scale-invariance

5 items

A cross-corpus navigation page. Check each item’s declared scope and evidence status.

Primary research (4)

PrimaryPaperv1.02026-07-10

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

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.

PrimaryPaperv2.22026-07-09

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*).

PrimaryPaperv1.22026-07-09

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.

PrimaryPaperv1.32026-07-09

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.

Philosophical work (1)

PhilosophicalPaperv1.02026-07-10

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.