Results: checks, exclusions, and open tests

Use this page for verification status. Theory explains the constructions; Architecture records their contracts and assumptions; Comparison targets lists proposed numerical expressions.

This page separates checked mathematical constructions, conditional models, open physical identifications, and excluded branches. A checker pass, an exact numerical identity, or a research-ledger admission does not establish a physical theory. Verification levels below are those reported in the linked research; this synthesis is not a new proof certificate.

October 12: retained information and claim boundaries

The new research lab makes information loss, recovery permissions and numerical sensitivity inspectable. Its values come from pinned research receipts; publication does not create new scientific or physical acceptance.

Addition	Checked or declared result	Boundary
Arrow, phase and process	Existing offline SU(2) × SO(2) × Z2 display; open-path reversal and spinor return.	Traversal reversal is not an inverse projector or physical symmetry derivation.
What one arrow observes	Exact shielding falsifies universal remote sensitivity; a candidate spinor link has a dark direction and a two-reading decoder.	Unequal weights, retained input and additional readout permissions are explicit.
Proton / neutron tasks	Equal 1,836 counts hide different stage ranks and 24/33-address reconstruction thresholds.	Addresses are not detectors or mass units.
Reference and software transport	Conditional memory/port chain; pinned software 137→32→32 with 977 admitted contexts and extended branch summaries.	Physical preparation, calibration, reference transport, apparatus and connector creation remain separate.
Local phase clock	Actual incoming mixture gains readable coherence under existing matching; relational states are rate-independent.	Three finite audited readings, local chart only; no physical seconds or derived primitive update.
Spatial refinement	Expansion direction survives; combined-grid peak changes −27.482%.	Residuals are not spatial error bounds or a continuum certificate.

Three explainers separate further physical obligations: neutron rest-energy reference versus model prediction, finite electric bridges versus conditional Coulomb binding, and programme acceptance, falsifiers and open outcomes. The accepted finite structural prerequisite does not close the programme root; a passing hostile checker may certify a rejected conjecture.

Current research synthesis: October 8–10, 2026

The recent work advances source-controlled assembly, retained witnesses, analytic formalization, and energy-accounted models. It does not establish a replacement for the Standard Model or general relativity, derive the measured proton–electron mass ratio, or explain isotope stability.

Research track	Positive result	Remaining boundary
Common geometric assembly	One source-parameterized orbit/facet/cone procedure reconstructs the tetrahedron, six-panel belt, and pentachoron, with retained interfaces and reversible centroid-mode motion.	Metrics, symmetry generators, and seeds are supplied. Mode admission applies to maximal supporting facets: arbitrary cellwise subdivision admits 24 rather than 18 neutron triangles. No physical particle identity or universal dimensional reset follows.
Retained 1836-arrow construction	The exact fixed-stage coefficient protocol and its positive closed cycles are reconstructed and bound to a Merkle packet. Every nonempty deletion at unchanged weights changes the return.	This is pruning minimality within that protocol, not a minimum under refactoring, reweighting, or a different basis; it is not a mass prediction.
Operational analytic formalization	The research reports fresh safe Agda closure for completion-valued unit norm, metric regularity, unit-circle flow, and the assembled operational half-turn.	Identification with standard pi uses an explicitly accepted written proof, not a kernel-checked standard-real interpretation. Operational whole-return assembly is a separate unresolved goal in the cited completion net.
Quantum spinor model	Conditional quantization and an ideal endpoint-rotor parent have an explicit unitary equivalence. Four conserved-flux blocks give an exact invariant 16-dimensional simulation sector.	Parameters, sector preparation, assisted hopping, physical units, and a platform remain inputs. The sector is not the whole rotor theory, a realized device, or a particle mass prediction.
Merkle proof and assembly prototypes	Typed rational-polynomial proofs, bounded gluing discovery, affine global transport tests, explicit cone fillers, and scoped proof substitution have executable verifiers.	Content integrity, local identities, surface closure, global holonomy, and supplied fillers are distinct obligations. Arbitrary dependent higher coherence is not delivered.
Energy and memory models	Source-weighted matter/link feedback retains exterior field energy; reversible memory and finite-work transfer expose explicit resource costs.	Internal norm-charge is not electric charge. Excitation gaps, traversal work, stored occupation energy, and rest energy are distinct. No autonomous device or isotope-stability explanation is established.

Sources: common assembly, entry 4319, Merkle construction, entry 4314, operational half-turn, completion net, quantum construction, Merkle verifiers, entry 4313, and storage resource comparison.

Exclusions and unresolved selection

Failures below reject the stated branch or sufficiency claim, not every possible construction.

Tested proposal	Outcome	What would require new evidence
Common charging mass law	With a shared gap on 1836 occupied channels, a one-gap elementary baseline, coherent contacts, and the same normalized displacement field, matching the proton/electron ratio bounds the belt–proton splitting by approximately 42.5 eV, far below the retained approximately 1.293 MeV comparison. Changing the clock or common coupling cannot repair this branch.	A different source-supported charging or elementary interaction law, tested against both absolute and relative masses.
Deuterium binding in the current common-vacuum graph	Pair-minus-breakup energy is positive with independent exterior reservoirs and exactly zero with the same total exterior reservoir. Typed rim maps do not supply attraction.	A bounded, number- and charge-preserving cross-carrier interaction, using identical boundary and reservoir accounting for composite and breakup states.
Geometry fixes belt–proton energy ordering	In the source-weighted field model the ordering reverses as middle-mode exterior conductance changes.	Independently justified exterior attachment and conductance metric, rather than choosing them from the desired mass.
Existing arrows select opposite electric charges	Frozen and field-dependent attachments both satisfy the retained arrow equations. A neutral spinor pairing requires opposite phase weights, but neutrality and charge normalization are additional inputs.	A source-selected interaction and charge/current readout. The simple off-diagonal mass trial has equal singular masses, not a hierarchy.
Joint compatibility necessarily selects predictions	The tested quantum-state completion adds no prediction constraint: forgetting the completion recovers every original admissible annotation.	Additional independently justified selectors; mere coexistence of compatible structures is insufficient.
Braid topology fixes the two/three-output probability ratio	Preserving one attachment restricts endpoint channels to two or three components, but the proposed unitary model has free coupling, splitting, and duration. The 372:1 ratio is an input constraint.	A source-derived braid representation and amplitude law without fitting that ratio.

Sources: charging-law exclusion, deuterium breakup test, common vacuum and boundary test, entry 4317, spinor pairing, entry 4316, joint-completion falsification, and braid composition.

Local Tate incidence and elliptic descent

Object	Established scope	Remaining comparison
Finite-place incidence $C_{p,h}=R_pT_h(I-R_p)$	Exact residue-to-radial operator with nilpotence, adjoint, Fourier conjugation and dilation covariance on the appropriate carriers. The rational audit reports 48 finite radial cases and the independent four-state fixture.	Identify its radial image with the arithmetic primitive/square packet, including the $\log p$ and cycle $1/k$ weights.
Active singular-value gap	The finite-packet calculation gives nonzero singular values $1$ or $\sqrt{1-(p-1)^{-2}}$. Active gaps do not collapse under these refinements; exact kernels and zero-rank cases remain.	No restricted-product/corona completion or completed Weil positivity follows from this local bound.
Nine-state circuit resolution	Saturated rank-seven kernel with six within-support differences and one twisted circuit-relation line. This is an integral circuit result.	It is not an identification with the cosmology $M_9$. Recover the source-labelled comparison $J:C^{\rm or}_9\to M_{15}$ and test the quotient and symmetry squares.
Elliptic Green descent	The equation $BI=DH+C^{\rm ell}_pE$ packages the seven kernel fillers invariantly. Under the stated splitting assumptions it is equivalent to those seven tests.	Physical matrices, equivariant fillers, and a source-defined zero elliptic origin remain required.

Local theorem, comparison certificate and physical scope. These are mathematical constructions and unresolved comparisons, not numerical physical predictions.

Current comparison-tower checks

The specified diagram, retained source witnesses, and checked response adapters remain useful bounded constructions. Supplied matrix amplitudes and conditional family feedback are not derived physical laws.

Construction	Checked result or specified role	Open physical/architectural step
Rung diagram	Specified roles $9:12\to6$, $8:11\to5$, $7:10\to4$; retained-record candidates satisfy both squares and agree on the rung-4-relative readout.	Select the intended horizontal generator, physical reference, and metric.
Retained-family promotion	Fresh labels retain members and masses; different endpoint policies pass presentation checks.	Presentation coherence does not select next-level endpoints.
Mixed comparison data	The shared-leg additive path model has 109 rectangle relations, with factored responses $(\Delta y)(\Delta x)$ and a state analogue.	Identify the physical readout; these are not freely independent field parameters.
Witness and response transport	Retained witnesses, shared-leg coherences, reanchoring, associator/pentagon, and a marked decoder preserve the named responses.	Context, physical preparation, and measurement remain inputs. The fixture matrices are not a pure finite-groupoid functor.
Readout versus composition	Mean/fluctuation packets retain averaging corrections; endpoint policies agreeing at first moment can differ after composition.	Select operand ports, context incidence, and the intended operation.
Conditional preparation and feedback	Ordered preparation/transport updates are associative. One family-relaxation law preserves means, contracts disagreement in a declared metric, and reconstructs old members.	Initial amplitudes, gain, metric, and physical resource accounting are not selected. Contraction is not established energy dissipation.
Candidate $1,2,4$ progression	Independent products of the full off-diagonal relation have these second-homology counts.	Identify this operation with the intended tower successor before claiming a gauge correspondence.

Derivation and exact verification sources · system status.

Tetrahedral spin and charge audit

The 36-coordinate model has exact projector ranks $12,3,1$ and $LR=RL=N$. Its dense three-stage implementation has 1836 coefficient arrows; geometry, implementation support, and mass are different quantities.

Test	Verified result	Physical boundary
Binary tetrahedral bridge	$2T\to A_4$, $Q_8\to V_4$, and $\operatorname{End}(\mathbb C^2)=\mathbf1\oplus\mathbf3$ recover the three-axis action.	Operator-space equivalence does not derive physical spin or weak isospin.
Added spinor factor	$V_{36}\otimes\mathbb C^2$ has a collective doublet with central action $-I_2$.	The extra factor is an input, not selected by the native endpoint/filter model.
Native rotation-loop test	All six orthogonal-half-turn commutators return +1; a separate projection triangle gives $-13/3375$.	The native-selection conjecture fails in this model. Later declared spinor extensions do not reverse that failure.
Charge correction	$I$, $N$, and $2N-I$ refute the former universal charge no-go; a scaled half-turn has expectation +1 but variance 8.	These algebraic candidates are not identified electric-charge sectors.

Derivations, falsifiers and executable checks.

Physical hypotheses: corrected status

The previous broad labels “Established” and “new explanations” overstated the carrier-to-physics conclusions. The following statements replace those labels; numerical agreement alone is not a derivation.

Topic	Current status and missing construction
Quantum mechanics and Bell tests	Positive Gram matrices support normalized state/readout models. Rank-one factorization describes a pure-state case, not every Gram matrix. Born measurement and CHSH conclusions require a specified state, tensor structure, and observables; a generic overlap does not establish them.
General relativity	Finite stabilizer covariance and a canonical cotangent lift are available. The legacy ADM promotion, Lorentzian-signature certificate, and continuum interpolant claims are withdrawn. A field phase space, smeared constraints and Poisson comparison, action, and continuum construction remain missing.
Standard Model gauge group and generations	The natural four-point permutation representation is $\mathbf1\oplus\mathbf3$. Finite irreducible dimensions, a partition into three four-point blocks, and stable-stem analogies do not derive continuous gauge actions, matter content, or three physical generations.
CKM, PMNS, Yukawas, and Higgs	Proposed numerical expressions and supplied mixing structures remain comparison targets. Sector operators, symmetry breaking, scale conventions, and physical normalization must be derived before claiming masses or couplings.
Anomaly cancellation and beta decay	Conventional specified matter content and Standard Model dynamics can supply calculations. Their reuse does not derive that content, weak interactions, or their parameters from the carrier.
Proton, neutron, electron, and nuclei	Candidate geometries, projectors, conditional spinor extensions, and energy models are constructed. Charge, statistics, measured masses, nuclear binding, and isotope stability are not thereby explained.
Machian inertia, dark matter, dark energy, and cosmology	Relational interpretations and candidate density expressions remain hypotheses. No selected gravitational action, dark-sector particle content, or cosmological observable follows from overlap ratios alone.
Arrow of time	Choosing an oriented cycle does not establish physical time asymmetry. Hermiticity gives $G_{ij}=\overline{G_{ji}}$, not general real symmetry, and does not by itself determine time-reversal dynamics.
Inflation, baryogenesis, axions, Hawking radiation, and black-hole interiors	Proposed analogies lack the required dynamical and observable constructions; they are not completed carrier explanations.

ADM correction · withdrawn unification claim · representation and normalization boundaries.

Numerical comparison targets

Exact arithmetic establishes these expressions, not their physical identification. A quantitative test also needs units, scale/scheme, input provenance, theoretical uncertainty, and independently sourced measurements. Rejecting an expression does not automatically reject all carrier constructions.

Candidate	Mathematical statement	Physical status
Electromagnetic normalization	$11^2+4^2=137$; the specified comparison has 121 arrow slots and 16 state slots.	Equal-slot or equilibrium mismatch shares do not determine electromagnetic coupling. The exploratory feedback value 137.036195934 fails the quoted precision recoil targets.
Weak mixing	$3/13$ is a proposed expression.	Its cited matter-trace derivation fails colour counting; consistent traces give $3/8$ under the stated normalization. A scale-matched derivation remains open.
Proton/electron mass	$12(12^2+3^2)=1836$.	A count, not a derived mass ratio or fractional correction. The specified common charging branch is excluded above.
Higgs mass and vev	$11^2+4=125$ and $2\cdot11^2+4=246$.	GeV assignments and the Higgs interpretation are not consequences of these integer identities.
Flavor phases	$(12/10)\pi=216^\circ$ and $\pi/3+(4/12)^2\approx66.4^\circ$.	Proposed phase targets, not source-derived CKM/PMNS observables.
Cosmological budget	$6/121+6/23+11/16+91/44528=1$.	The arithmetic closes; identification with measured density fractions and curvature needs sector readout maps and dynamics.
Hierarchy and QCD scales	Expressions such as $11^{15}\,12\,Z$ and $M_{\mathrm{Pl}}/11^{19}$ are proposed.	Clock/action normalization, dynamical scale generation, and consistent measurement conventions are not established.

Electromagnetic trial and precision failure · weak-mixing audit · mass construction history.

Mathematical connections: identities versus proposals

• Boolean carrier: $\mathrm{Bool}\times\mathrm{Bool}$ has four elements. It is not the free Boolean algebra on two generators, which has 16 elements. A four-label basis can be used for a two-qubit Hilbert space only after linearization and tensor structure are specified; $S_4$ is not the Clifford group.
• Gram and information models: a nonzero positive Gram matrix gives a density matrix $G/\operatorname{Tr}G$ after choosing a Hilbert-space interpretation. Kernel, covariance, and entropy constructions are conditional on their declared probes, measures, and state semantics.
• Finite symmetries and braids: finite permutation actions and the map from braid groups to permutation groups provide concrete mathematical tools. Neither alone assigns physical interaction amplitudes or derives continuous gauge groups.
• Broader connections: modular weights, moduli spaces, stable homotopy, sporadic groups, division algebras, TQFT, and integrable systems remain separate proposed comparisons unless an explicit map and its laws are supplied. Matching dimensions or the identity $12^3=1728=j(i)$ does not establish those identifications; $i$ is not a modular cusp.

Next discriminating tests

1. Complete the separately scoped operational whole-return certificate without promoting written standard-real identification to kernel evidence.
2. Derive or calibrate physical charge/current, clock, and energy standards independently of desired constants.
3. Supply a stable cross-carrier attraction and compare composite and breakup with identical reservoirs.
4. Test source-selected boundary attachment and charging laws against both absolute and relative masses.
5. Preserve model exclusions, construction provenance, and distinct counting conventions in the matter atlas.