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FRC-830-005 · v0.2

FRC and Quantum Born Reciprocity v0.2: A Present-Structure Obstruction to Majid-Style Self-Duality

H. Servat2026-07-1523 minFRC 800 seriesFoundationalμ4 Logical / conceptual
Concept DOI10.5281/zenodo.21385391DOI10.5281/zenodo.21385392PDFDownload
born-reciprocitymajidself-dualityhopf-algebrasemidualisationledger-involutionnon-reconstructionlift-obstructionno-promotion

Reading status

Current statement

FRC's exact ledger involution is not conjugate to canonical Born exchange, does not reconstruct a state action, and fails several one-parameter and qubit lift gates. Its remaining open CPTP gate is real but does not promote it to Majid-style self-duality.

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

v0.2 · Current release

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FRC has an exact normalized entropy-coherence ledger involution D(s,y)=(-y,-s), a typed category of operational registers, and now both one-parameter and full-qubit lift obstructions. This paper asks whether those results constitute Born reciprocity or Majid-style representation-theoretic self-duality. They do not. The canonical Born exchange B_a(q,p)=(ap,-q/a) is order four and symplectic, whereas D is order two and anti-symplectic on the ambient ledger plane; indeed their different orders prevent conjugacy even by a bijection. The ledger datum also does not reconstruct a state-space action, and FRC 830.004 shows that this non-reconstruction occurs in natural qubit fibers. A primitive Hopf algebraization makes D only a Hopf automorphism of one chosen ledger algebra, without an independently defined dual object, pairing, semidualisation, representation exchange, or physical state-observable map. The general one-parameter identity-lift obstruction excludes every nonidentity lift under its monotonicity hypotheses, while the full qubit ledger excludes incoherent operations, unital qubit CPTP channels, and unitary or antiunitary Wigner symmetries as global lifts. A general nonunital, coherence-generating CPTP lift remains open. Present FRC therefore has exact coordinate, typed-morphism, dimension-threshold, and scoped no-go mathematics, but not a Born- or Majid-style self-duality.
Cover art for FRC-830-005: FRC and Quantum Born Reciprocity v0.2: A Present-Structure Obstruction to Majid-Style Self-Duality

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