Original ledger status
SYNTH.INVENTORY.02
RESIDUAL INVENTORY UPDATED (post v110-v122; supersedes the CONTENTS of SYNTH.INVENTORY.01 while keeping its cardinality): (1) thirteen new ledger rows machine-pinned (CAR.PAIR.02, CAR.QTRANS.01, CAR.COUNT.01, CAR.QFREE.01, GATE.UWALL.06-09, FLAV.H2.02-05, ARCH.TRIAD.01). (2) R2 CARRIES THREE LOADS: the single index-4 boundary-net statement closes, when proven, the metric gate (GATE.METRIC.06), the carrier choice (CAR.QFREE.01 upgrade contract) and the QBL programme (ARCH.QUAD.01) - one theorem, three doors. (3) UPDATED RESIDUAL TABLE, exactly FIVE structural classes: R1 seam quantum clock (produce the bend log_{3/2}3 at coupling ~1/3pi) [P]; R2 index-4 seam net (3 loads) [P]/[A]; R3 seam determinant => EH [A]; R4' SELECTOR ESTABLISHMENT (derive n = (5,-9,6) + the diamond determinants from the parabolic geometry; replaces the DISCHARGED 'H2 dictionary' class) [A]/[P]; R5 parabolic realisation of Q (GATE.QGEO; carries P1) [P] - plus the two irreducibles (v_geo, pi) and the frozen data surfaces; a sixth structural class would FAIL the script. (4) THE FLAVOR SIDE HAS NO OPEN ANALYSIS CLASS OF ITS OWN: H2 values exact (FLAV.H2.02), addresses pinned (FLAV.H2.04), margins theorems (FLAV.H2.05); residue = five frozen selector integers. Ledger-bookkeeping module, Python-only by nature
Recorded status: Identity [I] (machine bookkeeping + typing contract)
Dependencies, status detail and source
Canonical status: Inventory: five classes re-pinned (R1 clock; R2 index-4 net with 3 loads; R3 EH; R4' selectors; R5 Q); flavor side discharged; sixth class fails the script
Dependencies: SYNTH.INVENTORY.01; GATE.METRIC.06; CAR.QFREE.01; ARCH.QUAD.01; FLAV.H2.05; HOR.CLOCK.02; GATE.QGEO
Scripts: v123_inventory_update.py
Location: origin_theory; introduction
Original CSV, line 207Original ledger status
SYNTH.INVENTORY.03
TERMINAL RESIDUAL INVENTORY (post premise-(A) closure; supersedes the CONTENTS of SYNTH.INVENTORY.02): after the (A)-chain (v160-v165) premise (A) is NO LONGER an independent structural class. (1) (A) CLOSED AS A CLASS - the four (A)-closure rows exist (GATE.METRIC.16 fixed-point theorem; .17 cone eliminated, cone gap = one-particle gap; .18 numbers forced by mu4-equivariance; .19 factors into A2 + GATE.QGEO + irreducible core). (2) THE FIVE v123 CLASSES COLLAPSE: R1 clock, R2 index-4 net and R5 Q-realisation all merge into ONE Tier-1 hinge (the seam=flavour=horizon identification = A2 net existence [assembly of established net constructions, GATE.METRIC.11/13] + GATE.QGEO [seam boundary = P^1 minus mu4; cohomology b1=N_fam=3, cusp grading = A3 exponents]); R3 (EH step) folds into v_geo (SEAM.EHMODEL.03/v152: the normalisation IS the anchor); R4' (selectors) was already discharged. (3) TERMINAL STRUCTURE: Tier 0 = the irreducible core {pi, v_geo}, a THEOREM by the No-Unit Theorem (ANCHOR.VGEO.01/02), nothing to close; Tier 1 = ONE hinge; Tier 2 = folded (EH -> v_geo, ambient QG -> G_net via GATE.METRIC.02/v76, gap-decoupled); Tier 3 = F_transfer, ONE functor with four typed CONDITIONAL interfaces (Koide FR.KOIDE.05/06, eta_B FR.ETAB.01, m_p/m_e QCD.LAMBDA.01 [ratio stays open/not forced], RG-stable lepton mixing FLAV.RGSTAB.01; axion = scenario), eta_B carrying the most open computational room. (4) COMPLETENESS: the structural residual is now ONE hinge + ONE transfer functor + the {pi, v_geo} core; a sixth independent structural class - or a new irreducible - would FAIL this script. HONEST: a unification + re-typing, NOT an unconditional proof
Recorded status: Identity [I] (machine bookkeeping + typing contract; ledger-row membership)
Dependencies, status detail and source
Canonical status: Terminal inventory: (A) no longer a class; ONE hinge (A2+GATE.QGEO) + F_transfer + irreducible {pi,v_geo}; Tier 2 folded; sixth class fails the script
Dependencies: SYNTH.INVENTORY.02; GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; GATE.METRIC.19; ANCHOR.VGEO.02; FR.ETAB.01
Scripts: v167_inventory_post_closure.py
Location: origin_theory
Original CSV, line 208Original ledger status
HOR.CLOCK.03
THE RESUMMED CLOCK (R1's bend acquires a closed form; the HOR.CLOCK.02 job description transforms): (1) THE SPECTRUM READS (1 - n/N)^{p2} [I]: the frozen transfer eigenvalues {1, (2/3)^6, (1/3)^6} (v54/v69/v95) are EXACTLY lambda_n = (1 - n/N_fam)^{p2} for n = 0, 1, 2, with p2 = 6 = |R+(A3)| the hexagon size. (2) CLOSED-FORM CLOCK [I]: rate(n) = -p2 ln(1 - n/N_fam) reproduces {0, Delta, 6 ln 3} exactly; the HOR.CLOCK.02 bend rate(2)/rate(1) = log_{3/2}3 becomes a one-line consequence. (3) THE LINEARISATION CARRIES THE SHEET [I]: rate(n) = |Z2| n + n^2/3 + 2n^3/27 + ... - the linear (one-loop) term has slope exactly |Z2| = 2 relative to the integer classical Ginsparg-Perry clock {0,-1,-2} (HOR.CLOCK.01): the quantum clock is the SHEET-DOUBLED classical clock plus the geometric tail sum_k (n/N)^k/k. (4) THE WALL AT N_fam [I]: rate -> infinity as n -> N_fam (pole of the resummed logarithm at the family count) => the cusp ladder ends at n = N_fam - 1 = 2: the three-level transfer spectrum is forced by the clock itself. (5) R1 RE-SHARPENED [P] (recorded, not claimed): closed-form semiclassical target - derive rate(n) = -p2 ln(1 - n/N_fam) from the near-Nariai one-loop at kappa = 1/(3pi); the linear response must give slope |Z2| x classical and the resummation must exponentiate the geometric series; all spectra frozen in v54/v69/v95/v104/v107 - nothing fitted
Recorded status: Identity [I] (exact spectral reading + series) + Physical [P] (semiclassical derivation)
Dependencies, status detail and source
Canonical status: Identity: transfer spectrum = (1 - n/N)^6; rate = -6 ln(1 - n/3); linearisation slope |Z2|; pole at N_fam forces three levels; R1 target now closed-form
Dependencies: HOR.CLOCK.02; HOR.CLOCK.01; FR.KOIDE.06 (transfer spectrum); SYNTH.INVENTORY.02 (R1)
Scripts: v124_resummed_clock.py
Location: tfpt_horizon_readouts
Original CSV, line 209Original ledger status
GATE.METRIC.08
THE GLUE Q-SYSTEM (the index-4 mu4 extension exists as an explicit Longo Q-system; the R2 gate sharpens from 'find a Q-system' to 'match the constructed one'): (1) Q-SYSTEM AXIOMS [I] on A = C[Z4] (the glue group algebra; multiplication delta_a x delta_b -> delta_{a+b}, unit delta_0): associativity, unit law, FROBENIUS (m x 1)(1 x m*) = m* m = (1 x m)(m* x 1), and SPECIALNESS m m* = |Z4| id all hold exactly => a special C* Frobenius algebra = a Longo Q-system with dim theta = 4: JONES INDEX [B:A] = 4 = |mu_4| - exactly the GATE.METRIC.06 Carrier Index Lemma value; KLM bookkeeping mu_carrier = 16 = 4^2 x mu_E8 re-verified. (2) LOCALITY = ISOTROPY [I] (GATE.METRIC.07 re-derived in Q-system language): on the Lagrangian glue <(1,1)> the discriminant form q = (5x^2+3y^2)/8 gives q(k(1,1)) = k^2 = (0,1,4,9), all integers - the Q-system braiding obstruction vanishes (local/bosonic extension); the two Lagrangian glues = the sheet pair are the only maximal isotropic choices. (3) THE HALFWAY SUB-Q-SYSTEM [I]: {0,2} < Z4 closes multiplicatively => the unique intermediate Q-system C[Z2] = the SO(16)_1 step of the tower (GATE.METRIC.07/CAR.QFREE.01), index factorisation 4 = 2 x 2. (4) R2 SHARPENED [P] (recorded, not claimed): the gate's algebraic object now EXISTS explicitly; what remains is the operator-algebraic IDENTIFICATION 'the seam-Calderon inclusion of the 16-Majorana net realises THIS Q-system' - matching two constructed objects, not a search; the three loads (metric + carrier + QBL, SYNTH.INVENTORY.02) hang on this one identification; gate typing [P]/[A] unchanged [2026-08-03 LIII: the index side is now MEASURED on the CAR ladder (v726, 57/57, GNET.PPINDEX.01): the mu4-average expectation has optimal Pimsner-Popa constant EXACTLY 1/4 and Watatani index EXACTLY 4 via an explicit quasi-basis with FORCED weights, with mu4 DERIVED from the clock (not inserted) and the Ramond sector healed state-preservingly by the v679 Klein dressing; the remaining half of the gate is the IDENTIFICATION of this ladder Q-system with the constructed GATE.METRIC.08 object -- registered as the open contract half of GNET.RAMIFIED.01 (kills: Frobenius mismatch, index != 4 on the state-preserving ladder, dressing incompatible with the sigma descent). No status move.] [2026-08-05 LXII (v779): the finite precursor of the R2 identification is measured -- the coherent COMMUTING system of index-4 expectations along the Haar tower (restriction coherence, [E_I, E_J] = 0, joint idempotency, all exact) is the finite half of the Longo Q-system identification, and the exact dim law d_c(l) = 4^(l-1) + 2^(l-1) cos(pi c/2) makes the 4-element C[Z4] group-layer quasi-basis obstruction exactly 2^-l at every finite level (d_0 - d_2 = 2^l > 0), restored only asymptotically -- the crossed-product structure is exactly asymptotic; d_2(1) = 0 IS the l = 1 index-3 anomaly. No status move.]
Recorded status: Identity [I] (exact finite Frobenius/Q-system axioms + isotropy) + Physical [P] (identification)
Dependencies, status detail and source
Canonical status: Identity: C[Z4] is a special Frobenius algebra (Longo Q-system) of index 4 = |mu4|; locality = isotropy; halfway C[Z2] = SO(16)_1; R2 = identification of constructed objects
Dependencies: GATE.METRIC.06; GATE.METRIC.07; CAR.QFREE.01; SYNTH.INVENTORY.02 (R2)
Scripts: v125_glue_qsystem.py
Location: tfpt_research_contracts
Original CSV, line 210Original ledger status
HOR.CLOCK.04
THE CLOCK AND THE WALL SHARE A SPECTRUM (the v124 resummed-clock weights ARE the Mehta-Seshadri parabolic weights; R1's first checkpoint passes classically): (1) THE WEIGHTS ARE THE PARABOLIC WEIGHTS [I]: the arguments n/N_fam = {0, 1/3, 2/3} of the resummed logarithm are EXACTLY spec A0* (the exact U_wall residue, GATE.UWALL.07); the spectral bridge lambda_n = (1 - alpha_n)^{p2} over alpha in spec A0* reproduces the frozen transfer spectrum {1, (2/3)^6, (1/3)^6} - the horizon clock and the flavor wall share their spectrum through the complement map alpha -> 1 - alpha: the transfer eigenvalues are the hexagon-power of the COMPLEMENTARY parabolic weight. (2) CHECKPOINT 1 PASSES CLASSICALLY [I]: the resummed clock's linear coefficient p2/N_fam = 2 = |Z2| equals the established classical entropy-deviation rate 2H = |Z2| x Hubble (HOR.CLOCK.01) - the slope-2 linear response demanded by HOR.CLOCK.03 is already the classical entropy rate; the genuinely QUANTUM content of R1 isolates to the geometric tail sum_{k>=2} alpha^k/k. (3) THE DETERMINANT IS THE ENTROPY CURVATURE [I]: det(1 - A0*) = (1)(2/3)(1/3) = 2/9 = |Z2|/N_fam^2 - exactly the established gravity entropy curvature at the anchor (HOR.ORIENT.01), a fourth independent appearance; tr(1 - A0*) = 2 = |Z2|; det A0* = 0 (the parabolic degree-0 marker). (4) R1 RE-TARGETED [P] (recorded, not claimed): derive 'rate = -p2 ln(1 - alpha)' with alpha the parabolic weight - first order is classical (HOR.CLOCK.01's entropy rate), the tail is the quantum part; ONE SPECTRUM, TWO GATES, ONE OBJECT A0*
Recorded status: Identity [I] (exact spectral bridge + coefficient identities) + Physical [P] (re-target)
Dependencies, status detail and source
Canonical status: Identity: clock weights = parabolic weights (spec A0*); lambda = (1-alpha)^6; linear term = classical entropy rate |Z2|H; det(1-A0*) = entropy curvature 2/9; quantum content = geometric tail
Dependencies: HOR.CLOCK.03; HOR.CLOCK.01; HOR.ORIENT.01; GATE.UWALL.07 (A0*); SYNTH.INVENTORY.02 (R1)
Scripts: v126_clock_wall_bridge.py
Location: tfpt_horizon_readouts
Original CSV, line 211Original ledger status
HOR.CLOCK.05
THE CLOCK IS A LOG-DETERMINANT (the geometric tail of HOR.CLOCK.03/04 is the standard ring/RPA resummation; the 'O(1) resummation' demanded by HOR.CLOCK.02 is now TYPED): (1) LOG-DET IDENTITY [I]: for a rank-1 insertion P (tr P^k = 1), -ln det(1 - alpha P) = -ln(1 - alpha) = sum_k alpha^k/k - so the resummed clock is EXACTLY rate = -p2 Tr ln(1 - alpha P): p2 = 6 identical one-loop ring towers, ONE PER HEXAGON SITE (= positive root of A3), with coupling alpha = the Mehta-Seshadri parabolic weight. (2) RING LADDER [I]: the k = 1 ring is the CLASSICAL term (6 alpha = |Z2| n = the HOR.CLOCK.01/04 entropy rate); the k = 2 ring is the first quantum correction (1/3 at weight 1); the partial sums converge to the exact rates {Delta, 6 ln 3} monotonically from below. (3) COUPLING CROSS-LINK [I, audit]: the established seam coupling kappa = (c/24pi)(Lambda/Mbar^2) at Lambda = Mbar^2 with c = 8 (HOR.CLOCK.02) is 8/(24pi) = 1/(3pi) = alpha_1/pi - the seam coupling is the first parabolic weight over pi. (4) THE WALL = RING DIVERGENCE [I]: radius of convergence |alpha| < 1; at alpha -> 1 (n -> N_fam) the sum diverges - the HOR.CLOCK.03 wall at the family count is the standard RPA instability. (5) R1 FINAL FORM [P] (recorded, not claimed): show that the near-Nariai one-loop effective action of the seam mode, with insertion strength = parabolic weight and multiplicity p2, is the ring sum - 'the seam clock is the RPA determinant of one mode on six sites'; the resummation type is identified, the derivation itself remains open
Recorded status: Identity [I] (log-det + ring ladder + coupling arithmetic) + Physical [P] (derivation)
Dependencies, status detail and source
Canonical status: Identity: clock = -p2 Tr ln(1 - alpha P) (ring/RPA determinant; one tower per hexagon site); k=1 ring = classical entropy rate; wall = RPA instability; kappa = alpha_1/pi
Dependencies: HOR.CLOCK.04; HOR.CLOCK.03; HOR.CLOCK.02; FLAV.H2.02 (hexagon); SYNTH.INVENTORY.02 (R1)
Scripts: v127_ring_resummation.py
Location: tfpt_horizon_readouts
Original CSV, line 212Original ledger status
E8.GRADE.01
THE GRADED HULL + THE ZERO-MODE MULTIPLICITY (both named computations gain their structural anchors): R2 HALF - (1) EXPLICIT COSET CONSTRUCTION [I]: the 240 E8 roots, built as explicit norm-2 vectors in D5 (+) A3 + glue coordinates, decompose over the glue group Z4 as 240 = 52 + 64 + 60 + 64 (C0 = carrier roots 40+12; C1 = (16, 4bar) from norm 5/4 + 3/4; C2 = (10, 6) from 1 + 1; C3 = (16bar, 4)) - exactly the GATE.METRIC.06 branching, now as vectors. (2) THE GRADING IS EXACT [I]: for ALL 6720 root pairs whose sum is again a root, coset(r1+r2) = coset(r1) + coset(r2) mod 4 - E8 IS A Z4-GRADED LIE ALGEBRA over the carrier subalgebra, and the grading group IS the glue = the GATE.METRIC.08 Q-system: the checksum hull is the Q-system's graded module realised in 248 dimensions (not merely 'compatible' with it). R1 HALF - (3) THE MULTIPLICITY IS THE ZERO-MODE COUNT [I]: the Ginsparg-Perry l = 1 sector (the zero modes, lambda in {0,-1}, HOR.CLOCK.01/02) has 2l+1 = 3 modes; sheet doubling gives 2 x 3 = 6 = p2 = |R+(A3)| - the ring multiplicity of the HOR.CLOCK.05 log-det clock equals the sheet-doubled zero-mode count; [P] reading (recorded, not claimed): zero modes are exactly the modes that force nonperturbative resummation in de Sitter one-loop physics - the natural home of the six RPA towers. (4) RESIDUE [P]: R1 = compute the RPA determinant on the six sheet-doubled l=1 zero modes; R2 = identify the seam-Calderon inclusion with the Z4-graded structure now exhibited inside E8 itself
Recorded status: Identity [I] (explicit construction + exact grading + arithmetic) + Physical [P] (anchors)
Dependencies, status detail and source
Canonical status: Identity: E8 = Z4-graded Lie algebra over the carrier (grading = glue Q-system; 6720 pair checks); ring multiplicity 6 = sheet-doubled GP zero modes
Dependencies: GATE.METRIC.08; GATE.METRIC.06; HOR.CLOCK.05; HOR.CLOCK.01; E8.GLU.01
Scripts: v128_graded_hull.py
Location: tfpt_research_contracts; tfpt_horizon_readouts
Original CSV, line 213Original ledger status
HOR.CLOCK.06
THE CLOCK IS AN ENTROPY POWER LAW (the transfer eigenvalues are the Nariai entropy fractions to the hexagon power; the ring coupling is the fractional entropy deficit): (1) THE THREE ENTROPY LEVELS [I]: the established Nariai bookkeeping (HOR.NARIAI.01) has S/S_dS in {1, 2/3, 1/3} (pure dS; two-horizon total; single horizon - deficit S_dS/3 per step) - EXACTLY the complementary cusp weights 1 - n/N_fam. (2) THE CLOCK IS AN ENTROPY POWER LAW [I]: lambda_n = (S_n/S_dS)^{p2} = the frozen transfer spectrum {1, (2/3)^6, (1/3)^6}; rate(n) = p2 ln(S_dS/S_n) = {0, Delta, 6 ln 3} - hexagon-weighted log-entropy deficits; audit: exponent p2 = 6 = 2h reads as the two-point form of a weight h = 3 = N_fam operator (recorded, not claimed). (3) THE COUPLING IS THE ENTROPY DEFICIT [I] (triple identity): alpha = n/N_fam = the Mehta-Seshadri parabolic weight (GATE.UWALL.07/HOR.CLOCK.04) = 1 - S_n/S_dS = DeltaS_n/S_dS - the RPA insertion strength is the fractional entropy deficit of the SdS configuration: the coupling is not a free parameter in ANY of its three readings. (4) ORIENTATION CONSISTENCY [I]: weight 0 <-> pure dS (max entropy, rate 0: the stationary attractor); weight 2 <-> single horizon (lowest level, fastest decay) - monotone, the established repeller -> attractor orientation (FR.KOIDE.05/HOR.NARIAI.01/HOR.ORIENT.01). (5) R1 THERMODYNAMIC FORM [P] (recorded, not claimed): derive Gamma_n ~ (S_n/S_dS)^{p2} from the near-Nariai one-loop - a Gibbons-Hawking-type entropy power law with exponent = the hexagon size; the exponent (weight h = N_fam) is the remaining quantum content
Recorded status: Identity [I] (entropy-level + power-law + triple-coupling identities) + Physical [P] (derivation)
Dependencies, status detail and source
Canonical status: Identity: lambda = (S/S_dS)^p2; rate = p2 ln(S_dS/S); alpha = entropy-deficit fraction = parabolic weight; orientation consistent; R1 = Gibbons-Hawking power law
Dependencies: HOR.CLOCK.05; HOR.CLOCK.04; HOR.NARIAI.01; HOR.ORIENT.01; GATE.UWALL.07
Scripts: v129_entropy_power_law.py
Location: tfpt_horizon_readouts
Original CSV, line 214Original ledger status
HOR.CLOCK.07
THE BORN SQUARE (the amplitude weight is h = N_fam = half the zero-mode count; the clock exponent p2 = 2h is its Born square - the HOR.CLOCK.05 multiplicity and the HOR.CLOCK.06 weight are ONE object): (1) EXPONENT BOOKKEEPING [I]: in the standard collective-coordinate treatment each zero mode trades a Gaussian integral for a moduli factor ~ S^{1/2}; with n_zero = 6 the transition AMPLITUDE scales as A ~ (S/S_dS)^{n_zero/2} = (S/S_dS)^3 and the PROBABILITY is its Born square Gamma = |A|^2 = (S/S_dS)^6 = the HOR.CLOCK.06 entropy power law => h = n_zero/2 = 3 = N_fam and p2 = 2h: the weight audit is DERIVED from mode counting; the factor 2 between weight and exponent is the Born rule, nothing else. (2) THE THREE ARE THE SPHERE'S CONFORMAL DIRECTIONS [I]: the l = 1 scalar eigenspace on S^2 has dimension 2l+1 = 3 = the number of proper conformal Killing vectors of the sphere (gradients of the l = 1 harmonics; the classic zero modes of near-Nariai physics, Ginsparg-Perry/Bousso-Hawking class, external standard); the doubling x2 is the HORIZON PAIR = the SdS mass-line deck (HOR.NARIAI.01): n_zero = |Z2| x 3 = 6 = p2 - every factor an established object. (3) CONSISTENCY [I]: multiplicity (E8.GRADE.01) = exponent (HOR.CLOCK.06) = Born square of the amplitude weight; h = N_fam ties the clock's conformal weight to the family count - the same 3 counts generations and the sphere's conformal directions. (4) RESIDUE [P] (recorded, not claimed): justify the per-zero-mode S^{1/2} collective-coordinate normalisation on the Nariai instanton for exactly these six modes - a textbook-class computation; no exotic object remains in R1 (log = ring sum, power law = entropy fractions, exponent = Born-squared mode count)
Recorded status: Identity [I] (exponent bookkeeping + mode-count identities) + Physical [P] (measure normalisation)
Dependencies, status detail and source
Canonical status: Identity: h = n_zero/2 = N_fam; p2 = 2h (Born rule); 3 = proper CKVs of S^2; x2 = horizon pair; R1 residue = standard zero-mode measure
Dependencies: HOR.CLOCK.06; HOR.CLOCK.05; E8.GRADE.01; HOR.NARIAI.01
Scripts: v130_born_square.py
Location: tfpt_horizon_readouts
Original CSV, line 215Original ledger status
HOR.CLOCK.08
THE MEASURE IS THE AREA (the per-mode S^{1/2} of the Born square is the zero-mode NORM, computed exactly; the R1 residue narrows to one determinant-ratio cancellation): (1) ZERO-MODE NORM = AREA [I]: on the sphere S^2(r) the L^2 norm^2 of each of the three normalised l = 1 harmonics is EXACTLY r^2 = A/(4pi) (all three modes integrated exactly) - the norm of every zero mode IS the horizon area, hence the entropy, up to the fixed 4pi. (2) JACOBIAN BOOKKEEPING [I]: the collective-coordinate Jacobian per zero mode is the mode norm ~ S^{1/2} (standard change of variables, no model input); with the six sheet-doubled modes (HOR.CLOCK.07) the amplitude ratio is (S_n/S_dS)^3 and the Born square gives Gamma_n/Gamma_0 = (S_n/S_dS)^6 = the HOR.CLOCK.06 entropy power law - every exponent factor now has a derivation-level origin: norm = area -> Jacobian = S^{1/2} -> six modes -> amplitude S^3 -> Born -> S^6. (3) UNIT CONSISTENCY [I]: the 4pi in norm^2 = A/(4pi) is the same Gauss-Bonnet 4pi that builds c3 = 1/(2 x 4pi) (ARCH.QUAD.01/P1 hardening); it CANCELS in all ratios - exactly why the clock sees only entropy FRACTIONS S_n/S_dS. (4) THE LAST STEP [P] (recorded, not claimed): show the non-zero-mode fluctuation determinants cancel in the ratio, det'_n/det'_dS = 1 + O(deficit) - plausible (same local near-Nariai geometry) but the one remaining computation; R1 = norm (exact, done) + Jacobian (standard) + Born (rule) + det-ratio (open)
Recorded status: Identity [I] (exact sphere integrals + bookkeeping) + Physical [P] (det-ratio)
Dependencies, status detail and source
Canonical status: Identity: ||Y_1m||^2 = A/(4pi) exactly (all three modes); Jacobian = S^(1/2) per mode; 4pi cancels in ratios; R1 residue = det-ratio cancellation only
Dependencies: HOR.CLOCK.07; HOR.CLOCK.06; HOR.NARIAI.01; ARCH.QUAD.01 (c3 primitive)
Scripts: v131_measure_is_area.py
Location: tfpt_horizon_readouts
Original CSV, line 216Original ledger status
HOR.CLOCK.09
THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the HOR.CLOCK.08 'last step' acquires its first exact invariant): (1) SPECTRAL SETUP (re-pinned): the Ginsparg-Perry sphere operator on the unit S^2 is L = -Delta - 2 (the -2 = -|Z2| = the HOR.CLOCK.01 modulus mass); eigenvalues mu_l = l(l+1) - 2 = (l+2)(l-1), degeneracy 2l+1; kernel = the 3 zero modes (l = 1); one negative mode (l = 0). (2) THE HEAT COEFFICIENT IS MADE OF ATOMS [I]: a_1 = (1/4pi) Int(R/6 - E) dA = 1/3 + 2 = 1/N_fam + |Z2| = 7/3 - the curvature third and the sheet mass, both compiler atoms. (3) THE ANOMALY IS THE KOIDE CONSTANT [I]: zeta(0)|det' = a_1 - dim ker = 7/3 - 3 = -2/3 = -|Z2|/N_fam, independently confirmed by numerical continuation of the heat trace (constant term of Tr' e^{-tL} - 1/t extrapolates to -2/3 at ~1e-7) - the EIGHTH appearance of 2/3 in the inventory (SYNTH.INVENTORY.01 counted seven) and the first as a SPECTRAL anomaly. (4) CONSEQUENCE [I]: det'(cL) = c^{zeta(0)} det'(L): the determinant ratio between configurations is NOT automatically 1 - the S^2-sector share of the scaling budget is exactly -2/3 per Hubble-unit conversion; the dimensionless tower itself is configuration-independent (pure-number GP spectrum, HOR.CLOCK.01): all scale dependence = this one anomaly number + the zero-mode Jacobians (HOR.CLOCK.08). (5) THE BUDGET STATEMENT [P] (recorded, not claimed): show the FULL zeta(0) budget of the 4d Nariai fluctuation problem (dS2 sector + gauge/ghost sectors + this S^2 sector) vanishes or is absorbed into the established power law; the S^2 share is pinned exactly at -|Z2|/N_fam - nothing claimed about the total
Recorded status: Identity [I] (heat-kernel arithmetic + numerical continuation) + Physical [P] (full budget)
Dependencies, status detail and source
Canonical status: Identity: zeta(0) of the det'-operator = -2/3 = -|Z2|/N_fam (a1 = 1/N_fam + |Z2| = 7/3); det-ratio question = one zeta-budget statement; S^2 share pinned
Dependencies: HOR.CLOCK.08; HOR.CLOCK.01; SYNTH.INVENTORY.01 (2/3 inventory); HOR.NARIAI.01
Scripts: v132_detratio_anomaly.py
Location: tfpt_horizon_readouts
Original CSV, line 217Original ledger status
HOR.CLOCK.10
THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not - the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S^2 x S^2, so the temporal dS2 sector continues to the SAME unit sphere and both candidate routes are exactly computable. (1) THE REDUCED ROUTE [I]: each 2d sector carries the HOR.CLOCK.09 operator with zeta(0)|det' = -2/3; two sectors give budget = -4/3 = -e1/p0 = MINUS THE SEED GAIN (the second ARCH.TRIAD.01 ratio; the first, -2/3, is the per-sector share); the six zero modes split 3 + 3 across the two spheres - the sheet doubling of E8.GRADE.01/HOR.CLOCK.07 IS the two-sphere structure of Euclidean Nariai (= the horizon pair, HOR.NARIAI.01). (2) THE NAIVE 4D ROUTE [I]: with the standard unit-S2 heat expansion 1/t + 1/3 + t/15 (verified numerically) and the symmetric split L4 = (-Delta1 - 1) + (-Delta2 - 1): per-factor trace 1/t + 4/3 + (9/10)t => a2(4d) = (4/3)^2 + 2(9/10) = 161/45; zero modes (1,0)+(0,1) = 6; zeta(0)|det'4d = 161/45 - 6 = -109/45 (numerical continuation ~1e-8) - NO anchor-atom reading. (3) ROUTE DISCRIMINATION [I arithmetic + P reading]: reduced-route anomalies = pure anchor ratios (-2/3, -4/3: two of the three triad values); 4d-route anomaly = -109/45, not an atom => the zeta budget structurally favours the REDUCED seam reading, consistent with the theory's 2d-seam architecture throughout; typed as route-selection evidence, not proof. (4) REMAINING [P] (recorded): the graviton/ghost shares on S^2 x S^2 (Volkov-Wipf-class computation, external standard) complete the budget; both scalar-sector shares pinned exactly - the remaining work is a finite list of known heat coefficients
Recorded status: Identity [I] (exact heat-kernel arithmetic both routes + numerics) + Physical [P] (route reading + remaining shares)
Dependencies, status detail and source
Canonical status: Identity: reduced budget = -4/3 = -seed gain (per sector -2/3); 4d route = -109/45 no atom; zero modes 3+3 = horizon pair; route selection -> reduced seam reading
Dependencies: HOR.CLOCK.09; ARCH.TRIAD.01 (triad); E8.GRADE.01; HOR.NARIAI.01
Scripts: v133_zeta_budget.py
Location: tfpt_horizon_readouts
Original CSV, line 218Original ledger status
FLAV.DUAL.01
THE DUAL ANCHOR LEMMA (the inverse flavor response of the anchor IS the Nariai root; the third purely algebraic leg of the flavor-horizon bridge; external review 2026-06-12, validated): (1) THE DUAL ANCHOR [I]: d := a^T R^-1 = a^T L^-1 = (-1/2, -1/2, 1) with d.1 = 0, d.a = 1 and d = (3/2)(a - (4/3)1)^T - the normalised TRACELESS anchor - and (1,1,-2) = -2d: the inverse flavor response stores EXACTLY the Nariai double-root structure (HOR.NARIAI.01) up to sign and scale; the horizon is not glued on afterwards - it sits inside the flavor compiler as a dual invariant. (2) WHY INVARIANT [I] (Sherman-Morrison, exact): L = R + 6*1 e1^T gives v^T L^-1 = v^T R^-1 <=> v^T R^-1 1 = 0; R^-1 1 = (1,1,-1)/4 (denominator 5/2); a.(R^-1 1) = 0 - the anchor lies on the 2-plane of invariant covectors: the winding deformation lives in the democratic direction 1, which d annihilates. (3) CONTROL [I]: 1, e1 and n = (5,-9,6) do NOT lie on the invariance plane (1/4, 1/4, -5/2) - the membership is special, not generic. (4) THE DUAL NORMAL PAIR [I]: d (sheet normal: kills 1, dual to a, proportional to the Nariai root) and n (torsion normal: n^T R = (8,0,0), n^T L = (20,0,0), n.a = 8, n.1 = 2 = |Z2| cf. FLAV.DIAMOND.02) form the dual basis of the flavor boundary. (5) CONSEQUENCE [P] (recorded): third algebraic bridge leg (besides the shared spectrum HOR.CLOCK.04 and the entropy power law HOR.CLOCK.06); supports the reduced seam reading (HOR.CLOCK.10); the R4' selector programme (FLAV.H2.05) acquires a geometric target: derive the PAIR (d, n), not n alone
Recorded status: Identity [I] (exact dual-vector + Sherman-Morrison + controls) + Physical [P] (bridge reading)
Dependencies, status detail and source
Canonical status: Identity: a^T R^-1 = a^T L^-1 = Nariai root/(-2); invariance <=> orthogonality to R^-1 1; dual normal pair (d n); R4' target = the pair
Dependencies: HOR.NARIAI.01; FLAV.DIAMOND.02; FLAV.H2.05 (selectors); HOR.CLOCK.04; HOR.CLOCK.06
Scripts: v134_dual_anchor.py
Location: tfpt_2; tfpt_horizon_readouts
Original CSV, line 219Original ledger status
FLAV.SURF.01
THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume walls at the discrete atoms; external review 2026-06-12, validated): (1) SURFACE + WALLS [I]: on the established diamond M(s,t) = R + Q diag(s,t,t) (FLAV.DIAMOND.01/02), det M(s,t) = 3s(t+1)(t+2) + t^2 + 5t + 8; two iso-volume WALLS independent of s: t = -2 => det = 2 = |Z2| (the Z2 wall), t = -1 => det = 4 = |mu_4| (the mu_4 wall; K = M(1,-1) lies on it - det K = 4 is a LAYER, not an isolated hit); the WINDING LINE t = 0 has det = 6s + 8 => (det R, det C, det L) = (8, 14, 20); the fourth canonical point closes the pattern: det F = det M(1,1) = 32 = 2^{g_car}. (2) ANCHOR BLOCK [I]: det B_{M(s,t)} = 6s(t+2) + 3t^2 + 15t + 16; on the winding line det B(s,0) = 2 det M(s,0) EXACTLY; own Z2 wall det B(s,-2) = -2 (s-independent); t = -1 is NOT a B-wall (6s+4, recorded honestly). (3) ROW-BUDGET AXES [I]: rowsum(C) = (7, 11, 13), rowsum(U) = (3,3,3) (democratic winding), rowsum(V) = (1,2,3) = Spec(Q_+) verbatim; audit: the centre budget (7, 11, 13) reads (scalaron, ||Pl(K)||_1, Delta_Q) - the three quark constants (audit, not load-bearing). (4) TWO ANCHOR MICRO-IDENTITIES [I]: e1^2 + e2^2 = 16 + 25 = 41 = 10 b1 (the anchor Pythagoras for the abelian coefficient, companion to Delta_Y = 25 = 9 + 16); p1^2 + p2^2 = 16 + 36 = 52 = the carrier coset root count (40 + 12, E8.GRADE.01). (5) READING [P] (recorded): the flavor algebra lives on a 2d surface whose walls are the discrete atoms and whose axes are democratic winding and the Q_+ progression - compiler semantics replacing the matrix list; no gate status changes
Recorded status: Identity [I] (exact surface/wall/budget identities) + Physical [P] (reading)
Dependencies, status detail and source
Canonical status: Identity: det M = 3s(t+1)(t+2)+t^2+5t+8; walls 2 and 4 (s-independent); winding line (8 14 20); det F = 32; det B = 2 det M on t = 0; V-rowsum = Spec(Q+); 41 and 52 micro-identities
Dependencies: FLAV.DIAMOND.01-02; FLAV.H2.04; ARCH.TRIAD.01; E8.GRADE.01 (52); FLAV.KQ.01 (11 13)
Scripts: v135_det_surface.py
Location: tfpt_2
Original CSV, line 220Original ledger status
GATE.UWALL.10
THE DUAL-NORMAL SELECTOR ((d,n) pins R columnwise; the R4' residue is bounded; external review 2026-06-12, validated and sharpened): (1) COLUMN NORMAL FORM [I]: d.c_j = a_j and n.c_j = 8 delta_1j for the columns of R; the common kernel of (d,n) is the primitive vector (6,8,7) (audit: p_2, rank E8, scalaron-7), so within the address box {0..5}^3 each line contains at most one lattice point; brute-force census (216 per column): c_1 = (1,1,2) = a, c_2 = (3,5,5), c_3 = (0,2,3) are each the UNIQUE solution - R4' shrinks from a 6^9 matrix census (FLAV.H2.04) to three 1-of-216 column problems: (d,n) => R. (2) HONESTY [I]: K is NOT pinned directly (d^T K = (1,1/2,1), n^T K = (14,1,-6)); det K = 4 follows from R via the diamond (mu_4 wall, FLAV.SURF.01). (3) SPECTRAL NORMAL [I]: the zero mode of the exact anchor residue A0* (GATE.UWALL.07) is v = (-sqrt2,3,-sqrt5)/3 with signed squares = -(2,-9,5) = -(|Z2|, -N_fam^2, g_car); NEW ATOMS: ||v||^2 = 16/9 (numerator 16 = dim S+) and adj(A0*) = (2/9) P_v with 2/9 = |Z2|/N_fam^2 = the SdS entropy curvature (HOR.NARIAI.01). (4) SIGMA RELATIONS [I]: sigma.1 = -|Z2|, sigma.a = N_fam, n.sigma = 121 = ||Pl(K)||_1^2 (the v119 audit constant). (5) ORBIT CONTROL [I]: exact enumeration |W(A3)| = 24 (GATE.UWALL.09); the only real orbit images of sigma are its signed copies; NO image is proportional to n - the naive cofactor/orbit lift FAILS as the review predicted; the step sigma -> n is a genuine mechanism beyond the monodromy group. (6) R4' RESTATED [P] (recorded): derive the PAIR (d,n); then R is forced columnwise; d is structural (FLAV.DUAL.01), the residue is the derivation of n - bounded by the sigma relations and the negative orbit control
Recorded status: Identity [I] (column census + spectral normal + orbit control) + Physical [P] (restated programme)
Dependencies, status detail and source
Canonical status: Identity: (d n) => R columnwise (each column 1-of-216); A0* zero mode = -(2 -9 5) signed squares; n.sigma = 121; W(A3) orbit excludes the naive lift
Dependencies: FLAV.DUAL.01; GATE.UWALL.07; GATE.UWALL.09; FLAV.H2.04 (superseded census); FLAV.SURF.01; HOR.NARIAI.01
Scripts: v136_dual_normal_selector.py
Location: tfpt_research_contracts; tfpt_2
Original CSV, line 221Original ledger status
FLAV.QGEO.04
THE Q+ GRADING IS COHOMOLOGY (the R5/GATE.QGEO dictionary at the spectrum level; external review 2026-06-12, validated and sharpened): (1) BASIS + CHARACTERS [I]: b_1(P^1 minus mu_4) = 3 = N_fam with holomorphic basis omega_k = z^(k-1)dz/(z^4-1), k = 1,2,3 (regular at infinity; the trivial character is absent - k = 4 would be the dlog form); the mu_4 character of omega_k is i^k, so H^1 = chi_1 + chi_2 + chi_3 with each nontrivial character exactly once; the residue vector of omega_k over the punctures is the character vector zeta^k/4 exactly. (2) THE GRADING IS Spec(Q+) [I]: the character degrees (1,2,3) are exactly Spec(Q+) (Q+ = 3*diag(cusp weights)+1, FLAV.QGEO.01); NEW: the cusp weights {0,1/3,2/3} are spec(A0*) (GATE.UWALL.07) - Mehta-Seshadri weights, cusp classes, cohomology characters and the flavor operator Q+ are ONE spectrum in four readouts. (3) A3 EXPONENTS [I]: (1,2,3) are the exponents of A3 (W(A3) = S4, GATE.UWALL.09) with Coxeter number h(A3) = 4 = |mu_4| - the Q+ generation grading IS the A3 exponent grading realised on the seam curve's cohomology: the R5 dictionary statement at spectrum level. (4) RESIDUE [P] (recorded): GATE.QGEO's remainder is the NATURALITY of the identification - the canonical map from the H^1 character basis to the V-axis generation basis (rowsum(V) = (1,2,3) verbatim, FLAV.SURF.01); spectrum equality is [I], the canonical map is the residue
Recorded status: Identity [I] (cohomology basis + characters + residues + spectrum match) + Physical [P] (naturality residue)
Dependencies, status detail and source
Canonical status: Identity: H^1 = chi_1+chi_2+chi_3 with degrees (1 2 3) = Spec(Q+) = A3 exponents; cusp weights = spec(A0*); residue = naturality of the canonical map
Dependencies: GATE.QGEO.01; FLAV.QGEO.01-03; GATE.UWALL.07; GATE.UWALL.09; FLAV.SURF.01
Scripts: v137_qplus_cohomology.py
Location: tfpt_2; tfpt_research_contracts
Original CSV, line 222Original ledger status
HOR.CLOCK.11
THE VOLKOV-WIPF FIREWALL (R1 typed closure: the external full-4d graviton/ghost value is pinned and the edge part is exactly two copies of the reduced seam budget; external values verified against arXiv:2506.02142 Table 4.1 which states agreement with Volkov-Wipf Nucl. Phys. B582 (2000) 313 = hep-th/0003081): (1) EXTERNAL DATUM [I typed external]: alpha_bulk = 22/45, alpha_edge = -8/3, alpha_PI = -98/45 for d = 3 (S^2 x S^2, 4d); arithmetic 22/45 - 8/3 = -98/45 exact; the review's arXiv citation 0204021 corrected to 0003081. (2) THE EDGE MATCH [I]: alpha_edge = -8/3 = 2 x (-4/3) - the external edge factor consists of TWO IDENTICAL COPIES (one per horizon) and the per-copy magnitude 4/3 = e_1/p_0 is EXACTLY the reduced seam budget of HOR.CLOCK.10 (= the seed gain; -2/3 per sector); the TFPT reduced route lands on the EDGE sector of the external bulk/edge split; the bulk 22/45 is the ideal graviton gas which the seam clock does not contain; two copies = the horizon pair = the sheet doubling (HOR.NARIAI.01; HOR.CLOCK.10's 3+3 zero-mode split). (3) FIREWALL ARITHMETIC [I]: -98/45 + 60/45 = -38/45 with 38 = 2*19; neither -98/45 nor -38/45 nor 22/45 is an anchor atom (census) - consistent with HOR.CLOCK.10 where the naive scalar 4d route (-109/45) was already non-atomic (different operator content: scalar split vs full graviton + ghosts + isometries, recorded). (4) TYPING DECISION [P] (recorded): R1 = the reduced zero-mode/RPA seam clock = an EDGE-sector object; the full 4d Volkov-Wipf determinant is the GRAVITY FIREWALL (its -98/45 absorbed in the mu_0/(Lambda G)^3 normalisation), not a TFPT atom; per-copy sign/orientation (the edge factor enters inverted) and the Lorentzian edge-mode reading stay [P]
Recorded status: Identity [I] (exact arithmetic vs external values) + Physical [P] (typing decision) + External (VW hep-th/0003081; arXiv:2506.02142)
Dependencies, status detail and source
Canonical status: Identity: -98/45 = 22/45 - 8/3 external; edge = 2 x reduced budget (-4/3); diff -38/45 no atom; typing: seam clock = edge object full 4d determinant = firewall
Dependencies: HOR.CLOCK.10; HOR.NARIAI.01; HOR.CLOCK.03-09 (the clock chain)
Scripts: v138_vw_firewall.py
Location: tfpt_horizon_readouts
Original CSV, line 223Original ledger status
GATE.UWALL.11
THE SELECTOR TRIANGLE (anchor + A0* zero mode + three atoms => R; the R4' residue shrinks to three pairings): (1) d IS ANCHOR DATA [I]: d = (3/2)a - 2*1 exactly - the dual anchor (FLAV.DUAL.01) has a closed form that never mentions R; the first selector of the pair (d,n) is DERIVED, not residual. (2) THE FRAME [I]: (1, a, sigma) is a basis of Z^3 with det(1|a|sigma) = 11 = ||Pl(K)||_1 - the quark constant as the frame volume (sigma = the A0* zero-mode signature, GATE.UWALL.10). (3) n FROM THREE ATOMS [I]: n = (5,-9,6) is the UNIQUE solution of n.1 = 2 = |Z2|, n.a = 8 = rank E8, n.sigma = 121 = 11^2 - the cofactor definition (FLAV.DIAMOND.02) is replaced by frame data plus three atoms. (4) THE SQUARE SELECTS [I]: on the line n.1 = 2, n.a = 8 (direction 1 x a) the sigma-pairing is 11(11+t) - divisible by 11 for every t and a positive perfect square exactly at t = 0 (window [-20,20]). (5) THE REVIEW LIFT EXACT (audit) [I]: n = reverse(sigma) + |mu_4| e_3 - the review's predicted mechanism (generation flip + mu_4 lift at the third slot) is an exact identity; n - sigma = N_fam e_1 + e_3; audit decompositions, not promoted. (6) RESIDUE [P] (recorded): R4' = derive the three pairings (|Z2|, rank E8, ||Pl(K)||_1^2) of n against the frame; everything else in the chain anchor -> (d,n) -> R (GATE.UWALL.10) is exact
Recorded status: Identity [I] (closed form for d + frame volume + uniqueness + square selection) + Physical [P] (three-pairing residue)
Dependencies, status detail and source
Canonical status: Identity: d = (3/2)a - 2*1 (no R); det(1 a sigma) = 11; n unique from pairings (2 8 121); square selects t = 0; review lift exact
Dependencies: FLAV.DUAL.01; GATE.UWALL.10; FLAV.DIAMOND.02; FLAV.KQ.01 (the 11)
Scripts: v139_selector_triangle.py
Location: tfpt_research_contracts
Original CSV, line 224Original ledger status
FLAV.QGEO.05
THE CANONICAL MAP EXISTS AND IS RIGID (the GATE.QGEO naturality residue collapses to ONE Z_3 choice): (1) THREE mu_4 ACTIONS ONE MATCH [I]: the deck U = diag(1,i,-i) has characters (0,1,3) (invariant line, misses 2 - cannot match H^1); the sheet-twisted deck -U has (2,3,1) and the cusp exponential i^{Q+} has (1,2,3) - both with character SET {1,2,3} = the H^1 set (FLAV.QGEO.04): only the SIGN-TWISTED actions match, the same sheet twist that builds the v118 hexagon (FLAV.H2.02). (2) RIGIDITY (Schur) [I]: both sides are multiplicity-free mu_4-modules with equal character sets, so the equivariant isomorphism exists and is unique up to one scalar per character (commutant = diagonal algebra); the explicit map is the character-matching permutation - the canonical map is WELL-DEFINED; existence and uniqueness are no longer open. (3) GRADING TRANSPORT [I]: under the i^{Q+}-equivariant map the H^1 Euler degree pulls back to Q+ itself (assignment (1,2,3)); under the -U-map to Q+ o rho with rho = the (123) family rotation (assignment (2,3,1)) - the two candidate actions differ by EXACTLY one Z_3 rotation. (4) RESIDUE [P] (recorded): GATE.QGEO collapses from 'prove naturality' to ONE discrete choice - which sign-twisted action is the geometric boundary deck on generation space (-U monodromy sheet twist vs i^{Q+} cusp exponential)
Recorded status: Identity [I] (character algebra + Schur rigidity + grading transport) + Physical [P] (one Z_3 choice)
Dependencies, status detail and source
Canonical status: Identity: only sign-twisted actions match H^1; equivariant iso Schur-rigid; i^Q+ assignment = Q+ and -U = Q+ o rho; residue = one Z_3 choice
Dependencies: FLAV.QGEO.04; FLAV.H2.02 (sheet twist); GATE.UWALL.09 (U); GATE.QGEO.01
Scripts: v140_canonical_map.py
Location: tfpt_2; tfpt_research_contracts
Original CSV, line 225Original ledger status
FLAV.QGEO.06
DECK SELECTION THEOREM (R5's Z_3 choice DERIVED, executing the v140 residue): the established integer deck G=T_A*Sigma (v97 anchor-forced conjugation; v98 integer mu4 on generation space) pairs the Q_+=1 cusp line with the SELF-CONJUGATE character 2 (G e1=-e1 exact eigenline; E-plane carries {1,3}); of the three Z_3 rotations only the sheet-twisted assignment (2,3,1)=chars(-U) is compatible - the cusp exponential i^{Q_+} (1,2,3) and the third rotation are EXCLUDED (same eigenvalue multiset, wrong grading pairing: (-1)-eigenlines on Q_+ degrees 1 vs 2). Explicit Q_+=1-line-preserving conjugacy S G S^-1 = -U constructed. SHEET ROBUSTNESS: under k->-k the B1 pairing (1->2) and plane set {1,3} are invariant - the only remaining freedom is the plane orientation = the established sheet Z_2 (v92 chirality pair), NOT a new residual. CONSEQUENCE: the H^1 Euler degree pulls back to Q_+ o rho (rho=(123)=coker-Q triality, v72): cusp grading and Euler grading differ by exactly one family rotation. STATUS: GATE.QGEO's discrete Z_3 residue CLOSED [L]; what remains of R5 is the realisation premise [P] the gate always carried (integer D4 model = parabolic geometry), with no discrete freedom left
Recorded status: Lattice/Lie [L] (derived selection + explicit conjugacy/obstruction) + [P] (realisation premise unchanged)
Dependencies, status detail and source
Canonical status: Lattice [L]: Z_3 choice derived - geometric deck = sheet-twisted class; residual = realisation premise only
Dependencies: FLAV.QGEO.05; FLAV.QGEO.04; v97; v98; v72
Scripts: v141_deck_selection.py
Location: tfpt_2
Original CSV, line 226