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FRC-830-004 · v0.1

Dimension Threshold for FRC Reciprocity v0.1: One-Parameter and Qubit Lift Obstructions

H. Servat2026-07-1517 minFRC 800 seriesFoundationalμ4 Logical / conceptual
Concept DOI10.5281/zenodo.21385391DOI10.5281/zenodo.21385392PDFDownload
Reciprocitydimension-thresholdlift-obstructionwrapped-cauchypoisson-kernelkuramotoqubitCoherencecptpwignerantiunitaryno-goexact-mathematics

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Current statement

Monotone one-parameter families cannot carry a nonidentity FRC ledger lift. The qubit ledger is two-dimensional and admits nonunique set-theoretic lifts, but incoherent, unital, and Wigner-class physical realizations each fail for a different exact reason; general CPTP realization remains open.

Evidence level

Frontier 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

v0.1 · Current release

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The FRC ledger involution D(s,y)=(-y,-s), with normalized entropy s=S_mu/k*_mu and y=ln C, cannot act nontrivially on any one-parameter family whose coherence is strictly monotone and whose normalized entropy decreases with log coherence. The preserved coordinate v=s-y is then injective, so every lift is the identity restricted to u=s+y=0. Exact normalized reciprocity ds+dy=0 sharpens the result: a connected curve lies on u=c; if c is nonzero there is no same-family lift, while c=0 permits only the trivial identity on a ledger-injective family. The wrapped-Cauchy family supplies an exact Poisson-kernel example with stationary coherence 1/sqrt(3) and algebraic fixed ledgers. The full qubit state space crosses the dimension threshold: its two-dimensional ledger image contains a nonempty D-invariant region K with a one-dimensional fixed leaf and admits explicit inequivalent set-theoretic fiber lifts. Those lifts are not physical promotions. No incoherent operation, no unital qubit CPTP channel, and no unitary or antiunitary Wigner symmetry realizes D on all of K. A general nonunital coherence-generating CPTP or resource-assisted lift remains open.
Cover art for FRC-830-004: Dimension Threshold for FRC Reciprocity v0.1: One-Parameter and Qubit Lift Obstructions

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