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FRC-100-100 · v1.0

FRC 100.100 - Standalone Stance: A Status-Labeled Snapshot of Fractal Resonance Coherence

H. Servat2026-07-1010 minFRC 100 seriesFoundationalμ4 Logical / conceptual
Concept DOI10.5281/zenodo.21298193DOI10.5281/zenodo.21298194PDFDownload
orientationstandalone-stancemachine-readingstatus-labelsscale-invarianceReciprocityCoherence

Reading status

Current statement

A standalone current-statement file for FRC: canonical relation, scale-invariant k*, evidence status, open gates, negative results, corpus map, and machine-reading rules.

Evidence level

Living core preprint

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

v1.0 · Current release

On this page
FRC 100.100 is a self-contained, status-labeled snapshot of the current Fractal Resonance Coherence program for human and machine readers. It states the canonical scale-invariant relation dS + k* d ln C = 0; separates definitions, exact mathematics, model-specific results, operational programs, conjectures, and philosophical notes; records the current scope of the chaos, collapse, Born-rule, Lambda, and mu-register lines; and preserves the program's negative results. It is a routing and grounding document, not a substitute for primary papers when a derivation, dataset, or citation is required.

Related

Paper

FRC 100.000 v1.2 - Start Here: Canonical Stance and Version-Aware Reading Map

FRC 100.000 is the version-aware front door to the Fractal Resonance Coherence corpus. Version 1.2 restores the owner-approved canonical relation dS + k* d ln C = 0. The starred k* is the scale-invariant Boltzmann bridge, not an outcome-fitted constant or evolving state variable; indexed notation belongs only to declared operational realizations. The relation is used operationally as bookkeeping and remains an open physical conjecture for real open systems. This document routes readers to current primary papers and separates definitions, mathematical results, model-specific tests, and conjectures. It is an index, not a substitute for the primary papers and not a minimum sufficient prompt for machine readers.

Paper

Entropy-Coherence Reciprocity and the Universal Coherence Condition v2.2

FRC 566.001 states entropy-coherence reciprocity in its canonical scale-invariant form dS + k* d ln C = 0. The starred Boltzmann bridge k* is not an ordinary tunable constant and is never fitted to an outcome or evolving state. Experiments and computations instantiate the same law at a declared register mu as dS_mu + k*_mu d ln C_mu = 0, with explicit entropy channel, coherence channel, units, and boundary. FRC uses the relation operationally as bookkeeping and proposes its open-system physical extension as a conjecture. Standard entropy production remains non-negative, but no toy closure is promoted into a universal directional replacement. The exact von Mises calculation and the Langevin boundary probe remain scoped results. The corrected information projection is retained: C[q]/C[p] depends on the entropy difference, not generally on D_KL(p||q), and C_XY = C_X C_Y exp(+I/k*).

Paper

Reciprocity in Action v1.3: Exact System-Only Motion and a Scoped Boundary Test

FRC 566.030 applies the canonical reciprocity law dS + k* d ln C = 0 through one explicit information-unit realization. With the predeclared representation k*_{mu_nat}=1, it computes Q=S+k*_{mu_nat} ln C exactly on the von Mises/Kuramoto family. Q is non-constant and reaches its unique stationary point at kappa r=1, kappa=1.608279 and C=0.621782. The exact identity is dS/d ln C=-kappa r, hence dQ/d ln C=k*_{mu_nat}-kappa r. This stationary point is dQ=0; it is not sigma_566=0 unless an explicit environment model supplies that additional equality. The family contains no bath and therefore measures neither irreversible production nor entropy export. A companion Langevin closure tests those quantities in one model class and finds no universal erasure floor in its declared normalization.

Paper

Coherence in Chaos: Diffusion, Localization, and Decoherence in the Standard Map / Quantum Kicked Rotor Family

FRC 100.002 v2.5 preserves the Standard Map / Quantum Kicked Rotor chaos program, the KAM-structure functional, localization/decoherence pilots, the Ruelle-Pollicott negative result, and the demoted stadium appendix. It corrects only the framework ledger notation. The canonical reciprocity law remains dS + k* d ln C = 0. In this paper's declared information-nat realization k*_{mu_nat}=1, and J_sys=d[S_sys,mu+k*_{mu_nat} ln C_mu]/dt is reported only as a system-only diagnostic. Because no environment is modeled, J_sys is not automatically entropy production or a boundary residual. The relation lambda=-d_eS is admissible under a declared boundary convention and is neither imposed universally nor rejected by fiat.

Paper

Accessible Phase-Space Geometry Predicts the Structure Functional in the Mixed Standard Map

FRC 100.002 v2.5 defined the structure functional Σ = S_vM(C) − S and deferred whether persistent mixed-regime Σ(∞) tracks measured phase-space geometry. Instrument A measures Σ(∞) from evolved ensembles over 12 seeds. Instrument B independently classifies the torus by finite-time Lyapunov exponent, flood-fills the accessible chaotic component from a wrapped seed region, and predicts Σ from the component's phase marginal with no fitted amplitude. Over K_c ≤ K ≤ 2.0, the prediction has 9.7% median relative error, versus 18.9% for a fitted island-area proxy. A 1000-realization fixed-area shuffle null gives zero exceedances and corrected empirical p = 1/1001 at K=K_c, 1.4, and 2.0; the real prediction lies 33.6–198.4 standard deviations above random placement. Thus spatial arrangement of the excluded regular region, not area alone, carries the predicted signal throughout the estimator-clean window. Grid, FTLE-time, and threshold convergence are reported. Below K_c the uniform-fill assumption fails by a factor of two; above K ≈ 2 histogram-bias corrections approach or exceed the signal.

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.