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Original ledger classification: Open (falsifiable kill-test; carrier-side K1-K4 [E], seam-side emergence deferred [O])

Recorded statement: BEDROCK AS A FALSIFIABLE KILL-TEST (2026-06-15): QGEO.SYM.01 (omega o rho = omega) is recast as four independently-falsifiable predictions about the raw seam DtN, NOT a proof (a foundational symmetry cannot be derived from nothing,…

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QGEO.KILL.01

Original ledger classification: Open (falsifiable kill-test; carrier-side K1-K4 [E], seam-side emergence deferred [O])

Original claim text

BEDROCK AS A FALSIFIABLE KILL-TEST (2026-06-15): QGEO.SYM.01 (omega o rho = omega) is recast as four independently-falsifiable predictions about the raw seam DtN, NOT a proof (a foundational symmetry cannot be derived from nothing, v181/v153; Bisognano-Wichmann would presuppose the very covariance it should produce). Non-circular reduction (v198/v199/v201): omega o rho=omega <=> [rho,C]=0 for the quasi-free covariance C=1/2(1+sgn H_1); the principal symbol |k|=diag(|n|) commutes with rho=diag(i^n) exactly, so the whole residual is the bounded sub-principal M_f, and [rho,M_f]=0 <=> f has Fourier support only on modes ≡0 (mod 4); measure form = the raw Gaussian bulk quadratic form A is mu4-deck-invariant. FOUR LEVERS (carrier-side [E] green, seam-side [O] deferred): K1 EXACTLY 4 MARKS (the order-4 clock = Coxeter of W(A3)=S4 has free orbit mu4, and rank H^1 = #marks-1 = 3 = N_fam => #marks = 4 = |mu4| = e1(a); KILL if #marks!=4, b1!=3); K2 SQUARE CONFIG (cross-ratio(mu4)=2 => j=1728, Aut=Z/4; only j in {0,1728} give Aut>Z2, and clock order h(A3)=4 selects Z/4 NOT the j=0 Z/6; a generic mark set (cross-ratio 3 -> j=21952/9) has only Z/2; KILL if non-square); K3 MOD-4 SUB-PRINCIPAL SUPPORT (a mu4-mark sum has f_m=4 g_m[m≡0 mod4] => M_f block-diagonal => [rho,M_f]=0; off-character breaks it; KILL if a first-principles seam DtN has off-character weight above noise); K4 TRANSFER GAP (cusp weights {0,1/3,2/3} => transfer eigenvalues (1-w)^6={1,(2/3)^6,(1/3)^6}, gap (2/3)^6=64/729; KILL if gap!=64/729). FREEZE-BOUND: freeze_file.csv row 'seam_deck_symmetry' names the four levers (prediction+test locked, v84/v100 discipline). The DECISIVE kill is DEFERRED (QGEO.REALIZE.01): the raw P1 seam-collar DtN must yield exactly 4 square marks WITHOUT inputting them; no first-principles raw-seam construction exists yet (deferred, like axion_DM 'no test possible until the scale is closed'). Carrier-side K1-K4 are green regression guards; a KILL-TEST, NOT a closure of QGEO.SYM.01. Python-only (falsification layer like v65/v100; exact sub-parts j=1728 + gap (2/3)^6 already Wolfram-mirrored via v214/v54/v56)

Original classification detail

Open / falsifiable: bedrock omega o rho=omega recast as four levers (exactly 4 square marks, mod-4 sub-principal support, transfer gap (2/3)^6), freeze-bound via seam_deck_symmetry; carrier-side [E] regression guards, decisive emergence test deferred to QGEO.REALIZE.01; not a closure and not a Bisognano-Wichmann proof

Dependencies as recorded

QGEO.SYM.01; QGEO.PILLOW.01; QGEO.SUBPRIN.01; v168_qgeo_rigidity.py; v201_seam_subprincipal_marks.py; v214_seam_pillowcase.py

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  • v215_seam_deck_killtest.pyRegistered verification module · registry
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    the bedrock QGEO.SYM.01 (ω∘ρ=ω) recast as a FALSIFIABLE kill-test (QGEO.KILL.01), not a proof-promise — a foundational symmetry cannot be derived from nothing (v181/v153), and Bisognano–Wichmann would presuppose the covariance it should produce. Non-circular reduction (v198/v199/v201): ω∘ρ=ω ⟺ [ρ,C]=0; the principal symbol |k| commutes exactly, so the residual is the sub-principal M_f with [ρ,M_f]=0 ⟺ f Z4-invariant; measure form = the raw Gaussian bulk form A is μ4-deck-invariant. Four levers (carrier-side [E], seam-side [O]): K1 exactly 4 marks (order-4 clock free orbit μ4 + b1=#marks−1=3=N_fam ⟹ #marks=4=|μ4|); K2 square config (cross-ratio 2 ⟹ j=1728, Aut=ℤ/4; order 4 selects ℤ/4 not the j=0 ℤ/6; generic ⟹ ℤ/2); K3 mod-4 sub-principal support (μ4-mark sum ⟹ f̂(m)=0 for m≢0 mod 4 ⟹ [ρ,M_f]=0); K4 transfer gap (2/3)⁶=64/729 (cusp weights {0,1/3,2/3}). Freeze-bound (freeze_file.csv seam_deck_symmetry). [O] the decisive kill is DEFERRED (QGEO.REALIZE.01): the raw ℙ¹∖μ4 collar DtN must yield 4 square marks without inputting them; carrier-side K1–K4 are green regression guards. A kill-test, not a closure.

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