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A registered result in its source context

Original ledger classification: SUCCESS ([E] exact integer/symbolic + 40-digit certificates; [C] measurement sketch principle-only); the bit remains formal input; NO marker moves

Recorded statement: THE ALIGNMENT BIT AS AN EXACT MEASURABLE TWIST-CLASS CHOICE (2026-07-23; one module, 18 checks, ~46 s; verdict SUCCESS -- the physical definition): the alignment bit is the choice of which twist class nature realizes, read out by the order…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

The exact identifier, original classification and full claim are available below.

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SEAM.BIT.TWISTCLASS.01

Original ledger classification: SUCCESS ([E] exact integer/symbolic + 40-digit certificates; [C] measurement sketch principle-only); the bit remains formal input; NO marker moves

Original claim text

THE ALIGNMENT BIT AS AN EXACT MEASURABLE TWIST-CLASS CHOICE (2026-07-23; one module, 18 checks, ~46 s; verdict SUCCESS -- the physical definition): the alignment bit is the choice of which twist class nature realizes, read out by the order parameter O. (1) FACET #14 (eta-flip <=> delta=pi/2): both directions exact (sigma o r = -sigma on all four fixing axes with eta jump +i->-i; off pi/2 on EVERY axis sigma o r = +sigma; CARDINALITY LEMMA: sigma o f = -sigma forces |A+| = |A-| => 4m = 32-4m <=> m=4; g-class census over all 224 axes: flip class exactly at {15,31} for m=4). (2) FACET #15 (twist-frustration <=> delta=pi/2): theta exchanges D_short <-> D_long exactly, minimal theta-closed insertion unique, Gram indefinite (4,4,0)/(8,8,0) exactly at pi/2; off reducible and PD; same cardinality lemma locks; side finding omega(D_s)=omega(D_l) (complement-string identity, 40-digit). (3) ORDER PARAMETER: O = flip-axis fraction = 1/2 at m=4, exactly 0 else (whole ladder + counterwitness + 2-mark anchor); class alternation (-,+,-,+) around the torsor = nontrivial Z2 character of the Z8 clock-tower shadow; gauge-robust under sigma global flip, admissible site redress, mu4 overlay in all variants, string orientation; rejected candidates with teeth (sign omega(D), spectral shift, v510 index). (4) UNIFICATION THEOREM: eta-flip = frustration = flag-transitivity are ONE Z2 invariant (same arc system, A+ = supp(D_short)); the v510 Kramers class is ANOTHER (constant on the family, exact Cl(16)) -- Kramers = POSITION half (derived), twist class = MODULUS half (the input). v512 web grows 13 -> 15 facets. [C] MEASUREMENT SKETCH (principle only): defect transport around the axis torsor accumulates the eta holonomy = relative pi phase iff bit set -- the bit is in principle interferometrically readable. Honest fence: the bit remains formal input -- a definition is not a derivation. Discovery provenance: seam_bit_twist_class_definition_probe.py (18/18). NO marker moves.

Original classification detail

SUCCESS: the bit is PHYSICALLY DEFINED as the twist-class choice (facets #14/#15 both directions; O=1/2 at m=4; unification with flag-transitivity; Kramers typed as POSITION half); [C] interferometric measurement sketch; bit remains formal input; v512 web 13->15; no marker moves

Dependencies as recorded

SEAM.TAU.FLAG.01; SEAM.BIT.RPBLIND.01; SEAM.BIT.TWISTBLIND.01; SEAM.BIT.FREEDOM.01; v510; v512; v521; v525

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Registered verification modules

  • v528_seam_bit_twist_class_definition.pyRegistered verification module · frontier
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    SEAM.BIT.TWISTCLASS.01: the alignment bit as an exact measurable TWIST-CLASS choice (the physical definition; 18 checks, ~46 s). Verdict SUCCESS. [E] Facets #14 (eta-flip <=> delta=pi/2) and #15 (twist-frustration <=> delta=pi/2) both directions exact (cardinality lemma |A+|=|A-| => m=4; g-class census over all 224 axes: flip class exactly at {15,31} for m=4); order parameter O=flip-axis fraction=1/2 at m=4 else 0; class alternation (-,+,-,+) = nontrivial Z2 character of the Z8 clock-tower shadow; gauge-robust; unification #14=#15=flag-transitivity = ONE Z2 invariant (v512 web 13->15); Kramers=POSITION half (derived), twist class=MODULUS half (the input). [C] measurement sketch: defect transport around the axis torsor accumulates eta holonomy = relative pi phase iff bit set -- in principle interferometrically readable. Honest fence: the bit remains formal input. Discovery provenance: experiments/tfpt-discovery/seam_bit_twist_class_definition_probe.py (18/18, 2026-07-23). NO marker moves.

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