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FRC-700-000 · v0.1

The Threshold Charter: Evidence, Interpretation, and Register Discipline v0.1

H. Servat2026-07-177 minFRC 700 seriesSpeculativeμ4 Logical / conceptual
thresholdsmu-levelsevidenceinterpretationregister-disciplinescope

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Current statement

This charter defines the FRC 700.00x series as threshold work: it governs transitions among physical observations, formal models, operational realizations, and FRC μ interpretations without treating those domains as interchangeable. It classifies claims, fixes a one-way evidence rule, specifies the μ topology as an FRC convention, and requires an interface record whenever a conclusion crosses a declared boundary. Exact results from the FRC 830 series may constrain μ interpretations; μ resemblance cannot prove those results. The charter adds no physical law or universal ontology.

Evidence level

Philosophical / formal framework note

preprint

Declared μ register

μ4 · Logical / conceptual

Logic, formal models, language as explicit reasoning, and computational design.

Open boundary

Review the paper’s declared scope, controls, limitations, and kill conditions.

Version lineage

v0.1 · Current release

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This charter defines the FRC 700.00x series as threshold work: it governs transitions among physical observations, formal models, operational realizations, and FRC μ interpretations without treating those domains as interchangeable. It classifies claims, fixes a one-way evidence rule, specifies the μ topology as an FRC convention, and requires an interface record whenever a conclusion crosses a declared boundary. Exact results from the FRC 830 series may constrain μ interpretations; μ resemblance cannot prove those results. The charter adds no physical law or universal ontology.

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Related

Paper

FRC 700.777 v1.0 - μ Registers: A Nested Scope Model for Scale-Declared Reciprocity

FRC 700.777 defines μ registers as a nested scope model for the FRC corpus. μ0 names the prior ground; μ1–μ4 describe an organism's interior registers; μ5–μ6 its symbolic and witnessing envelope; and μ7 the boundary-shell coupled to what lies outside the declared system. The note distinguishes this map from physical scale selection and from the starred Boltzmann bridge k*. A μ label declares where a claim speaks; it neither sets k*, proves cross-register causation, nor transfers evidence between registers. The paper supplies an interface record for any proposed cross-register study and keeps the canonical physical relation unchanged.

Paper

What Would Make FRC Reciprocity a Duality? v0.1

FRC uses dS + k* d ln C = 0 as an operational bookkeeping relation and proposes a wider open-system interpretation as a conjecture. This paper asks a prior mathematical question: what additional structure would make that reciprocity a duality? It separates five claim classes—coordinate transform, bookkeeping identity, balance law, duality, and self-duality—and supplies exact counterexamples showing that none implies the next. On the normalized ledger plane, the map D(x,y)=(-y,-x) is a sign-reversing involution satisfying D^2=id and D*omega=-omega for omega=dx+dy. On the operational domain y<=0 it is a self-map only when x>=0, and no present construction lifts it from derived ledger coordinates to independently defined FRC states, observables, dynamics, or operational registers. Present FRC therefore reaches an exact coordinate-level sign-reversing involution on a restricted domain, but not a physical, categorical, or Majid-style self-duality. The result is a terminology lock, a promotion test, and a research gate for the 830 series.

Paper

The Reciprocity One-Form v0.1: Affine Classification and Domain Rigidity

This paper classifies every invertible affine transformation of the normalized FRC ledger plane whose derivative preserves the reciprocity distribution ker(dx+dy). In coordinates u=x+y and v=x-y, the complete class is F(u,v)=(lambda u+c, alpha u+beta v+delta), with lambda beta nonzero. The paper derives the group law, inverse, leaf action, all affine involutions, and their fixed sets. Intersecting the classification with the operational half-plane M=R x (-infinity,0] yields a three-parameter family and a one-parameter family of sign-reversing involutions. Intersecting it with the nonnegative-entropy domain M+=[0,infinity) x (-infinity,0] is rigid: every kernel-preserving affine automorphism is either aI or aD, where a>0 and D(x,y)=(-y,-x). Consequently the identity is the unique exact form-preserving automorphism, D is the unique exact form-reversing automorphism, and D is the unique nonidentity involution in this bounded class. The result is an exact coordinate theorem pending independent proof review. It does not lift D to physical states, observables, distributions, dynamics, or operational registers and therefore does not establish a physical, categorical, Born, or Majid-style duality.

Paper

Operational Registers and Reciprocity-Preserving Morphisms v0.1

FRC uses several legitimate coherence routes, including phase order, the von Mises mean resultant, quantum purity, basis-dependent off-diagonal interference, and platform-specific composites. This paper formalizes how those routes may share a framework without being declared the same observable. A weak reciprocity map preserves the pulled-back ledger one-form up to a nonzero multiplier. A strong affine register morphism additionally supplies a state or model map and a commuting ledger square. Both classes compose; the strong class forms a category with explicit identities, associativity, exact-preserving and signed subcategories, and an invertible groupoid. One-form preservation alone is shown insufficient by an exact counterexample. The von Mises family supplies a nontrivial strong morphism into the phase-distribution register: the state-space inclusion commutes exactly with the entropy and mean-resultant ledger, but is not an isomorphism. A qubit no-go theorem proves that purity and fixed-basis off-diagonal coherence admit no single-valued ledger adapter under the identity state map, even though both are valid operational routes. Present FRC registers therefore form a typed formal category populated by a sparse graph of verified arrows, not one proven physical equivalence class.

Paper

Exact Phase-Family Test of FRC Duality v0.1: A Lift Obstruction on the von Mises Manifold

The fixed-mean von Mises family provides an exact test of whether the FRC ledger involutions classified in FRC 830.001 lift from derived coordinates to probability distributions. The family has genuine information-geometric structure: concentration kappa and mean resultant r are natural and expectation coordinates, the log-partition function is strictly convex, and minus the differential entropy is its Legendre dual potential. That structure is not the FRC ledger exchange. For the ledger ell(kappa)=(S(kappa),ln r(kappa)), introduce u=S+ln r and v=S-ln r. The function v is strictly decreasing, while u is strictly unimodal with its unique maximum at kappa r=1. Because D(x,y)=(-y,-x) preserves v, every proposed D lift must fix kappa and can exist only at the two isolated roots of u=0. The broader half-plane involutions R_p(x,y)=(-x-2y+p,y) likewise force kappa to remain fixed and survive at no more than two isolated fixed ledgers. Neither class lifts on any open concentration domain. The point kappa r=1 is a maximum of the system-only ledger total, not a D-fixed point or structural self-duality. FRC therefore retains a P2 coordinate involution and gains a precise P3 lift obstruction in this family; it does not gain a phase-family physical or Majid-style self-duality.