Skip to main content

Find the original argument.

Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.

=150 2026-08-27 (CXXXVI) (the transport-lift wave — the two external-review rounds on the quantum structure of the seam transport graduate from the experiments tree into the load-bearing suite as v976_seam_lift_birkhoff.py and v977_transfer_unistochastic_wilson.py (suite [formula in source] , ledger [formula in source] : new rows TRANSFER.HIDDEN.CIRCULATION.01 and TRANSFER.COHERENT.WILSON.01, both ``executed half [E] / selection open [O]''; the exploration probes transfer_ birkhoff_ circulation_ probe.py 42/42 and transfer_ coherent_ wilson_ probe.py 28/28 stay in experiments/tfpt-discovery/ as the discovery record). (1) v976 — the Birkhoff fibre and the entanglement-breaking no-go. The Birkhoff (random-permutation) fibre of the seam single step [formula in source] (exact sixth root of the v221 kernel, [formula in source] bit-exact) is exactly a one-parameter line [formula in source] ; the hidden coordinate is the sign-character Fourier coefficient [formula in source] , populations are exactly [formula in source] -free, and no fibre member is chiral ( [formula in source] forced). The one-step coherence spectrum is [formula in source] and the triangle loop current is an exact eigen-observable [formula in source] — one step plus one current readout measures [formula in source] without an ancilla. On the contrast qubit the Choi partial transpose has spectrum [formula in source] : the deployed sixth-root spectrum sits exactly on the entanglement-breaking boundary because [formula in source] (mutated spectra miss by [formula in source] ); at the full three-level the family stays NPT at every tested iteration with [formula in source] , [formula in source] -independent. The no-go that sharpens DYN.UNITARY.DILATION.01: the deployed Kraus dilation [formula in source] is measure-and-prepare, hence entanglement breaking with quantum capacity [formula in source] and [formula in source] exactly — any dilation closing that contract must be a genuinely different object. Shannon KKT certificates: [formula in source] is exactly capacity-achieving for both [formula in source] and [formula in source] ( [formula in source] bit, [formula in source] bit, ratio [formula in source] ) — the surviving classical message is binary on every scale. The defect–Birkhoff value coincidence (weights [formula in source] vs the v652 ladder [formula in source] ) is recorded typed [C] with its honest multiplicity audit; the forcing functor is the named open contract TRANSFER.DEFECT.BIRKHOFF.01. (2) v977 — the unistochastic [formula in source] lift and the 5-12-13 Wilson code. [formula in source] is unistochastic: an exact [formula in source] with [formula in source] entrywise, angles forced by [formula in source] ( [formula in source] , [formula in source] , [formula in source] ), [formula in source] unique, lift set [formula in source] up to rephasing; Jarlskog [formula in source] exactly, and the real part of every Wilson plaquette is fixed by [formula in source] through unitarity — the full rephasing-invariant Wilson data is classical up to the [formula in source] orientation bit [formula in source] . The main plaquette is [formula in source] , normalized [formula in source] with [formula in source] (atoms: [formula in source] , [formula in source] , [formula in source] ); all nine plaquettes close on four Gaussian phase types with norms exclusively [formula in source] . The center bridge: [formula in source] for the v530 atom matrix, [formula in source] , and the v530 sibling quotients fail the identity — the bridge selects the atom quotient. Rationality selection: [formula in source] is rational only at [formula in source] (the deployed step hits [formula in source] exactly, so [formula in source] ); census over 238 valid family points: exactly one full-code point [formula in source] the deployed [formula in source] ( [formula in source] the preregistered [formula in source] kill). No fixed microstep: [formula in source] and a Dirichlet recurrence witness ( [formula in source] ) shows no single closed unitary generates the relaxing sequence — repeated steps require dephasing between steps, the six-step macro-gate [formula in source] (the coherent sharpening of clock-vs-walk). The PMNS near-miss stays a negative control ( [formula in source] vs [formula in source] ; [formula in source] ; no PMNS derivation). Surfaces. Research-contracts document: the DYN.UNITARY.DILATION.01 section gains the executed lift-structure sharpening, the CCC reduced-channel prose and the two former ``exploration-only'' citations of rounds DCXCVI/DCXCVII are upgraded to veri citations; origin_theory gains the honest ``what the classical transport does not determine'' paragraph next to the v221 recoverability code; tfpt_2 gains the [formula in source] bridge corollary in the v530 center-quotient block. No status marker moves; both contracts stay open; no PMNS/CP/flavor claim.)

Research changelog · TFPT — Introduction and reading guide

Opening source excerpt. Formulas and the full argument remain in the original document.

Source location and explicit evidence links

documents/changelog/sections/001-source.tex · lines 307 to 308

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

What this source index covers

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.