A registered result in its source context
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,…
Statement, assumptions and sources
Paper context: tfpt research contracts
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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
Open the original ledger source, row 275Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
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- 2026-06-15 (QGEO: the bedrock recast as a falsifiable kill-test)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- Firewall Contract — GRAV.NONCIRCULAR.01 (the Bisognano–Wichmann direction discipline)tfpt research contracts
- 2026-07-22 (I) ( v512 — the flag-transitivity equivalence web promoted as SEAM.TAU.FLAG.01: the [formula in source] attack executed on the free RP seam circle — BARE MARK-TRANSITIVITY IS FALSIFIED as a selector (on the test family [formula in source] , [formula in source] , the symmetry group is the pair-exchanging [formula in source] for EVERY [formula in source] , simply transitive on the four marks; complete census: deck-commuting M\"obius maps are diagonal/antidiagonal; hardening: ALL undirected per-mark data are identical for every [formula in source] — no local jet sees the bit), and THE SHARP SELECTOR is FLAG transitivity (marks AND their two sides indistinguishable) [formula in source] the clock — stabiliser jump [formula in source] , flag/arc orbits [formula in source] , order- [formula in source] rotation ( [formula in source] solveset [formula in source] ), mark mirror [formula in source] ; welded into a [formula in source] -FOLD EQUIVALENCE WEB (every link exact): clock rotation, [formula in source] , mark mirror, flag transitivity, three spectral degeneracies (odd-doublet split [formula in source] , zero only at [formula in source] — counterwitness exactly [formula in source] ; arc-Laplacian degeneracy [formula in source] ; the v215-K3 indicator in CLOSED FORM [formula in source] — the v503 lattice curve analytically), [formula in source] -twist existence ( [formula in source] ; Atiyah–Bott rationality [formula in source] -BLIND — [formula in source] for all [formula in source] , [formula in source] rational non-CM: rationality selects NOTHING), cusp- [formula in source] -cycle implementability (H4 rigidity: [formula in source] with orders [formula in source] cannot induce it; centraliser scalar, [formula in source] nonscalar [formula in source] no projective involution — projective order exactly [formula in source] , [formula in source] -shadow consistent v510), harmonic, [formula in source] ; NEGATIVE CONTROLS: hexagonal (not concyclic, fails preconditions), silver (harmonic but topologically dead), [formula in source] marks (impossible on the free circle: [formula in source] vs [formula in source] invariant subsets; bare [formula in source] transitivity already forces equal spacing — `` [formula in source] counts''); \ THE REST: the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit ( [formula in source] : side-indistinguishability of the four equally-decorated marks), v216 local equality does NOT deliver it, its negation is now concretely measurable; scoreboard: the counterwitness passes all [formula in source] established unsided tests, fails all [formula in source] clock-equivalent ones; Wolfram extension [formula in source] (verified engine run); NO marker moves — the bit stays , QGEO.REALIZE.01 and P2.TYPING.01/ AX.P2.01 text-precised only, SEAM.BIT.FREEDOM.01 cross-referenced)Research changelog; TFPT — Introduction and reading guide
- 2026-06-15 (QGEO: the four marks emerge from Gauss–Bonnet — K1 executed)Research changelog; TFPT — Introduction and reading guide
- The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
- Front matter / supportResearch contracts
- Firewall Contract — GRAV.NONCIRCULAR.01 (the Bisognano–Wichmann direction discipline)Research contracts
- Firewall Contract — GRAV.NONCIRCULAR.01 (the Bisognano–Wichmann direction discipline)tfpt research contracts
- 2026-07-21 (XIII) ( v503 — the v215 deferred emergence test (lever 7) executed light and promoted as QGEO.EMERGE.LIGHT.01: NO dynamical selection of the square modulus — the free field's global [formula in source] winner is the hexagonal torus, [formula in source] is a saddle, criticality at the square is Palais symmetry; the square is pinned by rigidity alone (the raw DtN is mod- [formula in source] block-diagonal iff [formula in source] , an isolated zero); and the residual converges: QGEO-R1 [formula in source] P2-R1 [formula in source] one common rest, ``why does the raw seam carry the order- [formula in source] clock''; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / , AX.P2.01 stays a declared axiom)Research changelog; TFPT — Introduction and reading guide
All 12 linked sections
- 2026-06-25 (External AQFT citations [formula in source] the four-fold [formula in source] identity sharpened)
- The celestial and twistor continuum route
- 2026-06-30 (six convergent attacks on the one SEAM.EQUIV.01 continuum residual — intrinsic Bisognano–Wichmann, a Lieb–Robinson continuum motor, the [formula in source] -homotopy, an applicability audit, uniform rigidity, and falsifiable kill tests; none closes the keystone, together they reduce it to a single analytic fact and make the claim falsifiable)
- The celestial and twistor continuum route
Registered verification modules
- v215_seam_deck_killtest.pyRegistered verification module · registry
Read the description recorded in the module registry
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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