Original ledger status
QGEO.CFACTOR.01
The translator factorization (one module, 8 checks, ~8 s; discovery probe translator_factorization_probe.py 8/8, verdict C-FACTORIZATION-LANDED). THE MIRROR INTERTWINER [E]: the intertwining system d A = Gamma(A) d for the realized pair (A in {U_1, V_1^J}; Gamma = the v599 real-structure conjugation) has a 1-DIMENSIONAL solution space -- d exists, is unique up to scale, and intertwines the pair with its mirror image exactly. UNIMODULAR AND INTEGRAL [E]: in the canonical normalization det d = 1 exactly and d is integral over Z[omega]. GAMMA-INVOLUTIVE [E]: Gamma(d) d = 1 exactly -- the mirror twist squares to the identity through d. THE FACTORIZATION [E]: with K_1 = J^-1 conj(F_2)^T M^-1 (the polarization J, the transported RP metric F_2 = g^T Sigma g, the real structure M), the v605 translator element factorizes EXACTLY: c = lambda K_1 d (lambda the free scale), and inner(K_1 d) reproduces phi on the pair -- structurally theta_corpus = Jadj o inner(K_1) o inner(d). THE READING [C]: the geometric identity of c -- the last of the three v605 residuals -- is CLOSED: c is not an unexplained element but the product of the canonical form comparison (polarization x RP metric x real structure) with the unique unimodular integral mirror intertwiner of the realized pair. Honest scope: F_2 carries the corpus datum Sigma by definition of the translator (nothing else could); the v606 arithmetic negative (cubic field S_3) stands as the reason the cyclotomic route had to fail. GATE.QGEO does not move; no marker changes.
Recorded status: Exact [E] uniqueness/unimodularity/integrality/involutivity/factorization identities + [C] the closed-identity reading (exact sympy)
Dependencies, status detail and source
Canonical status: C-FACTORIZATION-LANDED: d unique (1-dim), det 1, Z[omega]-integral, Gamma(d)d = 1; c = lambda K_1 d exact with K_1 = J^-1 conj(F_2)^T M^-1; theta_corpus = Jadj o inner(K_1) o inner(d); c geometrically identified; 8/8 checks
Dependencies: QGEO.TRANSLATOR.01; QGEO.MODESEP.01; QGEO.REAL.01; v599; v605; v606
Scripts: v609_translator_factorization.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 627Original ledger status
QGEO.LANDSCAPE.01
The curve landscape round -- what else the mu3-cover carries (one module, 9 checks, ~1 s; discovery probe curve_landscape_probe.py 9/9, verdict LANDSCAPE-MAPPED). THE JACOBIAN SPLITS [E chars + C reading]: the three holomorphic differentials of C: y^3 = x^4 - 1 carry (deck, rotation) characters of combined orders (12, 12, 6) (dx/y ~ (w^-1, i), dx/y^2 ~ (w, i), x dx/y^2 ~ (w, -1)); by standard CM theory the Jacobian splits up to isogeny as Jac(C) ~ A_2(CM Q(zeta_12)) x E(CM Q(omega)) -- with Q(zeta_12) = Q(i, sqrt3) THE FIELD GENERATED BY THE DECK AND THE MARK ROTATION TOGETHER, and E: y^3 = u^2 - 1 the x -> -x quotient curve. THE SPLITTING CONFIRMED BY POINT COUNTS [E]: a_p(C) = a_p(E) EXACTLY for all ten tested primes p != 1 mod 12 (5,7,11,17,19,23,29,31,41,43) -- the zeta_12 surface is supersingular there, as CM theory demands; the surface contributes nonzero traces exactly at p = 1 mod 12 ((13, 37, 61, 73) -> (-8, 4, -20, -32)); and a_p(C) = 0 for every tested p = 2 mod 3 (inert in Q(omega)). THE INTEGER-SPECTRUM CENSUS [E + honest relativization]: in the declared degree <= 2 J-projector pool, integer characteristic polynomials are COMMON (7894 entries) -- single spectra are CHEAP on the curve; the ANCHOR CLASS ((x+1)^2(x+2), i.e. {1,1,2} up to negation/shift) is the MOST FREQUENT nontrivial family (286 = the maximum), and non-compiler spectra exist ({1,1,3}: 254 entries): the compiler's distinction is the JOINT algebra structure (v600: rank 7, joint traces, saturation 81), not individual characteristic polynomials -- the v598/v599 char-level hits were correctly typed candidates. NEW NAMED RESOURCES [C]: the zeta_12 CM surface and the omega CM elliptic curve are two canonical objects of the cover not yet used by the program; their periods are classical Beta values -- the named resource for future RP/Hodge rounds. GATE.QGEO does not move; no marker changes. [2026-08-01 XXIX: the period resource is made concrete -- v611: all five basic periods are exact Beta values on the zeta_12 grid, the rotation acts with the exact characters, Omega_E is the classical omega-CM period, and the two CM factors are period-independent (PSLQ null), as the splitting demands; see QGEO.PERIODS.01.]
Recorded status: Exact [E] characters/point-counts/census + [C] CM-theory reading and named resources (deterministic integer computations; no floats beyond the census prefilter)
Dependencies, status detail and source
Canonical status: LANDSCAPE-MAPPED: differential characters (12,12,6); Jac ~ A_2(zeta_12) x E(omega) point-count-confirmed (10 exact zero-differences; surface traces only at p = 1 mod 12); anchor class most frequent nontrivial integer family (286); single spectra cheap, joint structure the distinction; periods named; 9/9 checks
Dependencies: QGEO.COVER.01; QGEO.DICT.01; QGEO.EMBED.01; v597; v598; v600
Scripts: v610_curve_landscape.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 628Original ledger status
QGEO.PERIODS.01
The periods round -- the analytic layer of the cover is classical (one module, 6 checks, ~1 s; discovery probe periods_probe.py 6/6, verdict PERIODS-CLASSICAL). EXACT BETA IDENTITIES [E, symbolic]: the five basic period integrals I_{k,j} = int_0^1 x^k (1-x^4)^{-j/3} dx equal (1/4) B((k+1)/4, 1-j/3) EXACTLY; the Gamma denominators (Gamma(11/12), Gamma(7/12), Gamma(5/12), Gamma(1/12)) all live on the ZETA_12 GRID -- the analytic layer carries the same 12 = |mu4| x |mu3| structure as the algebra. THE ROTATION ACTS EXACTLY [E, 40-digit certificates]: substituting x -> ix maps the [0,1]-period to the [0,i]-period and multiplies by EXACTLY i^(k+1) -- the v610 differential characters act on actual periods (three cases). THE OMEGA-CM PERIOD [E, symbolic]: the quotient curve E: y^3 = u^2 - 1 has real period Omega_E = B(1/3,1/6)/2 = Gamma(1/6)Gamma(1/3)/(2 sqrt pi) exactly -- the classical CM period of the omega curve. CROSS-FACTOR INDEPENDENCE [E, must-fail consistency]: the ratio I_{1,2}/I_{0,2} -- periods of differentials on DIFFERENT CM factors (v610) -- admits NO integer polynomial relation of degree <= 4 with coefficients up to 10^6 at 40 digits (PSLQ null): the zeta_12 surface and the omega curve are period-independent, exactly as the splitting demands. THE PERIOD DICTIONARY [C]: every cover period is a Beta/Gamma monomial on the 12-grid -- the named analytic resource for the future Hodge/RP period comparisons. GATE.QGEO does not move; no marker changes. [2026-08-01 XXX: the form-level bridge lands -- v612: J diagonalizes exactly in the rotation eigenbasis and the unique positive (Hodge) direction is the primitive zeta_12 eigenspace; the canonical period normalization (Beta weights) is the named remaining step; see QGEO.POLFRAME.01.] [2026-08-01 XXXII: the canonical period normalization lands -- v613: r = deck o rotation exactly (char(r) = char(omega*M)), the period rows realize the rotation eigenframe, the Hodge weights are explicit Gamma monomials, and J = -h per character (Riemann-Hodge positivity realized by the compiler polarization); v612's named step B5 executed; see QGEO.PERNORM.01.]
Recorded status: Exact [E] symbolic Beta identities + 40-digit certificates + PSLQ-null consistency + [C] the period-dictionary reading
Dependencies, status detail and source
Canonical status: PERIODS-CLASSICAL: five Beta identities exact (zeta_12-grid Gamma denominators); rotation characters act on periods exactly; Omega_E = B(1/3,1/6)/2; cross-factor PSLQ null (splitting-consistent); period dictionary named; 6/6 checks
Dependencies: QGEO.LANDSCAPE.01; QGEO.COVER.01; v597; v610
Scripts: v611_periods.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 629Original ledger status
QGEO.POLFRAME.01
The polarization frame round (one module, 9 checks, ~2 s; discovery probe polarization_frame_probe.py 9/9, verdict POLARIZATION-FRAMED). THE ROTATION SPECTRUM [E]: the braid rotation r has three SIMPLE eigenvalues = zeta_12 x {1, -1, -i} (e^{i pi/6}, e^{-i 5pi/6}, e^{-i pi/3}), det r = -1 exactly -- the twelfth roots organize the spectrum. J DIAGONALIZES IN THE ROTATION FRAME [E]: in the left-eigenvector basis W of r the polarization becomes EXACTLY diagonal, (W^dag)^-1 J W^-1 = diag((1+sqrt3)/2, (1-sqrt3)/2, -1) (canonical normalization). Honest typing: the diagonality is the standard consequence of r being J-unitary with simple unimodular eigenvalues (eigenspaces to distinct eigenvalues are J-orthogonal); the CONTENT is the exact values and the signature distribution. THE HODGE DIRECTION IS THE ZETA_12 EIGENSPACE [E]: the unique POSITIVE direction of J (signature (1,2), v597/v599) is EXACTLY the eigenspace of the primitive twelfth root e^{i pi/6} -- the h^{1,0} = 1 Hodge line of the omega-sheet sits on the zeta_12 eigenvector of the rotation: the analytic Hodge structure and the finite rotation agree on where positivity lives. CONSISTENCY [E]: r^dag J r = J re-verified; the product of the diagonal values equals det J / |det W|^2 = 1/2 exactly. THE READING [C]: with v611 (periods = Beta values on the zeta_12 grid) the analytic bridge is one step from closing -- the canonical period normalization of the eigenvectors (fixing the diagonal weights as explicit Beta monomials) is the named next step. GATE.QGEO does not move; no marker changes. [2026-08-01 XXXII: the canonical period normalization lands -- v613: r = deck o rotation exactly (char(r) = char(omega*M)), the period rows realize the rotation eigenframe, the Hodge weights are explicit Gamma monomials, and J = -h per character (Riemann-Hodge positivity realized by the compiler polarization); v612's named step B5 executed; see QGEO.PERNORM.01.]
Recorded status: Exact [E] spectrum/diagonalization/signature identities + [C] the bridge reading (exact sympy)
Dependencies, status detail and source
Canonical status: POLARIZATION-FRAMED: r eigenvalues zeta_12 x {1,-1,-i} simple; J exactly diagonal in the rotation frame (values (1+sqrt3)/2, (1-sqrt3)/2, -1); the positive Hodge direction = the primitive zeta_12 eigenspace; product = det J/|det W|^2 = 1/2; period normalization named; 9/9 checks
Dependencies: QGEO.PERIODS.01; QGEO.LANDSCAPE.01; QGEO.REAL.01; v597; v599; v610; v611
Scripts: v612_polarization_frame.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 630Original ledger status
QGEO.PERNORM.01
The canonical period normalization -- the analytic bridge closes (one module, 19 checks, ~6 s; discovery probe canonical_periods_probe.py 19/19, verdict PERIOD-NORMALIZED; executes v612's named step B5). DECK-FREE ROTATION [E, 40-digit certificates]: the quarter rotation x -> ix maps the four branch-point segments of y^3 = x^4 - 1 cyclically with NO deck correction (all 12 wrap factors exactly 1); the single omega-sheet homology relation is seg1+seg2+seg3+seg4 = 0; a MUST-FAIL control documents that the raw period rows are NOT r-eigenvectors (naive ansatz falsified, residual 0.42). THE EXACT DICTIONARY r = deck o rotation [E, exact]: char(r) = char(omega*M) EXACTLY for the induced companion rotation M (M^4 = 1) -- the reduced Burau rotation at t = omega is GL3-conjugate (explicit conjugator G) to the geometric quarter rotation composed with EXACTLY ONE deck step; explains v597's r^4 = omega structurally; the deck power is UNIQUE among the four scalar twists c*M with (cM)^4 = omega. THE EIGENFRAME REALIZED [E]: the period rows (hol dx/y^2, hol x dx/y^2, ANTIHOL conj(dx/y)) are left eigenvectors of M with characters (i, -1, -i); transported through G they are r-eigenvectors with eigenvalues omega*(i,-1,-i) = spec(r); character match: antihol <-> zeta_12. THE HODGE WEIGHTS ARE GAMMA MONOMIALS [E]: h0 = (3/4) pi G(1/4)G(1/3)G(5/12)/(G(3/4)G(2/3)G(7/12)), h1 = (3 sqrt3/16 pi) G(1/3)^2 G(1/6)^2, h2 = (3/4) pi G(1/4)G(2/3)G(1/12)/(G(3/4)G(1/3)G(11/12)) (complex Beta/Gelfand-KLT formula, verified to <= 1e-25); omega-sheet signature (2,1), unique NEGATIVE = the antiholomorphic line conj(dx/y). THE SIGN BRIDGE [E]: all three character-matched sign products are negative -- J = -h PER CHARACTER: the compiler polarization is the NEGATIVE of the analytic Hodge form up to per-line positive scales; J's unique positive line (zeta_12, v612) = h's unique negative line (antihol): Riemann-Hodge positivity is realized by J. THE RESIDUE [C]: the canonical fork-basis identification (basepoint bookkeeping for G), named, not claimed. GATE.QGEO does not move; no marker changes. [2026-08-01 XXXIII: the residue F1 is closed at the transport level -- v614: the deck step is DERIVED as the boundary monodromy t^4 = omega (Gauss-Manin transport along the rotation loop; transported periods factorize exactly, the canonical transport matrix is omega*M): the dictionary r ~ omega*M is canonical; see QGEO.TRANSPORT.01.]
Recorded status: Exact [E] dictionary/uniqueness identities + 40-digit certificates + Gamma-monomial closed forms + [C] the fork-basis residue (sympy + mpmath)
Dependencies, status detail and source
Canonical status: PERIOD-NORMALIZED: rotation deck-free on segments (12 wrap factors = 1); r = deck o rotation exactly (char(r) = char(omega*M), deck power unique); period rows realize the eigenframe (antihol <-> zeta_12); Hodge weights = explicit Gamma monomials, signature (2,1); J = -h per character (Riemann-Hodge positivity realized); 19/19 checks
Dependencies: QGEO.POLFRAME.01; QGEO.PERIODS.01; QGEO.LANDSCAPE.01; QGEO.REAL.01; v597; v599; v610; v611; v612
Scripts: v613_canonical_periods.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 631Original ledger status
QGEO.TRANSPORT.01
The Gauss-Manin transport round -- the deck step IS the boundary monodromy (one module, 12 checks, ~7 s; discovery probe transport_deck_probe.py 12/12, verdict TRANSPORT-CANONICAL; closes v613's named residue F1 at the transport level). THE FACTORIZATION [E, symbolic]: transporting the segment cycles along the rigid quarter-rotation loop of the four branch points (p_k(tau) = e^{i pi tau/2} p_k, the rotation braid), the discriminant lambda(tau) = e^{2 pi i tau} winds ONCE around 0 and the transported periods factorize EXACTLY: I_m(tau) = e^{i pi tau (m+1)/2} e^{-2 pi i tau j/3} I_m(0) (rotation substitution identity). THE DECK STEP = BOUNDARY MONODROMY [E]: at tau = 1 the deck factor is omega = t^4 on the t = omega sheet, UNIFORM across all three rows (j = 2 forms AND the conjugated antiholomorphic row), and omega-bar = (omega-bar)^4 on the conjugate sheet -- the deck step is t^4 on EVERY sheet; must-fail controls: t^3 = 1 != omega and t^5 != omega (the exponent 4 = |mu_4| is forced by the puncture count). THE CANONICAL MATRIX [E]: the transport matrix in the segment basis is EXACTLY omega*M -- no conjugator freedom left: the v613 dictionary r ~ omega*M is CANONICAL (Gauss-Manin transport); (omega*M)^4 = omega*1 re-derives v597's r^4 = omega; char(transport) = char(r) exactly. CERTIFICATES [E, 25-digit]: direct branch-tracked integration at tau = 1/3, 1/2, 2/3, 1 (dps 80) matches the closed factorization (max rel diff 5e-28); transported seg_1 at tau = 1 equals omega * (static seg_2) to 2.7e-81. THE READING [C]: the braid fixes the boundary, the rigid rotation does not -- their homological difference is one boundary loop of local-system monodromy (t^4 = omega); the rotation-braid convention (rigid quarter rotation realizes delta = s1 s2 s3) is the typed literature identification, carried by the exact char identity. GATE.QGEO does not move; no marker changes.
Recorded status: Exact [E] factorization/deck/uniqueness identities + 25-digit transport certificates + [C] the boundary-monodromy reading (sympy + mpmath)
Dependencies, status detail and source
Canonical status: TRANSPORT-CANONICAL: transported periods factorize exactly (rotation substitution identity); deck step = boundary monodromy t^4 = omega on every sheet (exponent 4 = |mu_4| forced); canonical transport matrix = omega*M (v613 dictionary canonical, r^4 = omega re-derived); 25-digit certificates; 12/12 checks
Dependencies: QGEO.PERNORM.01; QGEO.POLFRAME.01; v597; v612; v613
Scripts: v614_transport_deck.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 632Original ledger status
WOIT.GAMMA.TOY.01
The interacting gamma slice at toy level (one module, 11 checks, ~2 s; discovery probe gamma_toy_interacting_probe.py 11/11, verdict GAMMA-TOY-LANDED). The gamma battery executed ON the RP-surviving interaction class (the alignment bit: delta = pi/2, positive coupling, v534) of the 16-Majorana FK seam toy (v529). TWO PARENTS [float]: chiral (2-point I + iC, the v519 kernel) and MIRROR (I - iC), both gap 1. SURVIVOR ANCHOR [float, v534 regression]: chiral interacting Grams PD (37,0,0) at the forced twist eta = +i on all four admissible cuts for g in {1/32, 1/4, 1, 8}. THE INTERACTING MIRROR FLIP [float, central]: at the SAME eta the mirror state splits sector-exactly on EVERY cut and EVERY g -- even (29,0,0) PD, odd (0,8,0) STRICTLY ND with max odd eigenvalue <= -1.5e-3 (bounded away from zero over the whole grid): every mirror fermion vector has strictly negative OS norm AT THE INTERACTING LEVEL -- in the doubled vector-like system any OS-positive subspace meets the mirror odd sector in {0}: KILL TEST (3) CANNOT FIRE on the surviving interaction class (upgrade of v608 G3 from g = 0 to the full coupling grid). CONVENTION CONTROL [float]: eta = -i swaps the roles exactly -- the datum is the RELATIVE chirality. MARK TRANSPORT INTERACTING [exact + float]: alpha_4 maps the mark-A quartet algebra exactly into the mark-B sites (16/16), and both the mark Gram G_A and the transport form T_4 are Hermitian PD (16,0,0) at every g -- KILL TEST (7) DOES NOT FIRE at the interacting toy level. MULTIPLICITY-FREE [float]: the generalized odd-block transfer spectrum has 8 SIMPLE positive eigenvalues at every g (min pairwise gap 2.3e-5 > 1e-5; honest finding: strong-coupling near-doubling at g = 8 without closing); g = 0 baseline locked (top 1.641438 -- numerically the v524 compressed-clock top: the quarter-turn transfer datum recurs across N). DEAD-MEMBER CONTROL [float]: (m = 2, s = +, g = 1/2) is indefinite (21,16,0) on its straddled cut while the avoiding cut stays PD -- off the survivor the gamma battery has no RP home: the dynamical bit selection (v534) and the chirality data CO-LOCATE on the same member. FIREWALL [C]: one toy, one interaction class (FK quartets, flat-band parent), deg <= 2 cut bases + the full 16-dim mark algebra, finite grid -- NO continuum claim, NO statement about A_hol beyond this model class; kill tests (3)/(6)/(7) stay formally live on A_hol; kill test (6) untouched; WOIT.OS.TWISTOR.01 does not move. [2026-08-01 XXXV: the last untouched kill test gets its first slice -- v616: the internal SU(2) separates from the Euclidean rotation group at the kinematic twistor level (rho_tw = right-j, clock = left-u o right-u, deck = left-i, internal SU(2) broken to U(1) by the complex choice with the mark torsor as its mu4); kill test (6)'s kinematic branch does not fire, the dynamical half stays live on A_hol; see WOIT.SU2.KIN.01.] [2026-08-01 XXXVI: the net-dynamics slice lands -- v621: the Klein-Landau semigroup contracts at g > 0 to the mu4-commensurate steps {4, 6, 7} (the survivor interaction is alpha_4-invariant exactly, breaking translation invariance to the quartet stabilizer), and the clock step k = 4 stays a positive transfer ((11,0,0)) over the whole grid: the reconstructed rotation group of the interacting toy is the clock tower; see WOIT.GAMMA.SEMI.01.]
Recorded status: Float-track certificates (tolerances declared) + exact combinatorics + [C] toy fence (numpy/sympy)
Dependencies, status detail and source
Canonical status: GAMMA-TOY-LANDED: interacting mirror flip sector-exact on every cut/coupling (odd strictly ND, bounded away from zero -- kill test (3) cannot fire on the survivor); mark transport Hermitian PD at every g (kill test (7) does not fire); odd transfer spectrum multiplicity-free; dead member has no RP home (bit selection and chirality co-locate); 11/11 checks
Dependencies: WOIT.GAMMA.FREE.01; SEAM.STRADDLE.CONE.01; SEAM.INT.FKTOY.01; WOIT.THETA.FREE.01; WOIT.BETA2.OS.01; v519; v524; v529; v534; v608
Scripts: v615_gamma_toy_interacting.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 633Original ledger status
WOIT.SU2.KIN.01
The internal SU(2), kinematic separation at twistor level (one module, 17 checks, <1 s; discovery probe su2_internal_kinematic_probe.py 17/17, verdict SU2-KINEMATIC-SEPARATED; the first executed slice of gamma kill test (6)). THE QUATERNION SPLIT [E]: on C^4 = H^2 the right multiplications close the (opposite) quaternion algebra exactly, and Woit's Euclidean structure IS an internal direction: rho_tw = right-j VERBATIM (v519/v565 conventions). THE INTERNAL ALGEBRA [E]: right-sp(1) is a 3-dim real Lie algebra with exact su(2) brackets preserving EVERY fiber of PT -> S^4 (trivial on spacetime; control: left-j moves a generic fiber). THE SEPARATION [E, the kill-test datum]: the internal su(2) commutes EXACTLY with the full spacetime quaternion action and the two algebras intersect in {0} -- kill test (6)'s KINEMATIC branch does not fire. THE CLOCK FACTORIZATION [E]: RHO4 = left-u o right-u with u = e^{i pi/4} EXACTLY (must-fail: neither factor alone); the ALE deck is PURELY spacetime-side (DECK4 = left-i) and RHO4^2 = DECK4 o right-i. THE BREAKING [E]: the complex-linear part of the internal algebra is exactly span{right-i} -- the Euclidean/complex choice breaks the internal SU(2) to U(1), and the v519 mark torsor is exactly {right-mu o sigma_std : mu in mu4}. OS COMPATIBILITY [E]: sigma_std fixes right-j, inverts the internal charge, and inverts both clock factors simultaneously. THE READING [C]: kinematic twistor level only -- the dynamical half of kill test (6) stays open and formally live on A_hol; consistent with (not derived) the electroweak reading. WOIT.OS.TWISTOR.01 does not move.
Recorded status: Exact [E] operator identities (sympy) + [C] the kinematic fence
Dependencies, status detail and source
Canonical status: SU2-KINEMATIC-SEPARATED: rho_tw = right-j; internal su(2) fiber-preserving, commutes with spacetime, intersection {0} (kill test (6) kinematic branch does not fire); clock = left-u o right-u exact; deck = left-i; broken to U(1) with mark torsor = internal mu4; 17/17 checks
Dependencies: WOIT.GAMMA.TOY.01; WOIT.BETA3.DUALITY.01; WOIT.THETA.FREE.01; v519; v565; v608; v615
Scripts: v616_su2_internal_kinematic.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 634Original ledger status
QGEO.SEAMFORCE.01
The seam forcing round -- the conformal seam axioms force the mu3-cover y^3 = x^4 - 1 up to the conjugate sheet (one module, 14 checks, <1 s; discovery probe seam_cover_forcing_probe.py 14/14, verdict SEAM-FORCES-COVER; a constructive slice of the bedrock premise QGEO.SYM.01). Z4-MOBIUS RIGIDITY [E]: any 4-point configuration on P^1 cyclically permuted by an order-4 Mobius map is Mobius-equivalent to mu4 (multiplier forced primitive); the cross-ratio census is the HARMONIC orbit {2, 1/2, -1} (must-fail: 4/3 not in the orbit). THE WEIGHT CENSUS [E]: among 81 mu3-weight vectors exactly FOUR are clock-equivariant; the mark-EQUIVALENCE demand kills the alternating pair -- weights FORCED uniform, j in {1,2} = the conjugate sheet pair (v613). THE CURVE [E]: j = 1 gives y^3 = x^4 - 1 EXACTLY; full ramification at infinity (v603); Riemann-Hurwitz genus 3 exactly. THE SEAM GEOMETRY [E]: marks ON the unit circle, doubling reflection fixes seam and marks; the OS-cut (bond) reflection z -> -i conj(z) permutes the marks by EXACTLY the (k,5-k) pattern of the v599 real structure and meets the circle at the two v519 cut points; the mark-fixing reflection is the site-type axis v519 excludes. THE READING [C]: the seam axioms (disk + Z4 clock + four equivalent marks + cyclic-3 grading) force the cover; the bedrock residue narrows to (i) the cyclic-3 choice (N_fam = 3, anchored in the E8 glue 240 = 16 x 5 x 3) and (ii) the physical-seam <-> conformal-seam identification. GATE.QGEO does not move. [2026-08-01 XXXVI: residue (i) is made CONDITIONAL -- v620: the cyclic-N census shows the seam admits exactly N in {3, 5} as primitive-Lorentz orders (N = 6 reduces to N = 3), and the compiler's machine-checked integral constants (27 = 3^3 deck determinant, 81 = 3^4 saturation) pin N = 3 uniquely; the residue moves to N_fam = 3 (E8-anchored); see QGEO.NCENSUS.01.] [2026-08-01 XXXVII: residue (ii) closes at the kernel + dictionary level -- v622: the v519 seam kernel is EXACTLY the discrete NS chiral mode sum (flat band = NS spectrum, Ramond must-fail), the mark-bond midpoints sit exactly at mu4, the group dictionary is exact, and the straddle law is literal geometry (straddled = axis through marks); the remaining continuum residue is the covering-level identification; see QGEO.SEAMID.01.]
Recorded status: Exact [E] rigidity/census/genus identities (sympy) + [C] the residue typing
Dependencies, status detail and source
Canonical status: SEAM-FORCES-COVER: Z4-Mobius rigidity (mu4 forced, harmonic CR orbit); weights forced uniform j in {1,2}; y^3 = x^4-1 exact, genus 3; seam reflections = the v599 (k,5-k) pattern with the v519 cut points; residue = cyclic-3 choice + physical<->conformal identification; 14/14 checks
Dependencies: QGEO.COVER.01; QGEO.REAL.01; QGEO.SEAMMARKS.01; QGEO.PERNORM.01; v597; v599; v603; v613
Scripts: v617_seam_cover_forcing.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 635Original ledger status
QGEO.NCENSUS.01
The cyclic-N census -- the seam admits N in {3, 5} as primitive-Lorentz orders and the compiler's integral constants pin N = 3 (one module, 9 checks, <1 s; discovery probe cyclic_n_census_probe.py 9/9, verdict N3-PINNED; makes the first v617 bedrock residue CONDITIONAL). RAMIFICATION [E]: points over infinity = gcd(N, 4): full ramification everywhere iff N in {3, 5} among N = 2..6. GENUS [E]: Riemann-Hurwitz table g = 1, 3, 3, 6, 7 with complete character decomposition. SHEET DIMENSIONS [E]: primitive sheets have the compiler's rank 3 exactly for N in {3, 5, 6}, rank 2 for N in {2, 4}. CHEVALLEY-WEIL [E]: N = 3 has BOTH primitive sheets Lorentz ((1,2)/(2,1), the v599/v613 signature); N = 5 has a Lorentz pair; N = 6 has NO primitive Lorentz sheet (its Lorentz content = the order-3 characters: N = 6 REDUCES to N = 3) -- the seam-admissible orders with a primitive Lorentz sheet are EXACTLY {3, 5}. THE PINNING [E]: det_Z(1 - deck) = Phi_N(1)^3 = N^3 for prime N: 27 for N = 3 (the machine-checked v597 constant) vs 125 for N = 5; saturation 81 = 3^4 vs 625 = 5^4: N = 3 UNIQUE. THE READING [C]: the residue moves one level down -- WHY the compiler is 3-adic is N_fam = 3, anchored in the E8 glue (240 = 16 x 5 x 3), named, not derived. GATE.QGEO does not move.
Recorded status: Exact [E] ramification/genus/Chevalley-Weil/pinning identities (sympy) + [C] the conditional typing
Dependencies, status detail and source
Canonical status: N3-PINNED: seam-admissible primitive-Lorentz orders = {3, 5} exactly (N = 6 reduces to N = 3); compiler constants 27/81 pin N = 3 uniquely (vs 125/625 for N = 5); residue = N_fam = 3 (E8-anchored); 9/9 checks
Dependencies: QGEO.SEAMFORCE.01; QGEO.COVER.01; QGEO.PERNORM.01; v597; v600; v613; v617
Scripts: v620_cyclic_n_census.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 636Original ledger status
WOIT.GAMMA.SEMI.01
The interacting Klein-Landau semigroup -- the clock survives the interaction as a positive transfer exactly on the mu4-commensurate steps (one module, 6 checks, ~2 s; discovery probe interacting_semigroup_probe.py 6/6, verdict CLOCK-SURVIVES-INTERACTING; the gamma net-dynamics slice after v615/v616). FREE BASELINE [E-float]: at g = 0 all seven steps tau_k (dims 29, 22, 16, 11, 7, 4, 2) are Hermitian with normalized vacuum; even steps PD; odd steps k = 1, 3, 5 indefinite with EXACTLY ZERO one-particle diagonal; k = 7 parity-trivial -- the v524 pattern at N = 16. THE INTERACTING LAW [MEASURED, central]: at g > 0 exact Hermiticity survives PRECISELY on {4, 6, 7} and is lost on {1, 2, 3, 5} (dev > 0.1): the semigroup CONTRACTS to the mu4-commensurate window. THE CLOCK ACTS [MEASURED]: k = 4 stays Hermitian PD ((11,0,0)) over g in {1/32..8} -- the mu4 clock is a positive transfer on the interacting net. THE MECHANISM [E, exact]: the survivor interaction is alpha_4-invariant EXACTLY and not alpha_1/alpha_2 invariant -- translation invariance breaks to the quartet stabilizer {0, 4, 8, 12}. SUBSTEP TYPING [E/measured]: k = 6 even quartet-contained (protected); k = 5 quartet-contained but odd (NOT protected -- both conditions needed); k = 7 parity-trivial. THE READING [C]: the reconstructed rotation group of the interacting toy is the CLOCK tower, not the full circle; one toy, one interaction class; gamma proper stays open on A_hol. WOIT.OS.TWISTOR.01 does not move.
Recorded status: Float-track certificates (declared tolerances) + exact Clifford combinatorics + [C] toy fence
Dependencies, status detail and source
Canonical status: CLOCK-SURVIVES-INTERACTING: free v524 pattern reproduced at N = 16; at g > 0 Hermiticity survives exactly on {4, 6, 7} (mu4-commensurate); clock step PD over the whole grid; mechanism = alpha_4-invariance exact (quartet stabilizer); 6/6 checks
Dependencies: WOIT.GAMMA.TOY.01; WOIT.BETA2.OS.01; SEAM.STRADDLE.CONE.01; v524; v534; v615; v616
Scripts: v621_interacting_semigroup.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 637Original ledger status
QGEO.SEAMID.01
The seam identification round -- the physical seam IS the conformal seam (one module, 10 checks, ~1 s; discovery probe seam_identification_probe.py 10/10, verdict SEAM-IDENTIFIED; closes the second v617 bedrock residue at the kernel + dictionary level). THE KERNEL IDENTITY [E, exact]: the v519 chiral seam kernel c(d) = (2/N)/sin(pi d/N) for odd d and 0 for even d is EXACTLY the antiperiodic (NS) chiral mode sum on the 16-site circle, for ALL d = 1..15 INCLUDING the even-distance zeros -- the flat-band structure IS the NS spectrum (closed form sum_{j<8} sin((2j+1)x) = sin^2(8x)/sin(x) exact). MUST-FAIL [E]: the Ramond (periodic) mode sum does NOT reproduce the kernel -- NS is forced, not conventional. THE SITE MAP [E]: theta_a = (2a+1) pi/16 puts the four mark-bond midpoints EXACTLY at mu4 and no site coincides with a mark (v519 precision (ii), literal geometry). THE GROUP DICTIONARY [E]: alpha_1 = rotation by 2 pi/16, clock alpha_4 = z -> iz, refl_map(k) = the anti-holomorphic reflection about the axis (k+1) pi/16; cuts {3, 7, 11, 15} map to axes {pi/4, pi/2, 3pi/4, pi}. THE STRADDLE LAW IS GEOMETRY [E]: the through-mark axes are exactly the v534 STRADDLED cuts {7, 15}, the between-mark axes the avoiding cuts {3, 11}; v617's bond reflection is the cut k = 11 with the v599 (k, 5-k) mark permutation. THE READING [C]: the remaining continuum residue is the COVERING-level identification (the mu3-cover of the seam double carrying the full interacting theory), named, not claimed. GATE.QGEO does not move. [2026-08-01 XXXVIII: the covering residue gets its lattice skeleton -- v623: the lifted seam is ONE 48-site NS circle (uniform weights only; the alternating pair disconnects it -- a new independent kill), the lifted clock has exact order 12 with L^4 = deck (r^4 = omega as lattice combinatorics), and the deck-character mode grid is the 12-grid with the untwisted sector = the base seam verbatim; the residue narrows to the interacting/CFT orbifold statement; see QGEO.COVERSEAM.01.]
Recorded status: Exact [E] mode-sum/dictionary identities (sympy) + must-fail control + [C] the covering residue typing
Dependencies, status detail and source
Canonical status: SEAM-IDENTIFIED: v519 kernel = discrete NS mode sum exactly (flat band = NS spectrum; Ramond must-fail); mark-bond midpoints = mu4 exactly; group dictionary exact; straddle law = axis-through-marks geometry; residue = covering-level identification; 10/10 checks
Dependencies: QGEO.SEAMFORCE.01; QGEO.NCENSUS.01; WOIT.THETA.FREE.01; SEAM.STRADDLE.CONE.01; v519; v534; v617; v620
Scripts: v622_seam_identification.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 638Original ledger status
QGEO.COVERSEAM.01
The covered seam round -- the lattice skeleton of the covering-level identification (one module, 9 checks, ~4 s; discovery probe covered_seam_probe.py 9/9, verdict COVERED-SEAM-SKELETON; the named residue of v622, first executed slice). CONNECTIVITY CENSUS [E]: lifting the 16-site seam to the mu3-cover, the covered seam is ONE 48-site circle for the uniform weights j = 1, 2 and DISCONNECTS into 3 circles for the trivial AND the alternating weights (1,2,1,2) -- a NEW independent kill of the alternating pair (seam connectivity; total monodromy 6 = 0 mod 3). THE WALK [E]: closes after exactly 48 steps, covers the base three times, crosses marks 12 times. THE LIFTED CLOCK [E]: L^4 = deck and L^12 = id on ALL 48 points with proper order 12 -- v597's r^4 = omega and v614's boundary-monodromy transport are LATTICE COMBINATORICS on the covered seam. THE KERNEL [E]: the v622 NS mode-sum identity generalizes verbatim to N = 48 (all d = 1..47). THE 12-GRID [E]: the NS modes split under the deck into THREE classes of 16 modes with offsets {1/6, 1/2, 5/6}; the offset-1/2 class equals the BASE NS frequencies EXACTLY (the untwisted sector IS the base seam); the fermionic deck lift satisfies deck^3 = -1 (the spin double, resonating with the v510/v519 (-1)^F dichotomy) and the bilinear deck eigenvalue of the twisted pair is exactly omega -- the t = omega/omega-bar sheets live on the H^1/bilinear level. THE LIFTED MARKS [E]: the 12 crossings are equally spaced and form a SINGLE 12-cycle under the lifted clock. THE READING [C]: the remaining residue is the interacting/CFT-level orbifold statement (twist-field OPE, the full Z3 orbifold of the seam CFT), named, not claimed. GATE.QGEO does not move.
Recorded status: Exact [E] combinatorics + mode-sum identities (sympy) + [C] the orbifold residue typing
Dependencies, status detail and source
Canonical status: COVERED-SEAM-SKELETON: one 48-site covered seam (uniform weights; alternating pair disconnects -- independent kill); lifted clock exact order 12 with L^4 = deck (r^4 = omega as lattice combinatorics); N = 48 kernel identity; 12-grid mode split with untwisted = base verbatim, twisted pair = omega on bilinears; 12 marks in a single 12-cycle; 9/9 checks
Dependencies: QGEO.SEAMID.01; QGEO.SEAMFORCE.01; QGEO.NCENSUS.01; QGEO.PERNORM.01; v597; v613; v614; v617; v620; v622
Scripts: v623_covered_seam.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 639Original ledger status
EXTREV.LATTICE.01
The external-review lattice audit (one module, 14 checks, <1 s; discovery probe external_lattice_audit_probe.py 14/14, verdict LATTICE-AUDIT-PASSED; external review 2026-08-02, three claimed derivations machine-checked, one follow-up retyped honestly). THE FOUR-MARK CLOSURE [E, conditional]: generalizing the glue to D_{d+1} + A_{d-1}, THREE independent selectors each force d = 4 -- the disc-group census (Z_d = Z_4 with cyclic D-side; negative controls d = 3, 5, 8), the even-glue norm equation (d+1)/4 + (d-1)/d = 2 (unique positive solution; no other even target admits an integer d), and the Pythagorean selector (d-1)^2 + d^2 = (d+1)^2 (the (3,4,5) = (cycles, marks, carrier) triple); (1,1,2) is the unique 3-part partition of 4 and c_3 = 1/(2 e_1 pi) = 1/(8 pi): under the named architecture the two-input presentation reduces to ONE boundary degree d = 4 plus pi; honest: conditional on the glue architecture, the residue moves to why the boundary realizes the minimal cyclically-glueable genus-0 divisor. THE ANCHOR BYTECODE [E]: chi_a = (t-1)^2(t-2) carries (4, 5, 2); p_n = 2 + 2^n with p_{n+2} = 3p_{n+1} - 2p_n; Newton recovers the e_k; p_1 p_2 p_3 = 240, p_4 - p_3 = 8, 240 + 8 = 248 (H-realization v602). THE LORENTZ CONGRUENCE [E + X]: P^T J_det P = J_fix EXACTLY with det P = -6 -- the prime-front determinant form and the v604 cover polarization lattice are the SAME rational quadratic form, the cover an index-6 sublattice (36 = 6^2, 6 = p_2(a)); the review's follow-up (integer R to B = M^dagger J) is ILL-POSED as stated (B COMPLEX symmetric, det 8 verified); partial positive: the third symmetric-Gauss ratio is an exact Q(omega) square; P-canonicity and the Hodge-chamber question are the named opens. CITATIONS VERIFIED: Suzuki arXiv 2606.09096 (screw-function Weil framework, Yoshida odd-criterion) and arXiv 2607.24830 (numerical realization) -- the basis of the PRIME.WEIL.OPERATOR contract. No marker moves; AX.P2.01 keeps its typing; no RH statement. [2026-08-02 XL: the prime-shadow audit lands -- v625: the 'primes appear AFTER E8' reading is exact at the theta level (Theta_E8 = E_4, shell counts 240 sigma_3(n) multiplicative, commuting Hecke channels with the theta as simultaneous eigenvector, L(E_4,s) = zeta(s) zeta(s-3)); the direction of explanation (geometry first, primes as readout) is fixed within the narrative; see PRIME.SHADOW.01.] [2026-08-02 XLI: the Lorentz congruence P^T J_det P = J_fix is additionally machine-proved in Lean (experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean, kernel decide on the explicit integer matrices, lake build green, no sorry); P-canonicity and the operator construction of P executed by v635/v636 (see PRIME.PCANON.01 / PRIME.PCONSTRUCT.01).] [2026-08-02 XLV: look-elsewhere quantification -- v664: the observation 6 = Lorentz-congruence index = p_2(a) carries p_max = 0.169 under the most conservative null model: retyped as an observation WITHOUT statistical weight (the exact congruence P^T J_det P = J_fix itself is [E] and untouched).] [2026-08-28 CXL: v993 lifts the architecture conditionality at the census level -- full rank-8 ADE with cyclic Z4 both sides selects (D5, A3) uniquely; the D+A split is an OUTPUT. EXTREV.LATTICE.01's own v624 checks and typing UNCHANGED (they remain the architecture-conditional selectors).]
Recorded status: Exact [E] closure/bytecode/congruence identities + [X] the ill-posed retype + [C] conditional typing (sympy; citations web-verified)
Dependencies, status detail and source
Canonical status: LATTICE-AUDIT-PASSED: four-mark closure forces d = 4 three ways (conditional); bytecode exact (240 + 8 = 248); Lorentz congruence P^T J_det P = J_fix exact (index 6); B-test retyped ill-posed; Suzuki citations verified; 14/14 checks | 2026-08-28 v993: architecture conditionality lifted at census level (this row's v624 checks unchanged)
Dependencies: AX.P2.01; QGEO.EQORDER.01; QGEO.DUALFORMS.01; PRIME.UNIFC.01; v47; v602; v604; v618
Scripts: v624_external_lattice_audit.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 640Original ledger status
E8.CODE.01
The E8 code round (one module, 7 checks, ~2 s; discovery probe e8_code_probe.py 7/7, verdict E8-IS-A-CODE). Construction A on the self-dual extended Hamming code [8,4,4] yields the even unimodular rank-8 lattice = E8 (shells 240/2160 = the v625 theta); every single-bit error is exhaustively correctable (16 x 8, unique nearest codewords); the compiler ties (8 = rank, 4 = d = |mu4|, 16 = half-spinor, 14 = 2 x 7 parabolic) are typed observations. [2026-08-02 XLI: the code reading sharpens to an exact dictionary -- v638: the naive v626 placement itself is DEAD for the family 3-cycle (only 2/30 placements carry both compiler symmetries), and the unique equivariant placement C* is Reed-Muller RM(1,3) on AG(3,2) with information bits one per mu4 pair (3 families + 1 anchor), a syndrome flag carrying the sigma 3-cycle, and decode = projection verbatim; the v626 theorems are placement-independent, the SEMANTICS is not; see E8.CODESEM.01.] [2026-08-02 XLV: v664 types 14 = A_4 = 2 x 7 parabolics and 16 = |C| as FORCED (mathematically determined by the unique self-dual [8,4,4] code -- no free coincidence mass; their value is the theorem, not the number); LEAN ROUND 3: the code layer is machine-certified (HammingCode.lean: self-duality, weight distribution {0:1, 4:14, 8:1}, coset-leader weight distribution {0:1, 1:8, 2:7} with covering radius 2, all by kernel decide on explicit witnesses); lake build green.]
Recorded status: Exact [E] code/lattice identities + [C] typed compiler ties (integer combinatorics; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: E8-IS-A-CODE: Construction A(Hamming [8,4,4]) = E8 exactly; single-bit errors correctable; the error-correction reading is a theorem; no physics claim, no marker moves.
Dependencies: PRIME.SHADOW.01; EXTREV.LATTICE.01; v1; v625
Scripts: v626_e8_code.py
Location: tfpt_3
Original CSV, line 641Original ledger status
QGEO.ORBCAS.01
The orbifold Casimir round (one module, 5 checks, ~1 s; discovery probe orbifold_casimir_probe.py 5/5, verdict ORBIFOLD-CASIMIR-EXACT). The covered seam's three deck-mode classes {1/6, 1/2, 5/6} carry EXACTLY the Z3-twist Casimir data: exact closed form E0(nu, N) = -cos(pi(2nu-1)/(2N))/(2 sin(pi/(2N))); finite-size coefficient exactly pi(6nu^2 - 6nu + 1)/12; sector table (1/72, -1/24, 1/72); degenerate twisted pair; ratio -1/3; twist gap 1/18. [2026-08-02 XLI: the named interacting residue executed -- v639: twist-field weights from three exact routes (h_sigma = 1/36), lattice two-point 2 Delta = 2/9 at < 0.11%, crossing exactly symmetry-protected, closed four-point form, OPE data (c1 = 2/9 model-bound); RP validated in the real Z2 class, the complex Z3 pairing (parafermionic Klein twist) typed open; GATE.QGEO does not move; see QGEO.TWISTOPE.01.]
Recorded status: Exact [E] closed forms and expansions (sympy exact; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ORBIFOLD-CASIMIR-EXACT: the kinematic half of the Z3 orbifold statement is exact; the interacting statement (twist-field OPE, crossing, RP) stays the named residue; GATE.QGEO does not move.
Dependencies: QGEO.COVERSEAM.01; QGEO.SEAMID.01; v622; v623
Scripts: v628_orbifold_casimir.py
Location: tfpt_3
Original CSV, line 642Original ledger status
E8.INCIDENCE.01
The root incidence census (one module, 6 checks, ~1 s; discovery probe root_incidence_probe.py 6/6, verdict INCIDENCE-CENSUS-DECIDED). The naive 48 x 5 incidence to the 240 E8 roots is KILLED for the compiler-canonical order-12 element (orbit census 19 x 12 + 3 x 4, not 20 free zeta_12 orbits); positive residue: the mu4 clock alone acts FREELY with EXACTLY 60 orbits (60 = D_start) and the family 3-cycle fixes exactly 12 roots (the lifted marks). [2026-08-02 XLI: the positive residue sharpened two levels -- v633: the 60 free clock orbits ARE the hermitian-unimodular Z[i]-E8 with the ST31 hyperplane system (and the 60 -> 6 quotient-cascade route is killed); v634: G31 = the full unitary stabilizer with sigma = c^4, J = c^9 exact, and the honest sharpening that the compiler clock c is NOT the Springer-regular 12-element (the 19 x 12 + 3 x 4 census reproduced at the group level; the free 20-comb belongs to a different conjugacy class); see E8.ZIQUOTIENT.01 / E8.ST31.01.]
Recorded status: Exact [E] census (Fraction combinatorics) + honest kill + [C] typed observations (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: INCIDENCE-CENSUS-DECIDED: the naive 48 x 5 construction fails at the first hurdle; 48 x 5 = 240 stays an audit fingerprint; 60 = D_start is a free clock-orbit count on the roots.
Dependencies: EXTREV.LATTICE.01; QGEO.COVERSEAM.01; v623; v624; v626
Scripts: v629_root_incidence.py
Location: tfpt_3
Original CSV, line 643Original ledger status
FTR.PGL2.01
The F_transfer PGL2 round (one module, 25 checks, ~1 s; discovery probe ftransfer_pgl2_probe.py 25/25, verdict COMMON-ACTION-DISCRETE / UNIFLOW-CONTINUOUS -- NOT KILLED). The v533 preregistration executed in its LITERAL group form: the discrete transfer path alpha_t (disc -7 norm line, norms 2/4/14/32) carries the parabolic base translation T: alpha -> alpha + 2; the declared v183 Koide reading induces the parabolic step +9 = N_fam^2 and is EXACTLY intertwined with T (the reading map Phi is itself Moebius, Phi.T = g.Phi); CR = 4/3 exact; fit-free Moebius transport forces the F corner 53. Continuous half: the native time-1 maps constructed as explicit PGL2 elements -- g_pole hyperbolic with multiplier (2/3)^6, g_Boltzmann = g_pole IDENTICALLY (v425 single-flow theorem), g_QCD parabolic and EXPLICITLY conjugate to T (translation +7/(2pi) in the 1/alpha coordinate), g_relic = identity (degenerate); the v575 uniflow degeneration and the v578 own-clock equivalence reproduced. Five must-fail controls (raw determinant reading killed: transport predicts -16 != 32, CR 28/25; perturbed reading, elliptic clock, deck, dominant-eigenvalue export all killed).
Recorded status: Exact [E] PGL2/intertwining identities + [C] typed reading (sympy exact; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: COMMON-ACTION-DISCRETE / UNIFLOW-CONTINUOUS -- NOT KILLED: the kill criterion 'four incompatible arithmetic actions' is not met; one parabolic class on the discrete half (exact conjugations), uniflow degeneration on the native continuous half; residual = the external anchor clocks/jets, fenced by CONTRACT.F.01; no marker moves.
Dependencies: CONTRACT.F.01; FTR.DISC7.NORM.01; FTR.CRDISC.01; FTR.CRCONT.01; v533; v571; v575; v578
Scripts: v632_ftransfer_pgl2.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 644Original ledger status
E8.ZIQUOTIENT.01
The mu4-quotient round (one module, 17 checks, ~3 s; discovery probe orbit60_quotient_probe.py 17/17, verdicts ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED). The quotient of the 240 E8 roots by the free mu4 clock IS the hermitian-unimodular Z[i]-E8 with the 60-hyperplane system of ST31: H(x,y) = <x,y> + i<x,Jy> has H(v,v) = 2 on all 60 line reps; the Z[i]-span of the reps is the FULL E8 lattice (HNF covolume 256 in doubled coordinates) and a hermitian-UNIMODULAR Z[i]-basis exists among the reps (det Gram = 1); sigma acts on the 60 lines with census 19 x 3 + 3 fixed, the 3 fixed lines being exactly the J-orbits of the 12 sigma-fixed roots (v629 R4 closure); all 60 order-2 unitary reflections preserve the root set (order-4: none), and the line-permutation group has order 11520 = 46080/4 (the ST31 fingerprint: |G31| = 8*12*20*24 = 46080, hyperplanes 60 = 7+11+19+23; ST32 killed by its 40-hyperplane count). THE CASCADE HARD TEST: the 60 -> 6 route on the quotient is KILLED -- the hermitian Gram has rank 4 (no rank reduction), both |H|^2 graphs are REGULAR (any degree rule ill-defined), pair elimination has no canonical maximum (tie counts 14..360), no spectral run on the cascade grid.
Recorded status: Exact [E] quotient/lattice identities + [E, KILL] typed cascade negative (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED: the 'complex E8' reading of the 60 free clock orbits is exact (hermitian-unimodular Z[i]-E8, ST31 hyperplane system); the quotient-cascade route 60 -> 6 carries no canonical structure -- a typed negative; no marker moves.
Dependencies: E8.INCIDENCE.01; EXTREV.LATTICE.01; v626; v629
Scripts: v633_orbit60_quotient.py
Location: tfpt_3
Original CSV, line 645Original ledger status
E8.ST31.01
The ST31 structure round (one module, 56 checks, ~10 s; discovery probe st31_structure_probe.py 56/56). G31 = <the 60 unitary reflections> has order 46080 (BFS + independent Schreier-Sims) and IS the FULL unitary stabilizer of the mu4-quotient structure (exact backtracking count over Gram-matching images of a Z[i]-unimodular basis); degrees (8,12,20,24) UNIQUE via Molien among all divisor quadruples with product 46080 (exactly 60 reflections, all order 2); Springer regular elements of orders 8/12/20/24 with centralizers 192/288/20/24; the compiler data embeds canonically: J, sigma, c = J o sigma in G31 with the EXACT clock identities sigma = c^4 and J = c^9 (<c> = <J,sigma> = Z12, the mu4 center is a POWER of the clock); root stabilizer = G(4,2,3) of order 192 (Steinberg, generated by its 15 fixing reflections), line stabilizer = Z4 x G(4,2,3); the computed structure is G31 = (Z4 o 2^{1+4}).Sp4(2). THE NUMEROLOGY KILL: |G31| = |W(D5)| x |W(A3)| = 46080 carries NO structure -- G31 is NOT isomorphic to W(D5) x W(A3) (centers 4 vs 1, abelianizations 2 vs 4, element-order spectra differ), NOT a direct or semidirect product in either order (the join of all small normal closures has order 64: Lagrange kill), and W(D5) does not even EMBED in G31 (its smallest faithful complex rep has dimension 5 > 4); W(A3) = S4 does embed and sigma, c do NOT lie in the glue product. HONEST: the v629 compiler clock c is NOT the zeta12-regular element (census 19 x 12 + 3 x 4, |C(c)| = 72 != 288) -- the free 20 = 240/12 comb belongs to the REGULAR 12-clock of G31, a different conjugacy class. LEAN: the order identities 8*12*20*24 = 46080 = 1920*24 = |W(D5)|*|W(A3)| and 60 = 7+11+19+23 (+ 240 = 4*60) are machine-proved in experiments/lean4-carrier-rigidity/TfptCarrier/G31Orders.lean (lake build green, no sorry). [2026-08-02 XLIII: the degree-24/-20 round lands -- v647: the mu4 center is a POWER of both regular clocks (w^6 = +-J with chi_w = x^4 + i x^2 - 1 exactly primitive-zeta24; u^5 = +-J central), the clock question c = w^2 is KILLED by a parity theorem (census(c) = 19 x 12 + 3 x 4 has odd counts -- impossible even in S_240), and u^4 acts freely with census {5:48}, 48 = 240/5 (typed observation); see E8.ST31DEG.01.] [2026-08-02 XLV: the degree-8 round completes the clock census -- v654: the unified d/4-theorem (every Springer-regular d-clock has x^{d/4} = +-i Id, a generator of mu4; converse exact at d in {8, 20, 24}; the unique exception at d = 12 is the compiler-clock class, chi_c = (x-i)^2(x^2+ix-1) -- the only non-regular clocks whose d/4-th power generates the center); see E8.ST31D8.01.] [2026-08-03 L: G31 is the holomorphic mu4 shadow at the invariant-ring level -- v690: the restrictions F8|, F12|, F20|, F24| of the W(E8) root power sums to V^{1,0} are a system of BASIC G31 invariants (algebraically independent, degrees Molien-unique, product 46080 = |G31|, Chevalley cited) -- the holomorphic restriction generates the FULL G31 invariant ring; the vanishing half {2,14,18,30} is true but trivially mu4 (honest typing); the Jacobian carries the 60 mirror lines; see E8.QUARTICHALF.01.]
Recorded status: Exact [E] group/Molien/Springer census + [E, KILL] the numerology kill + honest clock typing (Python-only per GATE.WOLFRAM.02; Lean order identities).
Dependencies, status detail and source
Canonical status: ST31-STRUCTURE-DECIDED: G31 = full unitary stabilizer, degrees (8,12,20,24) Molien-unique, sigma = c^4 / J = c^9 exact, real structure (Z4 o 2^{1+4}).Sp4(2) computed; |G31| = |W(D5)|*|W(A3)| stays NUMEROLOGY (killed three ways); the compiler clock is NOT the regular 12-element; no marker moves.
Dependencies: E8.ZIQUOTIENT.01; E8.INCIDENCE.01; v629; v633
Scripts: v634_st31_structure.py
Location: tfpt_3
Original CSV, line 646