier-belt ordering for any shared positive mediator gap and nonzero displacement coupling. With spacing one elementary-gap unit and half-gap coupling, infinite-tail bounds certify belt-minus-proton between 0.13964821899185 and 0.13964821901016 units. The field and vertex rule are new inputs; no electron rest-energy identification or isotope binding follows from this single-particle calculation.", "source_ids": ["neutral-mediator-mass-bridge", "neutral-mediator-mass-results"]},
        {"status": "refuted", "statement": "Identifying the contact exchange with a complete elementary-gap involution generator does not preserve the heavier-belt result. Its required diagonal contact term leaves both ground energies equal; adding the same-gap internal occupation gives belt-minus-proton -0.0195710150122 elementary-gap units. An overall scale cannot repair either ordering.", "source_ids": ["elementary-gap-contact-bridge", "elementary-gap-contact-results"]},
        {"status": "checked", "statement": "The broader 126-pair contact audit gives 78 global positive certificates, 40 exact counterexample pairs and 8 uncertified cases. All six proton cross-face contacts pass against the belt cross-face bridge. Exact source-only elimination preserves zero ground energy, so it does not generate the proposed added auxiliary law.", "source_ids": ["source-channel-closure", "contact-source-closure-results"]},
        {"status": "conditional", "statement": "With equal phase and strength on all six actual cross-face contacts of each carrier, the proton profile is its coherent mode while the belt profile has weights 2386/4485 and 2099/4485 at energies 0 and 4485/3292. The resulting common-law dressing orders the belt above the proton; the field profile and auxiliary interaction remain inputs.", "source_ids": ["source-channel-closure", "all-face-contact-results"]},
        {"status": "conditional", "statement": "A shared internal-channel completion assigns each auxiliary the same declared charge and baryon label as its particle. The exchange preserves both labels; with a common internal gap and coupling, the positive belt-proton splitting is independent of the common bare offset. The physical channel and energy scale remain unidentified.", "source_ids": ["charge-compatible-contact", "charge-compatible-contact-results"]},
        {"status": "checked", "statement": "For the selected proton AB/BA and belt cross-face bridge contacts, the proton response exceeds the belt response at every negative spectral argument. This is not a theorem for arbitrary contacts.", "source_ids": ["common-contact-dressing", "common-contact-results"]},
        {"status": "conditional", "statement": "With an identical stable reference energy, coupling and bare carrier offset, the carrier-connected dressed belt excitation lies above the proton excitation. Finite dressing changes the bare return state; the physical charge-compatible reference and mass scale remain unconstructed.", "source_ids": ["common-contact-dressing", "common-contact-results"]},
        {"status": "checked", "statement": "The symmetric bridge contact has coherent overlap squared 1193/4485 and couples to two additional even modes with weights 2099/8970 and 1/2. Its exact response is derived without independent internal registers.", "source_ids": ["belt-coherent-port", "belt-coherent-port-results"]},
        {"status": "conditional", "statement": "A supplied neutral-reference exchange with the zero-offset carrier creates a negative one-excitation energy, so the empty reference vacuum is not a ground state. Stability with a positive offset requires epsilon>=g^2*S_plus(-mu); saturation gives zero gap, not a nonzero rest mass.", "source_ids": ["belt-coherent-port", "belt-coherent-port-results"]},
        {"status": "checked", "statement": "The actual paired-face bridge has a minimal three-coordinate linear response. Its boundary scalar alone does not close; two additional collective coordinates must be retained. The normalized static response is 1 and its derivative is 4485/1193.", "source_ids": ["belt-interface-response", "belt-interface-response-results"]},
        {"status": "checked", "statement": "Static elimination of the four interior amplitudes gives stiffness (1193/675)*[[1,-1],[-1,1]]. Equal endpoints cost zero, and the coherent return is dark to this mismatch port; a common physical vacuum interaction remains unconstructed.", "source_ids": ["belt-interface-response", "belt-interface-response-results"]},
        {"status": "checked", "statement": "Exact embedding identities H V=V K and [H,V V^sharp]=0 prove closure of the six aligned belt amplitudes. The reduced operator is the source-metric weighted seam Laplacian, with one zero and five positive modes.", "source_ids": ["collective-spectrum", "collective-spectrum-results"]},
        {"status": "checked", "statement": "The softest belt mode is face-odd and its energy lies strictly between 0.172938631059 and 0.172938631060 common units, certified by rational root isolation. The proton's lowest excitation is 1/2 unit.", "source_ids": ["collective-spectrum-results"]},
        {"status": "checked", "statement": "Exact operator decompositions account for all 36 eigenstates of each carrier. Both coherent ground states still have zero constraint energy; no rest-mass offset or electron normalization follows from these spectra alone.", "source_ids": ["collective-spectrum", "collective-spectrum-results"]}
      ],
      "open_obligations": ["Physically admit the source-controlled signed record gates and normalized pool: an explicit finite-record mediator constructor now exists and preserves heavier-belt ordering.", "Construct a source-supported charging form or elementary-sector interaction beyond the excluded common-gap/normalized-field family; the all-coupling absolute-and-relative mass bound rules out repairing it by clock, strength or belt-profile adjustment.", "Derive any additional physical excitation factors rather than assuming one independent resource per seam.", "Identify physical energy and particle sectors without interpreting arbitrary sums of finite-carrier eigenvalues as rest mass."],
      "source_ids": ["source-channel-closure", "contact-source-closure-results", "all-face-contact-results", "charge-compatible-contact", "charge-compatible-contact-results", "common-contact-dressing", "common-contact-results", "belt-coherent-port", "belt-coherent-port-results", "belt-interface-response", "belt-interface-response-results", "collective-spectrum", "collective-spectrum-results", "native-energy-lift", "seam-mass-comparison"]
    },
    {
      "id": "seam-occupation", "name": "Persistent belt-interface occupations", "status": "conditional",
      "summary": "Couples dressing registers to the actual belt interfaces and preserves the coherent return. A fixed single-clock variant supplies positive energy, but both direct electron-gap identifications overpredict the neutron-proton difference; this is not a neutron mass derivation.",
      "assumptions": ["Each actual seam has a neutral two-level resource register; this is a persistent bond resource, not an error bit.", "Use the shared coupling epsilon*n + J*(n-S)^2 - g*X with S=c-P for the actual mismatch projector P and a supplied conserved carrier sector c.", "J>epsilon>0 and kappa>epsilon suffice for the general family. The single-clock variant instead uses the sharper kappa>delta bound and explicitly admits three record involutions with equal generator normalization.", "Comparison uses the same inactive-register reference and equal bare carrier baselines; other particle contributions remain separate."],
      "results": [
        {"status": "refuted", "statement": "For equal bare carrier baselines and a seam-only splitting, identifying the isolated gap or inactive dressed gap with the electron rest energy predicts 6.632109 or 2.965969 MeV, versus the retained rounded reference 1.293333 MeV. Reducing to connected 15- or 18-seam networks still overpredicts it.", "source_ids": ["seam-mass-comparison", "seam-mass-results"]},
        {"status": "checked", "statement": "Actual seam success can be recorded by a reversible controlled flip. Two overlapping seam records retain operation order and are exactly recovered by the reverse schedule.", "source_ids": ["single-clock-seam", "single-clock-seam-results"]},
        {"status": "conditional", "statement": "Admitting occupation, consistency and flip involutions under one clock fixes epsilon=J=kappa=1 and g=1/2. The extra energy is 21*(sqrt(5)-1)/2 in the common energy unit; the carrier return is preserved. Matched registers have occupation 1/2, not classical full occupation.", "source_ids": ["single-clock-seam", "single-clock-seam-results"]},
        {"status": "conditional", "statement": "The isolated involution gap is one unit, but the inactive dressed register gap is sqrt(5) units. Neither reference is yet identified with the physical electron.", "source_ids": ["single-clock-seam"]},
        {"status": "checked", "statement": "All 21 actual seam projectors annihilate the retained belt return, do not all commute, and transform covariantly under the native threefold rotation.", "source_ids": ["seam-occupation-results"]},
        {"status": "conditional", "statement": "A positive-operator bound preserves the unique carrier return even with noncommuting seams. At zero record mixing all 21 registers are occupied; mixing gives coherent partial occupations.", "source_ids": ["seam-occupation", "seam-occupation-results"]},
        {"status": "conditional", "statement": "The additional energy is 21*delta, with delta=[sqrt((J+epsilon)^2+4g^2)-sqrt((J-epsilon)^2+4g^2)]/2>0. This reuses the existing dressing spectrum rather than fitting a neutron stage cost.", "source_ids": ["seam-occupation", "charged-core-dressing"]},
        {"status": "conditional", "statement": "Coupling the registers to defects P instead of satisfied interfaces c-P gives zero relative occupation contribution on the same coherent state. The physical role of the register is discriminating input.", "source_ids": ["seam-occupation"]}
      ],
      "open_obligations": ["Derive the physical excitation factors and their reference gap; the two direct electron identifications of the fixed single-clock model have failed the mass comparison.", "Integrate other particle contributions and a common vacuum into the mass comparison.", "Account for preparation and test the declared satisfied-interface coupling; no physical neutron mass is predicted yet."],
      "source_ids": ["seam-mass-comparison", "seam-mass-results", "single-clock-seam", "single-clock-seam-results", "seam-occupation", "seam-occupation-results", "native-energy-lift", "charged-core-dressing"]
    },
    {
      "id": "native-operation-lift", "name": "Native-operation energy and belt formation", "status": "conditional",
      "summary": "Native phase and rotation constraints leave one proton mode but six belt modes. Shared-edge amplitude matching inside the paired belt sectors supplies the missing coherence and recovers the existing collective return.",
      "assumptions": ["Use one positive defect-energy constructor, H_D=(pi/4) D^sharp D, which agrees with Nima's generator for an involution defect P-I.", "Retain the original character, geometric metric, mode references and local grouping.", "Across actual shared edges inside each local group, match coefficients of the retained triangle modes; use the canonical metric mismatch reflection for each seam.", "Order-three triangle cycles are not unitary in the retained metric; this construction is not an endpoint interpolation to those cycles."],
      "results": [
        {"status": "checked", "statement": "Native phase and alignment leave ranks 1 and 6 for proton and belt respectively. Each belt sector has six triangles joined by seven actual seams of incidence rank five; all three sectors supply 21 seams and 15 independent equations.", "source_ids": ["native-energy-lift", "native-energy-results"]},
        {"status": "checked", "statement": "Phase selection plus seam matching recovers the belt's rank-three local selection. Native alignment then recovers its exact rank-one return. The common construction also recovers the proton return.", "source_ids": ["native-energy-results"]},
        {"status": "checked", "statement": "The new belt energy operator transports exactly between intrinsic and ambient coordinates. Normalized seam reflections are involutive and insensitive to common rescaling of the mode references.", "source_ids": ["native-energy-results"]},
        {"status": "conditional", "statement": "Both constructed constraint-ground energies are zero. The belt's excitation trace is slightly smaller in this rule, so added seams alone do not establish a larger rest mass.", "source_ids": ["native-energy-lift", "native-energy-results"]}
      ],
      "open_obligations": ["The seam-occupation mechanism now supplies a conditional persistent-register coupling for the seam operations; identify its physical registers and extend the comparison to native-operation records.", "Connect the formation constraints to stored particle energy relative to a common vacuum.", "Test the physical role of the declared amplitude-matching rule rather than presuming its uniqueness."],
      "source_ids": ["native-energy-lift", "native-energy-results", "nima-uniform-core"]
    },
    {
      "id": "source-cost-selection", "name": "Source-coherent cost selection", "status": "checked",
      "summary": "Actual source interchanges constrain traversal accounting but do not select the ordering of stored selection/alignment gaps. This identifies the physical record-energy map still needed.",
      "assumptions": ["Use the 17820 operation-resolved edges and the admitted independent-operation interchange faces.", "For the simplest ansatz, every forward traversal costs only according to its departure slot's L/G/N label.", "Require additive traversal resource to agree along the two routes of each independent-operation square."],
      "results": [
        {"status": "checked", "statement": "All 52488 squares force departure-stage-only costs to satisfy c_L=c_G=c_N. This restricts traversal costs, not stored channel gaps.", "source_ids": ["cost-selection", "cost-selection-results"]},
        {"status": "checked", "statement": "Operation-kind cost plus V(target)-V(source) gives coherent positive traversal accounting with either ordering of stored stage gaps and exact battery/resource-sink balance.", "source_ids": ["cost-selection-results"]},
        {"status": "conditional", "statement": "A fresh-input measurement preparation trial costs 48 versus 39 unit attempts for proton versus belt under L-first, and reverses under G-first. Preparation schedule alone does not determine rest energy.", "source_ids": ["cost-selection", "cost-selection-results"]}
      ],
      "open_obligations": ["Identify the physical record changes and conserved resource exchanged by the source operations.", "Connect that resource to persistent occupations and their particle-sector energy, rather than equating traversal, preparation and rest costs.", "Reuse the existing Gauss/locality sector protection while selecting the diagonal energy law."],
      "source_ids": ["cost-selection", "cost-selection-results", "source-interchange", "local-sector-protection"]
    },
    {
      "id": "constraint-accounting", "name": "Constraint dynamics and retained energy accounting", "status": "conditional",
      "summary": "One positive Hamiltonian selects the existing proton and belt returns and preserves intrinsic energy through actual coordinate changes. Reversible records distinguish outcome recording from preparation work.",
      "assumptions": ["H=a(I-L)+b(I-G), with positive penalties a and b, is a declared common constraint-energy law.", "Use the existing orthonormal physical metric, including the belt numerator-coordinate metric factors.", "The ideal two-bit syndrome register has degenerate energy; readiness, control and erasure are separate resources."],
      "results": [
        {"status": "checked", "statement": "Both carriers have a unique rank-one zero-energy space im(N). At energies (0,b,a,a+b), proton multiplicities are (1,11,2,22), and belt multiplicities are (1,2,11,22).",
          "source_ids": ["constraint-energy", "constraint-energy-results"]},
        {"status": "checked", "statement": "The 36-to-54 belt embedding preserves the entire intrinsic energy operator. Transported local rank is 3, while the earlier ambient protocol has local rank 18: the latter is a different implementation, despite the same final return.",
          "source_ids": ["constraint-energy", "constraint-energy-results"]},
        {"status": "checked", "statement": "A reversible two-bit syndrome unitary commutes with H. Recording outcomes does not by itself enforce them. Reversible re-encoding adds 72 implementation arrows without changing intrinsic state energy.",
          "source_ids": ["constraint-energy", "constraint-energy-results"]},
        {"status": "conditional", "statement": "The common rule fixes excitation gaps and the selected state, but not a particle-sector rest-energy offset or the stored-channel stage gaps in the 324(Delta_L-Delta_G) expression.",
          "source_ids": ["constraint-energy", "geometry-energy-bridge"]}
      ],
      "open_obligations": ["Couple the retained dressing registers to the carrier constraints in one Hamiltonian.", "Identify what physically maintains the particle sector and supplies its stored energy relative to a common vacuum.", "Derive record-stage gaps relative to the elementary reference, with explicit reservoir accounting for preparation."],
      "source_ids": ["constraint-energy", "constraint-energy-results", "locking-controller"]
    },
    {
      "id": "geometry-energy-map", "name": "Geometry to energy-channel bridge", "status": "conditional",
      "summary": "The 1836 comparison slots now map invertibly to actual proton transfers. The belt exchanges local-selection and alignment budgets, giving a concrete candidate energy splitting.",
      "assumptions": ["Use the retained shared root A, reference transport AB and signed monomial charts.", "The belt support comparison reverses arrows and transposes the placement/coordinate rectangle; it is not a coefficient intertwiner.", "For the stored-channel expression, retain fully occupied intrinsic channels, common stage gaps and equal bare-sector contributions."],
      "results": [
        {"status": "checked", "statement": "Every comparison slot maps to one verified typed proton arrow, with an inverse. Proton L/G/N supports are 108/432/1296; belt supports are 432/108/1296.", "source_ids": ["geometry-energy-bridge", "geometry-energy-results"]},
        {"status": "checked", "statement": "The support relation is contravariant, with L and G exchanged. A nonuniform belt-L diagonal proves it is not coefficient equality.", "source_ids": ["geometry-energy-results"]},
        {"status": "conditional", "statement": "The common fully occupied stage-gap rule gives E_belt-E_proton=324(Delta_L-Delta_G). A separately tested coefficient-quadratic reader gives 9(gamma_G-gamma_L), discriminating the two energy mechanisms.", "source_ids": ["geometry-energy-bridge", "geometry-energy-results"]}
      ],
      "open_obligations": ["Select the energy reader from retained dynamics and derive stage costs.", "Construct a neutral belt sector and physical energy scale.", "Connect the elementary energy reference to the electron spinor.", "Use the common energy law in the hydrogen and deuterium readouts."],
      "source_ids": ["geometry-energy-bridge", "geometry-energy-results"]
    },
    {
      "id": "core-dressing", "name": "Charged-core dressing", "status": "conditional",
      "summary": "A positive core recruits stored energy into neutral comparison channels; an independent elementary excitation supplies the light reference.",
      "assumptions": ["H = Delta_e e + mu c + sum[Delta_s n_s + J_s(n_s-c)^2].", "The 1836-channel domain, gaps, stiffnesses and charge Q=c-e are declared physical inputs.", "Complete dressing requires every J_s > Delta_s."],
      "results": [
        {"status": "checked", "statement": "E_minus = Delta_e; E_plus = mu + sum Delta_s in the fully dressed sector. Equal unit gaps and mu=0 realize the energy ratio 1836.", "source_ids": ["charged-core-dressing"]},
        {"status": "checked", "statement": "Allowed changes give 1944, 918 or 1837; neutral quantum mixing also changes the energy ratio. The mechanism works, but does not select its parameters.", "source_ids": ["charged-core-dressing"]}
      ],
      "open_obligations": ["Use the constructed marked proton record map and belt support comparison to derive physical operation costs.", "Derive relative gaps, bare-core energy and admissible quantum corrections.", "Apply one energy rule to both proton and neutron candidates."],
      "source_ids": ["charged-core-dressing", "comparison-resource"]
    },
    {
      "id": "primitive-charge", "name": "Primitive quotient charge and collective energy", "status": "conditional",
      "summary": "A collective rotor and an independent elementary rotor carry opposite unit charges while admitting a conditional 1836 energy ratio.",
      "assumptions": ["Identify the physical external U(1) with the primitive quotient circle.", "Supply the connected-graph Gauss constraint and charging inertias.", "Identify the elementary rotor separately from the later 144-transfer spinor encoding."],
      "results": [
        {"status": "checked", "statement": "Q=k-n_e and E=(k^2/2) sum(1/C_s)+n_e^2/(2C_e). Equal inertias give opposite unit charges and energy ratio 1836.", "source_ids": ["quotient-charge"]},
        {"status": "checked", "statement": "Other allowed inertias give ratio 1944 with the same charges. Charge conservation alone permits mixing into a lighter antiparticle-like elementary sector.", "source_ids": ["quotient-charge"]},
        {"status": "conditional", "statement": "Existing exact Gauss constraints plus Hamiltonian terms supported on fewer than 1837 rotor factors block same-charge collective/elementary conversion. A one-site diagonal perturbation can still change their energy difference.", "source_ids": ["local-sector-protection"]}
      ],
      "open_obligations": ["Source the quotient action and common charging law.", "Connect the existing exact-Gauss/locality sector protection to the geometric carrier; determine its diagonal energy law.", "Construct the elementary-rotor to geometric-spinor comparison."],
      "source_ids": ["quotient-charge"]
    },
    {
      "id": "locking-dynamics", "name": "Phase locking, charge locking and retained preparation", "status": "conditional",
      "summary": "Explicit actions distinguish two opposite energy scalings; a reversible controller prepares charge locking while retaining work and history.",
      "assumptions": ["Supply either a phase-rigid action or auxiliary gauge fields enforcing equal charges.", "The driven preparation uses a chosen schedule, root charge, charging energy and reservoirs."],
      "results": [
        {"status": "checked", "statement": "Under the same microscopic external charge convention, phase locking gives energy ratio 1/1836 and charge 1; charge locking gives ratio 1836 and charge 1836. The quotient-charge mechanism is a distinct repair.", "source_ids": ["rotor-actions", "quotient-charge"]},
        {"status": "checked", "statement": "1835 reversible preparation gates fill the 1836-charge pattern, with 1835 units supplied by each declared charge/work reservoir and all old records retained.", "source_ids": ["locking-controller"]}
      ],
      "open_obligations": ["Derive autonomous dynamics rather than a controller schedule.", "Choose the physical charge action and energy law together."],
      "source_ids": ["rotor-actions", "locking-controller"]
    },
    {
      "id": "neutral-pair", "name": "Phase attachment and neutral spinor-pair coupling", "status": "conditional",
      "summary": "A field-dependent phase attachment and a bilinear neutral pair vertex are explicit alternatives, not yet a binding-energy law.",
      "assumptions": ["Retain the field-dependent common phase instead of freezing or normalizing it away.", "Supply spinorial inputs and independently neutral output for the bilinear vertex."],
      "results": [
        {"status": "checked", "statement": "The field-dependent attachment reverses variable phase weights. The neutral bilinear B(p,e)=p0 e1-p1 e0 requires opposite input weights.", "source_ids": ["pair-coupling"]},
        {"status": "refuted", "statement": "The minimal off-diagonal mass matrix with entries g yields equal singular masses |g|, so this particular mass interpretation does not produce the proton/electron hierarchy.", "source_ids": ["pair-coupling"]}
      ],
      "open_obligations": ["Select the attachment contract from the source.", "Transport the vector construction into the spinorial carriers with all enlargement costs.", "Construct binding dynamics beyond a neutral pair vertex."],
      "source_ids": ["pair-coupling"]
    },
    {
      "id": "hydrogen-accounting", "name": "Hydrogen atom plus photon mass accounting", "status": "conditional",
      "summary": "A constructed mass readout retains the input records, atom recoil and radiation while conserving total four-momentum.",
      "assumptions": ["Supply proton and electron rest energies and B=13.5984 eV.", "Use the declared one-photon final channel at initial center-of-momentum threshold, with c=1."],
      "results": [
        {"status": "checked", "statement": "For incoming rest energy I, atom rest energy F=I-B and photon energy E_gamma=B-B^2/(2I). Atom and photon satisfy their mass shells and their four-momenta sum to (I,0).", "source_ids": ["hydrogen-mass"]},
        {"status": "checked", "statement": "The atom is lighter while the closed atom-plus-photon system retains the incoming invariant mass. Aggregation weight two is not physical mass.", "source_ids": ["hydrogen-mass"]}
      ],
      "open_obligations": ["Derive the constituent energies and binding input.", "Supply a radiation transition amplitude or capture rate.", "Extend and check the readout for the proposed deuterium assembly."],
      "source_ids": ["hydrogen-mass"]
    },
    {
      "id": "gram-energy-test", "name": "Direct Gram-energy alternative", "status": "refuted",
      "summary": "The specified static Gram Hamiltonian does not reproduce 1836 as an excitation-energy ratio; this does not refute history-retaining energy models.",
      "assumptions": ["Use H_slot=F* M F on an orthonormal 1836-label basis, retaining separate arrow and state feature blocks."],
      "results": [{"status": "checked", "statement": "Exact rank is 54, with 1782 zero modes; positive eigenvalues are 10648, 13552, 17248 and 681472. The largest/smallest positive ratio is 64, not 1836.", "source_ids": ["gram-spectrum"]}],
      "open_obligations": ["If path-history energy is used instead, specify the independent record-energy law rather than discarding coherent terms silently."],
      "source_ids": ["gram-spectrum", "comparison-resource"]
    }
  ],
  "constituents": [
    {
      "id": "proton-candidate", "status": "conjectural",
      "name": "Proton-like tetrahedral construction",
      "mechanism_ids": ["retained-phase-energy-memory", "common-geometric-assembly", "weighted-matter-link", "collective-carrier-spectrum", "seam-occupation", "native-operation-lift", "source-cost-selection", "constraint-accounting", "geometry-energy-map", "core-dressing", "primitive-charge", "locking-dynamics", "neutral-pair", "gram-energy-test"],
      "claims": [
        {"status": "checked", "statement": "The common source-driven constructor recovers the tetrahedron, four constituent cones, twelve centroid-edge triangles and retained attachment face. All four maximal facets have moving centroid channels. This geometric reconstruction does not replace the existing coefficient protocol.", "source_ids": ["relative-geometric-results", "geometric-mode-motion-results", "common-assembly-ledger"]},
        {"status": "checked", "statement": "Full retained geometric records now reconstruct all twelve native triangle modes, the coherent return and constraint Hamiltonian with explicit native adapters. This does not identify centroid rotation with the local phase cycle or derive rest mass.", "source_ids": ["geometric-phase-bridge", "geometric-phase-bridge-results"]},
        {"status": "checked", "statement": "A retained tetrahedral construction and its coefficient protocol are available. This status applies to the mathematical construction, not particle identification.", "source_ids": ["proton-research"]},
        {"status": "unconstructed", "statement": "A common electromagnetic coupling establishing sharp opposite proton and electron charges has not been derived from the retained readouts.", "source_ids": ["electron-frontier"]}
      ]
    },
    {
      "id": "neutron-candidate", "status": "conjectural",
      "name": "Neutron-like six-piece belt",
      "mechanism_ids": ["retained-phase-energy-memory", "common-geometric-assembly", "weighted-matter-link", "collective-carrier-spectrum", "seam-occupation", "native-operation-lift", "source-cost-selection", "constraint-accounting", "geometry-energy-map", "core-dressing"],
      "claims": [
        {"status": "checked", "statement": "The common geometric procedure recovers the six-panel belt, eighteen centroid-edge triangles and two rim interfaces. Reversible mode construction uses a source with no explicit rim protection: six maximal facet centroids move and two cap-centroid channels remain fixed and retained. Applying admission to arbitrary subdivided cells instead incorrectly restores both caps.", "source_ids": ["relative-geometric-results", "geometric-mode-motion-results", "centroid-refinement-results", "common-assembly-ledger"]},
        {"status": "checked", "statement": "The geometric bridge reconstructs eighteen native triangle modes, the Hamiltonian and all 21 admitted seam projectors. The existing reversible memory lift is now checked on eighteen phase and twenty-one seam amplitude records with full 75-dimensional inverse recovery and record-reuse back-action. This is not stationary storage or neutron stability.", "source_ids": ["geometric-phase-bridge-results", "native-phase-seam-memory", "native-phase-seam-memory-results"]},
        {"status": "conditional", "statement": "The shared stored-channel rule now yields the intrinsic difference 324(Delta_L-Delta_G), because the belt exchanges the proton's local-selection and alignment budgets. Deriving the stage gaps, neutral sector and physical mass scale remains the next task.", "source_ids": ["belt-core", "geometry-energy-bridge"]},
        {"status": "checked", "statement": "The intrinsic core has three sectors with twelve coordinates each and 1836 transfers. Including the declared ambient adapters costs 2040 transfers; local selection changes.", "source_ids": ["belt-geometry", "belt-core"]},
        {"status": "conjectural", "statement": "Identification of this belt with a neutron is a physical hypothesis, not a consequence of its geometry or support count.", "source_ids": ["belt-geometry", "isotope-attachments"]}
      ]
    },
    {
      "id": "electron-candidate", "status": "conjectural",
      "name": "Electron-like spinor with proposed pentachoron carrier",
      "mechanism_ids": ["retained-phase-energy-memory", "common-geometric-assembly", "weighted-matter-link", "collective-carrier-spectrum", "core-dressing", "primitive-charge", "neutral-pair"],
      "claims": [
        {"status": "checked", "statement": "The common geometric constructor generates the regular pentachoron from its supplied four-dimensional metric and seed action, matching all five boundary cells and the retained attachment cell. All five facet-centroid channels move. This does not extend the existing rank-two tetrahedral spinor to a five-cell coefficient protocol.", "source_ids": ["relative-geometric-results", "geometric-mode-motion-results", "common-assembly-ledger"]},
        {"status": "unconstructed", "statement": "The source five-cycle moves the retained spinor attachment cell through all five tetrahedra. Compatible five-cell spinor and energy transport is missing; the proton/belt energy and memory bridge does not close this electron gate.", "source_ids": ["geometric-phase-bridge", "geometric-phase-bridge-results"]},
        {"status": "checked", "statement": "The hard-flux classical pure-amplitude ground state is globally classified at the existing field fixture: four source-equivalent rays minimize the energy at 0.1798077094008586 before an occupation offset. Exact binary rotations preserve their orbit and full-turn sign; their nonlinear ground set is not a linear logical doublet.", "source_ids": ["spinor-ground-orbit", "spinor-ground-orbit-results"]},
        {"status": "conditional", "statement": "In the exact source-flux sector, charged density relaxation lowers the bare coherent energy. The existing field fixture has global correction bounds 0.17940817039929 to 0.17980770940086; the feasible deformed state retains source holonomy but is not entirely inside the bare coherent doublet.", "source_ids": ["spinor-fixed-flux-relaxation", "spinor-fixed-flux-results"]},
        {"status": "checked", "statement": "The actual spinor lines have an exact weighted matter/link adapter with source face-loop phases +/-i. It preserves signed continuity and Gauss identities. An unconstrained electric-only field can cancel that curvature and lose the logical doublet, identifying a concrete missing face-holonomy action.", "source_ids": ["spinor-matter-link-adapter", "spinor-matter-link-results"]} ,
        {"status": "checked", "statement": "The tetrahedral spinor's equal-phase sum over all six projected face-edge contacts normalizes exactly to its encoding J; the neutral field therefore couples through N_e=J J_dagger without selecting one logical spin.", "source_ids": ["interacting-elementary-results"]},
        {"status": "conditional", "statement": "With the existing one-unit elementary occupation baseline and the same neutral field used for proton and belt, the coherent spinor doublet has exact rest energy 3/4 unit. Positive carrier-defect weights do not change that value; the occupation-sector charging law remains to be sourced.", "source_ids": ["interacting-elementary-reference", "interacting-elementary-results"]},
        {"status": "checked", "statement": "The retained tetrahedral cell supports a rank-two spinorial return with 144 transfers. This is not a derived five-cell transfer protocol.", "source_ids": ["electron-frontier"]},
        {"status": "conjectural", "statement": "The regular pentachoron is a proposed electron carrier, not an established particle identification.", "source_ids": ["isotope-attachments"]},
        {"status": "checked", "statement": "For the tested geometric spin transports, exact matching has zero global states. The separately declared equal-weight squared-mismatch rule has a four-dimensional lowest eigenspace for either chirality.", "source_ids": ["spin-interfaces", "spin-interface-results"]},
        {"status": "unconstructed", "statement": "Conditional elementary-energy and opposite-charge mechanisms exist, but their identification with this geometric spinor is missing. Fermionic exchange selection and a five-cell physical-electron return remain unconstructed.", "source_ids": ["electron-frontier", "spin-interfaces", "charged-core-dressing", "quotient-charge"]}
      ]
    },
    {
      "id": "positron-candidate", "status": "conjectural",
      "name": "Conjugate-data positron hypothesis",
      "mechanism_ids": ["primitive-charge", "neutral-pair"],
      "claims": [
        {"status": "illustrative", "statement": "The viewer compares identical pentachoron geometry with conjugate coefficient phases. Its arrows do not establish opposite electric charge.", "source_ids": ["viewer-source", "viewer-checker"]},
        {"status": "unconstructed", "statement": "A charge-conjugation operator and a derived electron-positron annihilation composition law are missing.", "source_ids": ["electron-frontier", "recombination-note"]}
      ]
    }
  ],
  "elements": [
    {
      "atomic_number": 1,
      "symbol": "H",
      "name": "Hydrogen",
      "isotopes": [
        {
          "id": "H-1",
          "mass_number": 1,
          "name": "Protium",
          "observations": {"protons": 1, "neutrons": 0, "neutral_atom_electrons": 1, "stability": "observationally_stable", "source_ids": ["nudat", "nist-hydrogen"]},
          "model": {
            "status": "conjectural",
            "constituent_ids": ["proton-candidate", "electron-candidate"],
            "mechanism_ids": ["retained-phase-energy-memory", "common-geometric-assembly", "constraint-accounting", "geometry-energy-map", "core-dressing", "primitive-charge", "neutral-pair", "hydrogen-accounting"],
            "mass_readout": {"status": "conditional", "statement": "A witness-retaining atom-plus-photon mass readout is constructed, with recoil and four-momentum conservation. Constituent energies, binding and the output channel are supplied rather than derived.", "source_ids": ["hydrogen-mass"]},
            "geometry": {"status": "checked", "statement": "In the proposed arrangement, proton ABC matches the ABC triangle of the electron pentachoron's ABCD cell, with opposite tetrahedral apices. The common source-driven constructor now reproduces both constituent geometries and their retained attachment marks. Geometric coincidence does not establish a bound atom.", "source_ids": ["isotope-attachments", "viewer-checker", "relative-geometric-results", "common-assembly-ledger"]},
            "binding": {"status": "unconstructed", "statement": "Phase attachment and a neutral spinor-pair vertex supply candidate interface types, not the hydrogen binding operator. A prior attractive shell trial reaches negative energy but its twelve-site position reader fails spherical-density tests. The required electronic interaction must preserve the typed attachment and improve that spatial readout.", "source_ids": ["pair-coupling", "hydrogen-shell-benchmark", "isotope-attachments", "interface-contract"]},
            "stability_explanation": {"status": "unconstructed", "statement": "Observed isotope stability is not explained by matching triangular faces or by the animation.", "source_ids": ["isotope-attachments", "interface-contract"]},
            "open_obligations": ["Derive typed proton-electron interface maps.", "Derive the charge coupling and neutral-atom readout.", "Connect the existing mass mechanisms and conservation readout to this attachment; derive the binding input.", "Explain stability rather than importing it from observation.", "Produce a distinguishing observable beyond the geometric match."]
          }
        },
        {
          "id": "H-2",
          "mass_number": 2,
          "name": "Deuterium",
          "observations": {"protons": 1, "neutrons": 1, "neutral_atom_electrons": 1, "stability": "observationally_stable", "source_ids": ["nudat", "nist-hydrogen"]},
          "model": {
            "status": "conjectural",
            "constituent_ids": ["proton-candidate", "neutron-candidate", "electron-candidate"],
            "mechanism_ids": ["retained-phase-energy-memory", "common-geometric-assembly", "deuterium-rim-response", "weighted-matter-link", "collective-carrier-spectrum", "seam-occupation", "native-operation-lift", "constraint-accounting", "geometry-energy-map", "core-dressing", "primitive-charge", "neutral-pair"],
            "mass_readout": {"status": "conditional", "statement": "The atom/deuteron readout retains separate nuclear and electronic binding inputs, exact mass shells and recoil. The complete common-field construction includes the actual elementary spinor, but closing it with one charging gap per retained channel fails both mass comparisons: an all-coupling bound excludes simultaneous proton/electron ratio and belt-proton splitting agreement. A new source-supported charging law is required; nuclear binding inputs remain separate.", "source_ids": ["deuterium-rim-response", "deuterium-mass-results", "hydrogen-mass", "interacting-elementary-results", "common-charging-mass-closure", "common-charging-mass-results"]},
            "geometry": {"status": "checked", "statement": "The proton face and electron-cell face match opposite belt rims in the displayed arrangement, using scale sqrt(8/3). The actual lower rim uses triangles 1,7,13 and the upper rim 4,10,16. Their joint coefficient trace has a checked minimum-energy extension retaining four residual coordinates; its declared tensor-spin lift preserves both spin components. A common source-driven constructor now recovers all three constituent geometries and attachment marks; its maximal-facet mode rule retains the two neutron interfaces without explicit rim exclusions. The rule is not valid on arbitrary mesh cells. Constituent couplings are not selected by face coincidence.", "source_ids": ["isotope-attachments", "viewer-checker", "deuterium-rim-results", "deuterium-typed-breakup", "deuterium-typed-breakup-results", "relative-geometric-results", "geometric-mode-motion-results", "centroid-refinement-results", "common-assembly-ledger"]},
            "binding": {"status": "unconstructed", "statement": "Joint rim matching costs (1499960093/591106225)*|lower-upper|^2 and supplies no attractive offset. In the current exterior model the pair-versus-breakup contribution is zero with the same total reservoir, or repulsive eta when pooling independent reservoirs. A number- and charge-preserving cross-carrier interaction is missing. Prior connected-energy and relaxed Coulomb benchmarks supply the binding test; the proposed nonlinear triangle gate was already found absent from the source stage algebra.", "source_ids": ["deuterium-rim-results", "deuterium-typed-breakup-results", "binding-connected-energy", "hminus-binding-benchmark", "inner-face-response-failure", "prior-deuterium-binding-search"]},
            "stability_explanation": {"status": "unconstructed", "statement": "The isolated belt return is coherent, but the present pair Hamiltonian has no nuclear bound state below breakup. Observed deuterium stability therefore remains unexplained by this construction; it requires the missing cross-carrier interaction and a coupled-sector stability calculation.", "source_ids": ["belt-core", "deuterium-typed-breakup-results", "isotope-attachments"]},
            "open_obligations": ["Source a constituent-preserving cross-carrier vertex on the checked spinor-valued rim ports; fixed neutral linear matching cannot join opposite-charge proton/electron amplitudes.", "Provide relative-motion kinetics and jointly relax the composite state; compare its connected energy with breakup under identical field, boundary and reservoir data.", "Derive nuclear and electronic binding separately, then use the checked mass readout rather than supplying the isotope deficit.", "Select the exterior coupling and energy scale: the existing carrier ordering reverses when belt middle-mode exposure crosses its tested threshold.", "Construct the physical neutron charge/spin sector and coupled isotope stability, including decay or separation channels.", "Retain the completed nonlinear triangle-gate failure as a control; do not identify generic native composition with an attractive interaction."]
          }
        }
      ]
    }
  ]
}