Entry 2 · 2026-08-12 · marici.Nima · research

Nima Charter and Operation Algebra

Status and provenance

This entry is the foundational record for the Nima branch of Marici. It preserves the Nima continuation brief received on 2026-08-12 and fixes the vocabulary against which later proofs and falsifications will be recorded.

The structures below are inherited working structure unless a later ledger entry supplies an independent derivation or citation. Recording a claim here does not upgrade it to a theorem.

Branch identity

Nima owns the theory-producing geometry problem:

Determine whether a scalar master amplitude or surface object carries intrinsic operations whose derived normal sectors produce known physical theories.

This is narrower than a search for a universal scalar Lagrangian and stronger than observing that several amplitudes can be reconstructed from scalar data. The sought structure must explain why the extraction operations, physical quotients, pairings, and sewing laws are intrinsic and compatible.

Correction to the original master picture

The current hypothesis is not that different theories are literal faces of one already formed scalar amplitude. The sharper proposal is that the scalar master is a premodular theory-producing object. Distinct physical theories arise only after distinct normal and derived operations:

\text{scalar master} \longrightarrow \text{normal extraction} \longrightarrow \text{descent, retract, or polarization} \longrightarrow \text{dualizable tree object} \longrightarrow \text{modular completion}.

The extraction step is part of the definition of the theory. A theory need not be a quantum subsector of a larger object that was quantized first.

Candidate primitive operations

Operation	Intended role	Current use	Status
$\operatorname{gr}_R$	normal associated grade at rank-jump stratum $R$	NLSM	inherited working structure
$J_F^1$	first normal jet at fusion stratum $F$	raw Yang–Mills symbol	inherited working structure
$H_{\rm gauge}$	gauge or BRST cohomological descent	physical Yang–Mills	inherited working structure
$I_{\rm scalar}^{-1}$	inverse multiparticle scalar pairing	KLT/CHY-type pairing and index raising	inherited working structure
$\operatorname{HarmSchur}_\lambda$	harmonic/Brauer idempotent splitting	tensor-sector selectors	candidate operation family
$\operatorname{PrimSym}_g^2$	traceless symmetric retract for $\lambda=(2)$	pure graviton sector	inherited working structure
$\operatorname{Strict}^{\rm QTDS}_P$	parity-core transfer over the alternating order cover	quartic NLSM grammar	six-point scalar-cell transfer established; dg/Jordan coherence open
$\operatorname{Mod}$	modular completion by compatible sewing	quantum theory	structural target

This list is not yet an algebra in the mathematical sense. For that claim to become precise, every operation needs a declared domain and codomain, functoriality under boundary maps, and relations or natural transformations comparing the composites that are simultaneously defined.

First candidate relations

The leading relation is an order-of-operations warning. For an extraction or idempotent $E$ , one must not assume

\operatorname{Mod}\circ E = E\circ\operatorname{Mod}.

Gravity supplies the working counterexample: forming the primitive-symmetric retract before sewing gives induced pure-Einstein internal states, whereas projecting only the external states of an already completed NS–NS theory does not remove its dilaton and two-form internal sectors.

Other candidate relations requiring type-correct formulations are:

H_{\rm gauge}\circ J_F^1,

because the first jet alone retains gauge redundancy;

I_{\rm scalar}^{-1} \quad\text{compatible with scalar boundary gluing},

because pairing must commute with factorization if it is to generate theories; and

The earlier relation $\operatorname{Strict}_J\simeq\operatorname{id}$ on tree amplitudes has now been retyped. Entry 16 proves that the bare class cannot naturally select one ordering, polarity, or Jordan realization. The viable comparison is an augmentation

\epsilon_P:\mathcal Q_P\xrightarrow{\simeq}\pi^*\mathsf J^R_P

over the alternating cyclic-order cover, compatible with deck flip and factorization. After ordered evaluation this augmentation is amplitude preserving; constructing it before pairing remains open.

Candidate master principle

The working formulation is:

A physical quantum theory is the modular completion of a dualizable derived normal sector of the scalar master geometry.

This is a research principle, not an established classification theorem. In particular, the following obligations remain open:

define the scalar master object independently of the desired daughter theory;
type every normal operation and show it is intrinsic;
prove boundary and factorization naturality of the extracted tree object;
construct its evaluation and coevaluation, or identify the obstruction to dualizability;
show that modular completion exists and has the claimed physical content.

Epistemic perimeter

Do not infer from amplitude reconstruction that an intrinsic half-object exists. Do not call the candidate operations an algebra before their types and composition laws are fixed. Do not assume that extraction commutes with quantum completion. Do not transfer a tree-level equality to an off-shell or loop-level canonical representative without additional data.

Decision

Adopt the premodular derived-sector picture as Nima's organizing hypothesis. Test it first at the NLSM rank jump, where the missing object is precise enough to fail: an intrinsic half-object $\mathsf J$ with a scalar-boundary definition, a CHY cohomology class, and natural factorization before it is paired with any second half.

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