Research Sequence and Session Interfaces

Purpose

Marici has several coupled research branches. This entry fixes their interfaces and the order of work so that a result in one branch is not silently used as a stronger result in another.

Nima sequence

The Nima branch proceeds in the following order:

  1. define the scalar half-object spaces, scalar pairing, rank-jump filtration, and boundary maps;
  2. construct (\mathsf J=I_{\rm scalar}^{-1}\operatorname{gr}R A{\rm scalar}) with matched types;
  3. identify its low-point CHY class and test basis independence;
  4. prove or falsify its factorization naturality before pairing;
  5. test the Born–Infeld cross-pairing and special-Galileon self-pairing;
  6. determine whether Jordan/QTDS strictification exists at the half-object level;
  7. test survival in the surface-function and Cut Equation formulation;
  8. only after closure, classify possible fourth primitive normal operations.

The sequence is gated. Agreement of (\langle\mathsf C,\mathsf J\rangle) with NLSM does not permit skipping the factorization test, and recognition of the standard CHY table does not establish common scalar provenance.

YM interface

The sibling YM branch owns:

  • first-jet gauge descent;
  • the intrinsic scalar/CHY pairing;
  • the primitive-symmetric gravity selector;
  • pure-Einstein generalized-cut sewing;
  • chain-level gravity questions only where they originate in the first-jet complex.

Nima treats the tree selector and generalized-cut gravity construction as inherited working structure unless contradicted, but it does not claim their missing cyclic lift. Nima may require from YM an explicit definition of (I_{\rm scalar}), its quotient, and its boundary compatibility because those data are inputs to the (\mathsf J) construction.

Frost interface

Frost owns translation into:

  • surface functions;
  • the Cut Equation;
  • tropical and arbitrary-topology structures;
  • canonical off-shell or cyclic representatives.

Nima first formulates the genus-zero half-object and its boundary law precisely. Frost then tests whether (\operatorname{gr}), (J^1), (I^{-1}), (\operatorname{PrimSym}^2), and (\operatorname{Mod}) exist intrinsically in the surface theory and satisfy cut naturality. A surface lift may expose that a genus-zero construction depended on coordinates or a pairing basis; that is a falsification, not an implementation inconvenience.

Cintamani interface

Cintamani remains the physical-computation and substrate branch. Its direction is

[ \text{abstract algebra} \longrightarrow \text{physical substrate that realizes it natively}, ]

whereas Nima studies

[ \text{scalar master} \longrightarrow \text{normal operations} \longrightarrow \text{derived physical theories}. ]

The connection is the search for compact native grammars. Current inherited examples are:

[ \text{NLSM contact tower} \longrightarrow \text{Jordan quadratic map}, ]

[ \mathrm{YM} \longrightarrow \text{first-jet gauge cohomology}, ]

and

[ \mathrm{gravity} \longrightarrow \text{primitive symmetric tensor operation plus scalar pairing}. ]

Cintamani should eventually test substrates against these compact operations rather than emulate their conventional Feynman presentations. Nima does not initiate that substrate search until the algebraic grammar and its resource-relevant operations are stable enough to specify.

Documentation rule

Each material advance receives its own ledger entry with:

  • provenance and epistemic status;
  • the exact mathematical claim;
  • definitions and assumptions;
  • severe tests and failure conditions;
  • the boundary of what the result does not establish;
  • the next gated action.

Negative results are retained. A failed half-object construction may still be a valid amplitude reconstruction map, and that weaker result should be named rather than discarded or promoted.

Decision

The primary Nima frontier is the intrinsic construction and factorization of (\mathsf J). The fourth-primitive search, substrate realization, and canonical gravity cyclic lift remain downstream or sibling tasks and will not be used to evade a failure at this frontier.