Original ledger status
HOR.CLOCK.01
THE CLASSICAL NARIAI CLOCK IS THE ANCHOR (third appearance) + honest (2/3)-test (executes the HOR.TRISECT.01 clock question at the classical level): STATIC PIN [I] - phi(rho) = rho solves d/drho[(1-L rho^2)phi'] = -2L phi EXACTLY on the dS2 static patch, so the exact SdS family itself pins the S^2-radius modulus mass m^2 = -2L = -|Z2|L (the Laplace-type form of the Nariai linearization is standard GR - Ginsparg-Perry 1983 / Bousso-Hawking 1997 - typed external; the VALUE is pinned internally). Horizon split linear in the canonical angle, coefficient 1/sqrt(N_fam) [I]. GINSPARG-PERRY TOWER [I]: (l(l+1)-2)L has exactly ONE negative mode -|Z2|L (l=0), zero modes l=1. THE CLOCK [I]: in Hubble units chi_clock(lambda) = lambda^2+lambda-2 = (lambda-1)(lambda+2) = THE ANCHOR QUADRATIC; eigenvalues {1,-2} = the distinct anchor roots; Nariai cubic = (t-1) x chi_clock - the anchor appears as configuration roots (HOR.NARIAI.01), curvature base (HOR.TRISECT.01) and clock spectrum; entropy-deviation rate = 2H = |Z2| x Hubble exactly [I]. HONEST (2/3)-TEST NEGATIVE for the classical clock: eigenvalues are integers (anchor roots), not (2/3)-powers; the 2/3-powers stay in the functional; the one-loop conversion curvature -> rate (quantum (anti-)evaporation) remains external [P] - the flavor-rate bridge is NOT closed; the seam variational principle now has exactly one missing object: the QUANTUM clock
Recorded status: Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)
Dependencies, status detail and source
Canonical status: Identity: clock spectrum = anchor roots; quantum clock = the one [P]
Dependencies: HOR.TRISECT.01; HOR.ORIENT.01; HOR.NARIAI.01; ARCH.CORE.01 (anchor)
Scripts: v104_nariai_clock.py
Location: tfpt_horizon_readouts
Original CSV, line 187Original ledger status
SYNTH.INVENTORY.01
THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide branch point, transfer-gap base (2/3)^6, attractor inside the physical basin; gravity: Nariai entropy bound, SdS branch separation, canonical amplitude+frequency, canonical curvature base (2/3)^N_fam); ANCHOR TRIPTYCH [I]: configuration chi_a = (t-1)^2(t-2), Nariai cubic (t-1)^2(t+2) = traceless anchor, clock quadratic (lam-1)(lam+2); Nariai = (t-1) x clock; a = e2+e3. (B) RELOCATION THEOREM [I]+[P]: the cosmological one-loop clock correction eps = (c/24pi) Lambda/Mbar^2 = 7.6e-122 (c = 8 = the seam central charge, frozen rho_L) is deficient by 121.5 orders against the needed O(1) gap, and the deficit IS the Lambda hierarchy 2 alpha^-1/ln10 = 119.0 (+2.5 prefactors, the v60 split) => the seam clock must live at the SEAM scale, where the only gapped generator is the established boundary transfer operator; the bridge reaches its final form: ONE [P] identification 'transfer operator = seam Nariai clock'. (C) RESIDUAL TABLE (typing contract): exactly FIVE structural objects remain - R1 seam quantum clock [P] (HOR.CLOCK.01), R2 seam net holomorphic + c=8 [P]/[A] (GATE.METRIC.05/06/07), R3 seam determinant => EH form [A] (SEAM.AREACOEFF.03 residual), R4 H2 dictionary [A]/[P] (GATE.RU.01/CONTRACT.U.01), R5 parabolic realisation of Q carrying P1 [P] (GATE.QGEO.01/FLAV.SHEET.03) - plus the two irreducibles (one scale v_geo by dimensional analysis v78; the primitive pi) and the frozen data surfaces (gamma_CP, n_s/A_s, theta13, m_tau, r). COMPLETENESS is itself the claim: a sixth structural gap would FAIL v105. Nothing closed here; everything that remains is named, typed and counted
Recorded status: Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)
Dependencies, status detail and source
Canonical status: Residual inventory: 5 named structural objects + 1 scale + pi; completeness machine-pinned
Dependencies: HOR.CLOCK.01; HOR.TRISECT.01; HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04/05/06; GATE.METRIC.05-07; GATE.RU.01; GATE.QGEO.01; ANCHOR.VGEO.01; REG.FREEZE.01
Scripts: v105_residual_inventory.py
Location: origin_theory;introduction
Original CSV, line 188Original ledger status
ARCH.QUAD.01
EXTERNAL-REVIEW VALIDATION + the DEGREE-2 pattern named: (1) SEED NORMAL FORM [I] - phi0 = (|mu4|/N_fam) c3 + Omega_adm c3^|mu4| exactly: the seed is a linear seam term plus a topological fourth-order correction over all admissible fermion states (4/3 = |mu4|/N_fam, 48 = Omega_adm = N_fam dim S+, exponent 4 = |mu4|) - a structured anchor readout, not a fitted formula. (2) HYPERCHARGE SECOND MOMENT [I] computed from the explicit charge table: Tr X = 0, Tr X^2 = 120 = 5! (X = 6Y on one 16-state generation). (3) FACTORIAL SPINE [I] (named lemma): 5! = 120 = |R+(E8)| = sum of E8 exponents = Tr X^2; 240 = 2x120; 1920 = 2^4 x 5! = |W(D5)| - the same factorial moment in four projections (hypercharge, E8 roots, D5 Weyl group, Hawking-power fingerprint): an anti-numerology structure statement. (4) DEGREE-2 INVENTORY [I]: six exact degree-2 structures (Pascal closure truncates at K=2 with UNIQUE solution g=5 on 1..40; glue norms 5/4+3/4 = 2 = root norm; c3 = (1/2) x 1/(4pi) = variational half x 2d-slice Gauss-Bonnet; pair sector C(5,2) = 10 = A_Lambda; second moments; codimension-2 seam). NAMED HYPOTHESIS [P] (recorded, NOT claimed): QUADRATIC BOUNDARY LOCALITY - the seam supports only bilinear data, hence the compiler truncation K=2 is forced rather than chosen; if proven, the Pascal SELECTION (red-team Target B residual, REDTEAM.B.01/CAR.PASCAL.01, typed [A]/[P]) upgrades to [L] and the chain locality => K=2 => g=5 => 16 => D5 => E8 closes the carrier choice - the named reduction target for Target B. (5) AUDIT: 240 = 16x15 (even-code transition reading) exact but non-unique (240 = 16x5x3 established, v1), no bijection exhibited - recorded like the v91 graph reading. NOTES: 'reality compiler = {a, pi, v_geo}' is a restatement of v23+v78 (confirmed); the requested grammar-freeze rule is already implemented by v84 (pre-data freeze) + v100 (declared-grammar census)
Recorded status: Identity [I] (seed NF, moment, spine, inventory) + [P] (named locality hypothesis) + audit
Dependencies, status detail and source
Canonical status: Identity: seed NF + factorial spine + degree-2 inventory; locality hypothesis [P] named
Dependencies: ARCH.CORE.01 (anchor); CAR.PASCAL.01 / REDTEAM.B.01 (the residual it names); FLAV.MASSVOL.01; HOR.01 (1920); REG.FREEZE.01; v100
Scripts: v106_review_validation.py
Location: tfpt_1;introduction
Original CSV, line 189Original ledger status
HOR.CLOCK.02
QUANTUM-CLOCK TARGET (R1 made quantitative; nothing fitted): the Ginsparg-Perry multi-mode clock has per-l equations lambda^2+lambda+(l(l+1)-2)=0 - l=0 anchor pair {1,-2}, l=1 zero modes {0,-1}, l>=2 complex with Re=-1/2=-delta (audit). NEW CROSS-LINK [I]: the classical decay set (l=0,1) = {0,-1,-2} = -Spec(V) = -N_fam x cusp weights - the classical seam clock decays exactly on the grading that carries the transfer operator's eigenspaces (FLAV.QGEO.01/FLAV.DIAMOND.02): structural support for the relocation identification (SYNTH.INVENTORY.01 R1). THE QUANTUM TARGET [I]: transfer rates {0, Delta, 6ln3} are not weight-linear; rate(2)/rate(1) = log_{3/2}(3) = 1+log_{3/2}(2) = 2.7095; exact identity (1/3)^6 = ((2/3)^6)^{log_{3/2}3}; required bend log_{9/4}(3) = 1.35476 per weight step. COUPLING LANDSCAPE [I]: kappa = (c/24pi)(Lambda/Mbar^2), c=8: cosmological 7.6e-122 vs seam 1/(3pi) = 0.106 - the only viable regime, borderline non-perturbative; one-loop linear response cannot fix the bend (O(1) resummation or exact seam construction required). STATUS [P]: R1 = 'produce the bend log_{3/2}3 on the cusp ladder at coupling O(1/3pi)'; identification NOT closed
Recorded status: Identity [I] (tower, cross-link, target arithmetic, coupling) + Physical [P] (identification)
Dependencies, status detail and source
Canonical status: Identity: clock lives on the cusp ladder; exact bend target; [P] identification open
Dependencies: HOR.CLOCK.01; SYNTH.INVENTORY.01 (R1); FLAV.QGEO.01; FLAV.DIAMOND.02 (Spec V); FR.KOIDE.04
Scripts: v107_quantum_clock_target.py
Location: tfpt_horizon_readouts
Original CSV, line 190Original ledger status
CAR.LADDER.01
PASCAL LADDER THEOREM (Target B residual sharpened to zero slack): the closure 2^{g-1} = sum_{k<=K} C(g,k) has for every K exactly one solution g = 2K+1 (K=1..6 scanned over g=1..60; structurally: odd-g midpoint identity by binomial symmetry, even-g strict straddle around 2^{g-1} excludes all even g). EXACT EQUIVALENCE [I]: the carrier selection g=5 <=> the truncation degree K=2 - the Pascal-selection residual (CAR.PASCAL.01/REDTEAM.B.01, typed [A]/[P]) is therefore EXACTLY the one named hypothesis Quadratic Boundary Locality (ARCH.QUAD.01). NEIGHBOUR WORLDS [I]: K=1 -> g=3 (one-family world), K=2 -> g=5 (three families), K=3 -> g=7 (nine families), K=4 -> g=9 inconsistent (N_fam = 255/9 not integer). OVERDETERMINATION [I]: only K=2 also satisfies the independent rank closure g+N_fam = 8 = rank E8 (CAR.UNIQ.01/v14) - two independent selections agree. THE ONE HYPOTHESIS [P] (recorded, not claimed): QBL = the seam Calderon datum is a single two-point kernel and the carrier code is generated by the degrees it certifies (K<=2); if proven from reflection positivity the carrier choice upgrades [A]/[P] -> [L] along QBL => K=2 <=> g=5 => 16 => D5 => E8
Recorded status: Identity/Lattice [I]/[L] (ladder, equivalence, controls, overdetermination) + [P] (QBL)
Dependencies, status detail and source
Canonical status: Identity: g=5 <=> K=2 exactly; Target B residual = one hypothesis (QBL)
Dependencies: CAR.PASCAL.01; REDTEAM.B.01; ARCH.QUAD.01 (QBL named); CAR.UNIQ.01 (v14)
Scripts: v108_pascal_ladder.py
Location: tfpt_3_e8_audit_bootstrap;tfpt_1
Original CSV, line 191Original ledger status
FORM.LADDER.01
LEAN FORMALISATION of the anchor ladder and the Pascal ladder (hardening round, 2026-06-11): new modules TfptCarrier/AnchorLadder.lean and TfptCarrier/PascalLadder.lean, built and audited with the existing project (lake build 3353 jobs; scripts/audit.sh AUDIT: PASS - no sorry/axiom/unsafe, only the three standard kernel axioms). AnchorLadder: p_n(a) = 2 + 2^n for ALL n (general theorem, not a finite check); ladder atoms (3,4,6,10); p1p2p3 = 240; p4-p3 = 8; 240+8 = 248; binary ladder p_{n+1}-p_n = 2^n (general); elementary symmetric (4,5,2). PascalLadder: the odd-midpoint identity sum_{k<=K} C(2K+1,k) = 2^{2K} for ALL K (via Mathlib Nat.sum_range_choose_halfway - the ladder SOLVES side of v108 is now formal); bounded uniqueness for the carrier case K=2 on 1<=g<=40 (kernel-decidable); carrier world (5,16,3,8); neighbour worlds (K=1 one-family, K=3 nine-family, K=4 inconsistent 9 ndvd 255). Strengthens the [F] layer of v23/v106 (ladder) and v108 (Pascal ladder); the unbounded K=2 uniqueness remains covered by CarrierRankUniqueness (division-free form)
Recorded status: Formal [F] (Lean kernel; no extra axioms)
Dependencies, status detail and source
Canonical status: Formal: anchor ladder general; Pascal ladder solves-side general + K=2 bounded uniqueness
Dependencies: ARCH.CORE.01; CAR.LADDER.01; FORM.P2.02
Scripts: lean4-carrier-rigidity (AnchorLadder.lean, PascalLadder.lean)
Location: tfpt_1;tfpt_3_e8_audit_bootstrap
Original CSV, line 192Original ledger status
CAR.PAIR.01
SHEET-PAIRING LEMMA (the first exact representation-theoretic anchor of the QBL programme; connects red-team Target B to the sheet Z2): character-exact weight-multiset results from the D5 spinor weights (+-1/2)^5 alone - (1) NO SCALAR WITHIN A SHEET: zero-weight multiplicity of S+xS+ (and S-xS-) is 0, because the odd slot count g=5 flips the sign parity of -w (a parity theorem of the five-slot code): there is no invariant bilinear pairing inside one chirality. (2) THE SCALAR LIVES ACROSS THE SHEETS: S+xS- has zero-weight multiplicity 16 = 1+5+10 (the Pascal triple) and equals exactly, as a weight multiset, the even-form tower Lambda^0 + Lambda^2 + Lambda^4 (256 = 1+45+210) with zero-mode grading (1,5,10) = the carrier code (Lambda^0,Lambda^1,Lambda^2)(C^5). (3) SHEET-DIAGONAL = ODD FORMS: (S+xS+) u (S-xS-) = 2Lambda^1 + 2Lambda^3 + Lambda^5 exactly (512 = 20+240+252): within-sheet pairings are odd-form-valued, never scalar. (4) the scalar-bearing tower tops at Lambda^{2K} with K=2 - bilinear seam data reach exactly the Pascal-ladder degree (CAR.LADDER.01). (5) QBL READING [P] (recorded, not claimed): the seam's single scalar two-point kernel is necessarily a SHEET PAIRING (chirality-off-diagonal, the same Z2 as GATE.METRIC.07 / FLAV.SHEET.01-03); the remaining step is to show the Calderon kernel supplies exactly this pairing and nothing beyond - then QBL => K=2 <=> g=5 closes the carrier choice
Recorded status: Identity [I] (character-exact multiset identities) + Physical [P] (QBL reading)
Dependencies, status detail and source
Canonical status: Identity: scalar pairing only across sheets; even tower tops at 2K; QBL anchored
Dependencies: CAR.LADDER.01; ARCH.QUAD.01 (QBL); GATE.METRIC.07 (sheet Z2); FLAV.SHEET.01-03; CAR.PASCAL.01
Scripts: v109_sheet_pairing.py
Location: tfpt_1
Original CSV, line 193Original ledger status
CAR.PAIR.02
CALDERON-SHEET SELECTION THEOREM (which Calderon involutions certify a scalar kernel; the v109 follow-up): on the carrier H = S+ (+) S- the certified bilinear data of an involution eps (eps^2 = 1) are the matrix elements <f, eps g>; the v109 singlet counts per sheet block (0, 0, 1, 1) give the exact selection statement - (1) SELECTION THEOREM [I] (finite model): a sheet-ODD involution (swapping S+ <-> S-) certifies EXACTLY 1+1 = 2 = |Z2| invariant scalar kernels (one per orientation), a sheet-EVEN involution certifies NONE: 'a scalar two-point datum exists IFF eps is sheet-odd'. (2) THE TWO KERNELS = THE GLUE AMBIGUITY [I]: the kernel count 2 = |Z2| matches exactly the two Lagrangian glues (GLUE.LAGR.01, swapped by single spinor conjugation) - the Calderon scalar channel carries precisely the glue ambiguity, resolved by the same sheet choice. (3) LADDER GENERICITY [I] (anti-overclaim control): for g = 3, 5, 7 the within-sheet zero-weight count is 0 and the cross count is 2^{g-1}; sheet-oddness forces the half-spinor relation K = (g-1)/2, NOT the value g = 5 - the g-selection stays with the independent rank-8/integrality closure (CAR.RANK / CAR.LADDER.01). (4) QBL RESIDUE SPLIT [P] (recorded, not claimed): (a) INTERFACE 'the seam Calderon involution is sheet-odd' - structurally natural, because the one-sided collar / double-cover deck is the SAME |Z2| that halves c3 = 1/(2 x 4pi) (exchanging cover sides is sheet-odd by construction); (b) ANALYTIC CORE 'the two-point kernel certifies only slot-degrees <= 2' - the genuine locality statement. Two named parts; proving both closes QBL => K=2 <=> g=5
Recorded status: Identity [I] (finite-model selection theorem + ladder control) + Physical [P] (residue typing)
Dependencies, status detail and source
Canonical status: Identity: scalar kernel exists iff involution is sheet-odd; 2 = |Z2| kernels = glue ambiguity; QBL residue split into interface + analytic core
Dependencies: CAR.PAIR.01; CAR.LADDER.01; ARCH.QUAD.01 (QBL); GLUE.LAGR.01 (two glues); GATE.METRIC.07 (sheet Z2)
Scripts: v110_calderon_sheet.py
Location: tfpt_1
Original CSV, line 194Original ledger status
CAR.QTRANS.01
QUADRATIC-TRANSPORT THEOREM (the transport half of the QBL analytic core becomes a theorem): grade seam transport by Clifford degree in the 10 field operators on the 5-slot Fock space (S = Lambda^*(C^5), 32-dim, S+ = 16 code states; integer Jordan-Wigner model, spanning claims via full-rank certificates mod p = 1000003, valid over Q) - (1) PARITY [exact block-zero]: all 10 linear words are sheet-ODD (map S+ -> S-), all 45 quadratic words are sheet-EVEN: code-preserving transport has even Clifford degree (the same Z2 as CAR.PAIR.01/02). (2) MINIMALITY: sheet-even words of degree <= 1 are the scalars alone (dim 1 < 256 = dim End(S+)): degree 2 is the first nontrivial code-preserving grade. (3) GENERATION: the 45 quadratic words (= dim so(10) = the Lambda^2 term of the certified tower 1+45+210) generate the ENTIRE code from the vacuum at word length <= 2. (4) COMPLETENESS (Burnside realised explicitly): products of length <= 2 of quadratics span the FULL operator algebra End(S+) = 256 - every code operation whatsoever is a word in pair transport; all higher even-degree elements (e.g. the 210 quartics) are redundant. CONSEQUENCE: THE TRANSPORT DEGREE IS EXACTLY 2 - degree <= 1 generates nothing, degree 2 generates everything; a theorem, not a hypothesis. (5) LADDER GENERICITY (anti-overclaim): the g=3 world behaves identically (15 quadratics = dim so(6) -> End = 16) - the theorem selects the DEGREE, not the rank g; g-selection stays with Pascal closure + rank-8 (CAR.LADDER.01/CAR.RANK). (6) CHANNEL READING: certified cross-sheet tower 256 = 1 + 45 + 210 = norm + transport generators + pair sector. (7) RESIDUE UPDATE [P]: QBL's remaining content = two interface statements - (a) seam Calderon involution sheet-odd (CAR.PAIR.02a); (b') certified STATE inventory = the <= 2-slot tower (Pascal-closure side, CAR.LADDER.01); nothing about transport remains hypothetical
Recorded status: Identity [I] (exact finite theorem; mod-p certificates valid over Q) + Physical [P] (residue typing)
Dependencies, status detail and source
Canonical status: Theorem: transport degree exactly 2 (minimal complete grade); QBL residue reduced to two interface statements
Dependencies: CAR.PAIR.01; CAR.PAIR.02; CAR.LADDER.01; ARCH.QUAD.01 (QBL); CAR.RANK
Scripts: v111_quadratic_transport.py
Location: tfpt_1
Original CSV, line 195Original ledger status
CAR.COUNT.01
SELF-COUNTING CHANNEL (the Pascal closure is an IDENTITY of the certified channel, not an extra requirement; closes the state half of the QBL analytic core at the structural level): (1) CANONICAL BIJECTION [I] - for odd g negation w -> -w maps the S+ weights bijectively into the opposite sheet (the CAR.PAIR.01 parity stated as a bijection), so the Cartan-neutral kernels of the certified channel S+xS- are exactly the pairs (w,-w), ONE PER CODE STATE: # neutral certified kernels = dim S+ = 2^{g-1} exactly (4, 16, 64 for g = 3, 5, 7) - the channel counts the code. (2) PASCAL PARTITION [I]: the same neutral set graded by pair-degree m (zero modes of Lambda^{2m}(C^{2g})) has sizes C(g,m) for m = 0..K = (g-1)/2; g=5 -> (1,5,10). (3) THE CLOSURE IS AN IDENTITY [I]: two countings of one set give 2^{g-1} = sum_{m<=K} C(g,m), symbolically verified for all odd g = 3..13 - the closure CONDITION of CAR.LADDER.01 is the channel counting itself. (4) HODGE FOLD [I]: the code's minus-sign grading C(g,2j) equals the folded binomial C(g, min(2j, g-2j)) with min(2j,g-2j) <= K - every code sector appears as a pair-degree <= K sector (g=5: code (1,10,5) vs channel (1,5,10), same multiset, folded order). (5) LADDER GENERICITY: the identity holds for every odd g and carries NO g-selection - the selection stays with rank-8 (g + N_fam = 8, CAR.RANK/v14) and ladder integrality (CAR.LADDER.01). (6) RESIDUE RE-TYPE [P] (recorded, not claimed): QBL clause (b') loses its closure burden - given the sheet-odd kernel (CAR.PAIR.02a) the channel automatically contains exactly one neutral kernel per code state at pair-degree <= K, so (b') is the definition of the channel; the remaining physical input is 'the seam certifies through a single scalar 2-point kernel' (for the established free c=8 seam net Wick extends the single kernel to the entire even tower by determinants); the carrier selection itself is carried by rank-8 + integrality - QBL is the structural consistency frame, no longer a missing selector
Recorded status: Identity [I] (bijection + exact multiset gradings + symbolic binomial identity) + Physical [P] (residue re-type)
Dependencies, status detail and source
Canonical status: Identity: Pascal closure = two countings of the channel's neutral set; one kernel per code state; QBL residue = single 2-point-kernel input
Dependencies: CAR.PAIR.01; CAR.PAIR.02; CAR.QTRANS.01; CAR.LADDER.01; CAR.RANK; ARCH.QUAD.01 (QBL)
Scripts: v112_selfcounting_channel.py
Location: tfpt_1
Original CSV, line 196Original ledger status
CAR.QFREE.01
ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise; anchors the carrier choice to the Gate-A objects): (1) MAJORANA BOOKKEEPING [I] - level-1 central charges c(D5)_1 = 45/9 = 5 = g_car, c(A3)_1 = 15/5 = 3 = N_fam, c(SO16)_1 = 120/15 = 8, c(E8)_1 = 248/31 = 8; the carrier net (D5)_1 x (A3)_1 = SO(10)_1 x SO(6)_1 = 10 + 6 = 16 FREE MAJORANA FERMIONS with c = 16/2 = 8; the whole extension tower carrier(mu=16) -> SO(16)_1(mu=4) -> E8_1(mu=1) carries the SAME 16 fermions, only the certified glue grows (index steps 2 x 2 = 4 = |mu_4|, GATE.METRIC.06/07). (2) WICK/PFAFFIAN [I] (exact, 10-Majorana Jordan-Wigner model): ALL 210 vacuum 4-point functions AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel - one kernel determines all correlations; quasi-freeness realised exactly. (3) THE KERNEL IS A CALDERON INVOLUTION OF RANK g [I]: M = I + iA with A integer antisymmetric, A^2 = -I; P = M/2 is a projection with rank P = 5 = g_car = c(D5)_1; eps = iA is an involution; at seam level (16 Majoranas) the rank is 8 = rank E8 - THE CENTRAL CHARGE IS THE RANK OF THE ONE KERNEL (5 carrier block, 8 seam hull). (4) ONE KERNEL <=> ONE STATE [I]: the joint kernel of the five annihilators is exactly 1-dimensional - the polarization fixes the vacuum uniquely; kernel => state => (Wick) all correlations. (5) PREMISE MERGE [P] (recorded, not claimed): QBL's remaining input 'single scalar 2-point kernel' = 'the seam state is quasi-free' = the defining property of the free-fermion net the R2 gate already posits (Gate-A (H') index-4 extension, GATE.METRIC.06); QBL adds NO assumption beyond R2; upgrade contract: R2 closes => the carrier choice closes [L] along free net => one kernel => sheet-odd (CAR.PAIR.02) => self-counting tower (CAR.PAIR.01/CAR.COUNT.01) => complete transport (CAR.QTRANS.01) => carrier; gate typing [P]/[A] unchanged
Recorded status: Identity [I] (exact Pfaffian/Wick + polarization theorems + bookkeeping) + Physical [P] (premise merge)
Dependencies, status detail and source
Canonical status: Identity: one quasi-free kernel determines the whole net (rank = c); QBL input = R2 premise; upgrade contract R2 => carrier [L]
Dependencies: CAR.PAIR.02; CAR.COUNT.01; CAR.QTRANS.01; ARCH.QUAD.01 (QBL); GATE.METRIC.03-07 (Gate A); CAR.LADDER.01
Scripts: v113_quasifree_kernel.py
Location: tfpt_1; tfpt_research_contracts
Original CSV, line 197Original ledger status
GATE.UWALL.06
TORSION NORMAL FORM + THE DELTA = 1/2 THEOREM (executes the GATE.UWALL.05 'genericity future work'; the distinguished lepton transport value delta = 1/2 stops being a point observation): (1) FLATNESS = mu4 TORSION [I, symbolic generic M] - prod_k U^k M U^{-k} = (MU)^4 exactly, so the Z4-family flatness constraint of the (U_wall) bundle IS the torsion statement 'T = MU is a fourth root of unity': the mu_4 atom appears as the ORDER of the twisted cusp generator. (2) DELTA = 1/2 THEOREM [I, both directions]: on the involutive branch (T^2 = 1) T is a Hermitian reflection 2vv^dag - 1 and the cusp trace condition 2v^dag U^{-1}v = 1 splits exactly into |v1|^2 = 1/2 (real part) + |v2| = |v3| (imaginary part), forcing diag M = (0, i/2, -i/2) with spec M = {1, w, w^2} AUTOMATIC (unitary + tr 0 + det 1 => char poly lam^3 - 1): delta = |M_22| = 1/2 EXACTLY AND CONSTANTLY on the whole 2-parameter branch - the value v20 used by hand and v40/v41 observed at the explicit point is a mu4-torsion identity. (3) REFLECTION LEMMA [I]: the D4 reflection forces diag M = (r, z, zbar) with r real and Re z = -r/2 - the D4 diagonal freedom is ONE real parameter, delta = 1/2 <=> r = 0. (4) BRANCH CENSUS [N, seeded scipy sampling, Python-only]: the full D4-fixed flat cusp locus realises only tr(MU) in {1, -1}; the involutive branch has diagonal CONSTANT (0, 1/2, 1/2) to 1e-15 across all samples; the {1, i, -i} branch has d1 varying over [0, 1] and the explicit v33/v40 point sits in its d1 = 0 slice - the same delta value. (5) RESIDUE [P] (recorded): whether the anchor splitting type O(-2)+O(-1)^2 (Mehta-Seshadri side) forces the d1 = 0 slice or selects the involutive branch is the remaining question; delta = 1/2 itself is no longer open
Recorded status: Identity [I] (symbolic theorems) + Numerical [N] (branch census) + Physical [P] (residue)
Dependencies, status detail and source
Canonical status: Theorem: delta = 1/2 is a mu4-torsion identity on the involutive branch; flatness = (MU)^4 = 1 normal form; residue = bundle-side branch selection
Dependencies: GATE.UWALL.04; GATE.UWALL.05; FLAV.DELTA.01; v20; v30; v33
Scripts: v114_torsion_delta.py
Location: tfpt_research_contracts
Original CSV, line 198Original ledger status
GATE.UWALL.07
THE ANCHOR PINS THE RESIDUE (exact normal form for the U_wall flat-bundle residue; answers the GATE.UWALL.06 branch question): (1) MU4-AVERAGE LEMMA [I, symbolic generic X] - sum_k U^k X U^{-k} = 4 diag(X): mu_4 conjugation-averaging is the diagonal projection, so the exponents at infinity are 4 diag(A0) and the anchor splitting O(-2)+O(-1)^2 holds IFF diag A0 = (2,1,1)/4 = a/|mu_4| - the residue diagonal IS the anchor over mu_4 (the v33 diagonal was forced, not chosen). (2) THE (8,0,5)/144 LEMMA [I]: anchor diagonal + cusp spectrum {0,1,2}/N_fam pin the off-diagonal weight sum to 13/144; with a13 = 0 the det = 0 condition solves UNIQUELY to (|a12|^2, |a23|^2) = (8, 5)/144 - numerators (rank E8, g_car), denominator (|mu_4| N_fam)^2 = 144, total 13 = Delta_Q = 2p_2(a)+1 (the quark denominator 117 = 9x13). (3) EXACT RESIDUE NORMAL FORM [I]: A0* = [[1/2, sqrt2/6, 0],[sqrt2/6, 1/4, sqrt5/12],[0, sqrt5/12, 1/4]] has char poly lam(lam-1/3)(lam-2/3) exactly. (4) A0* IS THE RIEMANN-HILBERT SOLUTION [N]: big-circle monodromy trivial to 1.6e-10, prod M_k = 1, unitarised |diag M~_0| = (0, 1/2, 1/2), tr(M~_0 U) = 1 - the v33/v40 numerical point is gauge-equivalent to this exact matrix (a12/a23 phases = diagonal gauge). (5) THE ANCHOR FORCES THE d1 = 0 SLICE [N]: multi-seed RH scan over the anchor-pinned spectral manifold lands at every flat solution on the SAME gauge orbit with |diag M~_0| = (0, 1/2, 1/2) - combined with GATE.UWALL.06 the whole harmonic diagonal is anchor + torsion forced; delta = 1/2 needs no selection. (6) RESIDUE [P]: a13 = 0 + gauge-orbit uniqueness numerical (one component across seeds); promotion to [I]/[L] via Groebner on the RH constraints = the remaining U_wall point-selection step
Recorded status: Identity [I] (mu4-average + (8 0 5)/144 + exact normal form) + Numerical [N] (RH verification + uniqueness scan) + Physical [P] (residue)
Dependencies, status detail and source
Canonical status: Exact residue normal form A0* (diag = anchor/mu4 spectrum = cusp weights off-weights = (8 0 5)/144); anchor forces d1 = 0; residue = Groebner promotion
Dependencies: GATE.UWALL.06; GATE.UWALL.04; v33; v40; CONTRACT.U.01
Scripts: v115_anchor_residue.py
Location: tfpt_research_contracts
Original CSV, line 199Original ledger status
GATE.UWALL.08
RESONANCE THEOREM (the GATE.UWALL.07 [N] findings promoted to [I] by a LINEAR computation - the anticipated Groebner step turned out unnecessary): (1) TWISTED-AVERAGE LEMMA [I, symbolic generic A0]: at infinity the equivariant Fuchsian system reads dY/dw = -(1/w)(B0 + B1 w + ...)Y with B_m = sum_k i^{km} U^k A0 U^{-k}; the twisted mu_4 averages collapse to B0 = 4 diag(A0) and B1 = 4 a12 E_12 + 4 conj(a13) E_31 - only the eigenvalue-ratio -i cells survive. (2) RESONANCE THEOREM [I]: the anchor exponents diag(2,1,1) have resonance gap 1; the level-1 formal-gauge equation (1 - ad R0)H1 = R1 is singular exactly on the cells {(2,1),(3,1)}, where the obstruction entries of B1 are (0, 4 conj(a13)); all levels k >= 2 are non-resonant and the formal monodromy e^{-2 pi i diag(2,1,1)} = 1, hence M_inf = 1 <=> a13 = 0 - the transcendental Riemann-Hilbert condition collapses to ONE linear equation. (3) UNIQUENESS COROLLARY [I]: a13 = 0 + the (8,0,5)/144 moduli (GATE.UWALL.07) + phases = diagonal gauge (commutes with U, fixes the diagonal, rotates arg a12 and arg a23 freely) => the flat anchor locus is EXACTLY ONE GAUGE ORBIT = the exact A0*; within the mu_4-equivariant anchor class the U_wall bundle datum is ALGEBRAICALLY unique. (4) FALSIFICATION CONTROL [N]: ||M_inf - 1|| = 1.6e-10 at a13 = 0 vs 0.17 / 0.43 at a13 = 0.02 / 0.05 - the obstruction is sharp (~8.5 |a13|). (5) HONEST SCOPE [P] (recorded): the equivariant ansatz A_k = U^k A0 U^{-k} is the established D4 selector input (v19/v30); the residue side is now [I]; the holonomy values (harmonic diagonal (0, 1/2, 1/2)) remain [N] - transcendental monodromy of an exact system
Recorded status: Identity [I] (twisted average + resonance theorem + uniqueness) + Numerical [N] (sharpness control) + Physical [P] (scope)
Dependencies, status detail and source
Canonical status: Theorem: M_inf = 1 <=> a13 = 0 (resonance obstruction); flat anchor locus = one gauge orbit = exact A0*; U_wall bundle datum algebraically unique
Dependencies: GATE.UWALL.07; GATE.UWALL.06; v19; v30; CONTRACT.U.01
Scripts: v116_resonance_uniqueness.py
Location: tfpt_research_contracts
Original CSV, line 200Original ledger status
GATE.UWALL.09
THE MONODROMY IS THE WEYL GROUP OF A3 (the U_wall holonomy is an EXACT 24-element representation; the harmonic diagonal becomes a theorem): (1) THE EXACT MONODROMY [I]: M0 = [[0, -(1+i)/2, (1-i)/2], [-(1+i)/2, -i/2, -1/2], [(1-i)/2, -1/2, i/2]] (entries in (1/2)Z[i]) is unitary with det 1, tr 0, char poly lam^3 - 1 (the cusp class {1,w,w^2} EXACT), M0^3 = 1, and diag M0 = (0, -i/2, +i/2) - d1 = 0 AND delta = 1/2 are exact matrix entries: the v20 hand value, the v40/v41 observation, the GATE.UWALL.06 torsion value and the GATE.UWALL.07 anchor slice meet in ONE exact matrix. (2) TORSION/FLATNESS [I]: (M0 U)^4 = 1 with tr(M0 U) = 1 (the {1,i,-i} branch, d1 = 0 slice - exactly where GATE.UWALL.06/07 located the physical point) and prod_k U^k M0 U^{-k} = 1 exactly. (3) THE GROUP IS W(A3) = S4 [I]: exact enumeration of <U, M0> gives order 24 with order statistics (1, 9, 8, 6) and character values (3, -1, 0, 1) - uniquely S4 in its standard x sign representation = the (twisted) reflection representation of the WEYL GROUP OF THE FAMILY LATTICE A3: the flavor-wall monodromy realises the A3 factor of the glue D5 + A3 + mu4 as its Weyl group; U = image of a 4-cycle (the mu_4 deck), M0 = a 3-cycle (the family rotation), 24 = |W(A3)| = 4!. (4) IDENTIFICATION [N]: the unitarised ODE monodromy of the exact A0* system equals the exact M0 to 3.5e-10 and the invariant form H is U-invariant to 2.5e-11 (the harmonic frame preserves the equivariance). (5) STATUS [P] (recorded): holonomy VALUES are now [I] (exact properties of the W(A3) representation); only the identification with the analytic monodromy of A0* stays [N] (ODE matching); the delta thread v20 -> v40/v41 -> v114 -> v115 -> v117 is closed end to end
Recorded status: Identity [I] (exact matrix + exact group enumeration) + Numerical [N] (ODE identification) + Physical [P] (status)
Dependencies, status detail and source
Canonical status: Theorem: U_wall monodromy group = W(A3) = S4 (order 24 exact); diag M0 = (0 -i/2 i/2) exact - delta = 1/2 and d1 = 0 are matrix entries; only ODE identification stays [N]
Dependencies: GATE.UWALL.08; GATE.UWALL.07; GATE.UWALL.06; E8.GLU.01 (A3 factor); CONTRACT.U.01
Scripts: v117_monodromy_weyl_a3.py
Location: tfpt_research_contracts
Original CSV, line 201Original ledger status
FLAV.H2.02
THE HEXAGON IS THE SIGN-TWISTED FAMILY SPECTRUM (first exact piece of the H2 dictionary; the v20 lepton coefficients are resolvent determinants of the exact W(A3) monodromy GATE.UWALL.09): (1) SIGN-TWIST LEMMA [I]: -M0 has order 6 ((-M0)^3 = -1) and spec(M0) u spec(-M0) = mu_6 - the 6-site hypercharge hexagon spectrum IS the family monodromy spectrum together with its sheet twist, Z6 = Z2 x Z3 realised as (-1) x <M0>; the v20 hexagon denominators 5/4 - cos(r pi/3) equal |1 - zeta_6^r/2|^2, the eigen-denominators of the two family resolvents (1 -+ M0/2)^{-1}. (2) CYCLOTOMIC DETERMINANT [I]: det(1 - t M0) = 1 - t^3 = (1-t) Phi_3(t) (the N_fam cyclotomic) => det(1 - M0/2) = 7/8 and det(1 + M0/2) = 9/8. (3) LEPTON COEFFICIENTS = RESOLVENT DETERMINANTS [I]: c_e = |mu_4|/(2 det-) = 16/7, c_mu = N_fam/(2 det+) = 4/3, c_tau = |mu_4| det-/N_fam = 7/6, and v20's product rule = |mu_4|/det+ = 32/9 - the lepton denominators 7 and 9 ARE the two family-resolvent determinants (x 2^3), and delta = 1/2 = |(M0)_22| is supplied by the monodromy matrix itself; the e/mu/tau LEG assignment (residues r, windings w) remains v20's established input - nothing re-fished. (4) SHEET-EXTENDED GROUP [I]: <U, M0, -1> has order 48 = Omega_adm = N_fam x dim S+ (the seed quartic coefficient, ARCH.QUAD.01) = |S4 x Z2| (exact enumeration; audit cross-link). (5) RESIDUE [P] (recorded): the dictionary's VALUES are exact; its ADDRESS TABLE (which hexagon site each fermion occupies; the quark-sector composition) remains open
Recorded status: Identity [I] (exact spectral + determinant identities + group enumeration) + Physical [P] (address table)
Dependencies, status detail and source
Canonical status: Identity: hexagon = spec(M0) u spec(-M0); lepton 7 and 9 = det(1 -+ M0/2) x 8; product rule = mu4/det+; H2 values exact - address table open
Dependencies: GATE.UWALL.09; FLAV.H2.01; v20 (leg assignment); ARCH.QUAD.01 (Omega_adm); E8.GLU.01
Scripts: v118_hexagon_family_dictionary.py
Location: tfpt_research_contracts; tfpt_2
Original CSV, line 202Original ledger status
ARCH.TRIAD.01
SECOND EXTERNAL-REVIEW VALIDATION (2026-06-11b): the anchor ratio triad, the 121 audit lemma and the normal-form micro-identities, all exact: (1) MICRO-IDENTITIES [I]: Omega_adm = 2 p1 p2 = 48; 10 b1 = 1 + p1 p3 = 41; Delta_Y = e2^2 = p0^2 + 2 rank E8 = 25; h(E8) = e3 p0 e2 = 30; rank E8 = p0 + e2 = 8; |R(E8)| = p1 p2 p3 = 240; dim E8 = 240 + (p4 - p3) = 248. (2) ANCHOR RATIO TRIAD [I] (named lemma): the three elementary symmetric values of the anchor normalised by the family count - e3/p0 = 2/3 (the Koide branch / sheet ratio, cf SYNTH.INVENTORY.01 seven appearances), e1/p0 = 4/3 (the seed gain |mu_4|/N_fam, ARCH.QUAD.01), e2/p0 = 5/3 (the carrier branch: the canonical flow's critical points are EXACTLY (2,5) = (e3,e2), FR.KOIDE.06, inflection 7/2 = (e3+e2)/2) - the recurring fractions 2/3, 4/3, 5/3 are the three normalised anchor coefficients, not scattered numbers. (3) THE 121 AUDIT LEMMA [I, typed AUDIT not load-bearing]: (1+a)^T R (1+a) = 121 = 11^2 = ||Pl(K)||_1^2 = (p3+1)^2 with the established residue operator R (det 8, SNF (1,1,8)) - the quark-ratio 11 (c_u/c_d = 5x11/(9x13)) appears a SECOND independent time as the quadratic anchor norm of R; sensitivity control: the 3 orderings of h = (2,2,3) give {105, 121, 135}, only the canonical anchor ordering yields 121; bonus checksums 1^T R 1 = 22 = 2x11 (entry sum) and a^T R a = 40 = p1 p3 = 10b1 - 1; the oriented Plucker mechanism (FLAV.KQ.01/v42/v49) remains the derivation. (4) FLAVOR SURFACE claim = established FLAV.DIAMOND.01/02 (re-verified, presentational). (5) BOOKKEEPING: mu4 projection = GATE.UWALL.07/08, triptych = HOR.CLOCK.01/SYNTH.INVENTORY.01, interior-free = CAR.QFREE.01 (all closed); anchor-first presentation recorded as editorial item
Recorded status: Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)
Dependencies, status detail and source
Canonical status: Identity: anchor ratio triad (2/3 4/3 5/3) = e/p0; 121 = anchor norm of R (audit); micro-identities exact
Dependencies: ARCH.QUAD.01; FLAV.KQ.01; FLAV.DIAMOND.01-02; FR.KOIDE.06; SYNTH.INVENTORY.01
Scripts: v119_review_validation_2.py
Location: introduction; tfpt_research_contracts
Original CSV, line 203Original ledger status
FLAV.H2.03
THE ADDRESS TABLE (the open FLAV.H2.02 item structured; exact arithmetic on FROZEN v18/v20 integers): (1) THE LEPTON WORDS ARE THE COMPILER ATOMS [I]: (L_e, L_mu, L_tau) = (8, 5, 3) = (rank E8, g_car, N_fam) = (p0+e2, e2, p0), in mass order (longest word = lightest lepton). (2) ADDRESSES = EUCLIDEAN DIVISION BY THE HEXAGON [I]: (r, w) = L divmod p2 with p2 = 6 = |R+(A3)| itself an atom: e -> (2,1), mu -> (5,0), tau -> (3,0); sum r = 10 = p3 = A_Lambda; sum L = 16 = dim S+ = 2^{g-1}. (3) SHEET PARITY [I] (the FLAV.H2.02 dictionary applied): e sits on the untwisted sheet (omega in spec M0), mu and tau on the twisted sheet (-omega, -1 in spec(-M0)); the anchor lepton tau occupies the unique REAL twisted eigenvalue -1 - exactly the site where v20's product rule replaces the resolvent. (4) QUARK SUM RULES [I] (frozen v18 words u,d,s,c,b,t = 7,7,5,3,2,0): up-type sum = 10 = p3; down-type sum = 14 = p1 + p3; ALL QUARKS = 24 = |W(A3)| (the flavor-wall monodromy group order, GATE.UWALL.09); ALL NINE CHARGED FERMIONS = 40 = p1 p3 = a^T R a (ARCH.TRIAD.01 bonus checksum); quark sum r = 12 = 2 p2, sum w = 2 = |Z2|; the top sits at the vacuum site (0,0) (zero word length, no suppression - the established ladder anchor). (5) RESIDUE [P] (recorded): five independent closures (16, 10, 14, 24, 40 - all anchor atoms or today's group orders) constrain the address map, but the per-fermion assignment remains the v18/v20 input; deriving it is the remaining H2 content. FIREWALL: all integers were frozen before today's readings - no degrees of freedom spent
Recorded status: Identity [I] (exact arithmetic on frozen integers) + Physical [P] (per-fermion derivation)
Dependencies, status detail and source
Canonical status: Identity: lepton words = (rank g N); addresses = divmod hexagon; quark sums = (p3 p1+p3 |W(A3)| p1p3); assignment derivation open
Dependencies: FLAV.H2.02; GATE.UWALL.09; ARCH.TRIAD.01; v18 (quark words); v20 (lepton words)
Scripts: v120_address_table.py
Location: tfpt_research_contracts
Original CSV, line 204Original ledger status
FLAV.H2.04
THE ADDRESS TABLE IS PINNED (the FLAV.H2.03 per-fermion item closed at the information level; exact census theorem): (1) THE WORD TABLE IS THE RESIDUE OPERATOR [I]: the established identity L = R + 2U (FLAV.DIAMOND.02, U = winding axis N_fam 1 e_1^T) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 word lengths verbatim; the addresses are R's entries plus one hexagon turn for generation 1, and R's first column is THE ANCHOR a = (1,1,2) - the first-generation residues are the anchor components. (2) THE MARGINS ARE ATOMS [I]: row sums of R = (4, 8, 10) = (e1, rank E8, p3); column sums = (4, 13, 5) = (e1, Delta_Q, g_car); total 22 = 2x11 (ARCH.TRIAD.01). (3) PINNING THEOREM [I, exact census]: among ALL 3x3 matrices with entries in the hexagon {0..5}, exactly 17 have the atom margins, and exactly ONE has det = 8 = rank E8 - and it is R (the same one is the unique one with SNF (1,1,8); all 17 determinants are distinct, 8 occurs once - control computed explicitly). The per-fermion assignment table carries ZERO residual information beyond the atom margins and the rank determinant. (4) within-sector assignment = the established transport reading (m ~ lambda_Y^L, longer word = lighter fermion). (5) RESIDUE [P] (recorded): the open H2 item shrinks from 'derive 9 per-fermion integers' to 'derive the six atom margins + det = rank'. FIREWALL: R, L and all word lengths were frozen in v4/v18/v20/v71 long before today's census - no degrees of freedom spent
Recorded status: Identity [I] (exact census/uniqueness theorem on frozen operators) + Physical [P] (margins)
Dependencies, status detail and source
Canonical status: Theorem: R = unique hexagon matrix with atom margins + det 8; address table = R + first-generation winding; H2 residue = the margins
Dependencies: FLAV.H2.03; FLAV.DIAMOND.02 (L = R + 2U); FLAV.H2.01; ARCH.TRIAD.01; v18; v20; v71
Scripts: v121_address_pinning.py
Location: tfpt_research_contracts
Original CSV, line 205Original ledger status
FLAV.H2.05
THE MARGINS ARE THEOREMS (the FLAV.H2.04 residue closed: the established frozen selectors pin R uniquely - the atom margins lose their input status): THREE ESTABLISHED SELECTORS, all frozen pre-v120 - (S1) the D4 annihilator n = (5,-9,6) with n^T R = (8,0,0) (FLAV.DIAMOND.01/tfpt_2: n kills the unchanged (c2,c3) plane; n.a = 8); (S2) det R = 8 = rank E8 (v71 determinant quartet (3,4,8,20), product 1920 = |W(D5)|); (S3) det K = 4 = |mu_4| with K = R + Q Sigma (the diamond); plus the definitional hexagon range {0..5}. (1) CENSUS [I]: hexagon columns with n.col = 8: exactly 4, with n.col = 0: exactly 4 => 64 (S1)-candidates; (S2) leaves 12; (S3) leaves EXACTLY ONE - and it is R. (2) COROLLARY [I]: the atom margins (4,8,10)/(4,13,5), the anchor column R e_1 = a = (1,1,2), and all FLAV.H2.03/04 sum rules (16, 10, 14, 24, 40) are CONSEQUENCES of (S1)-(S3) - input status revoked. (3) BONUS LEMMA [I]: on the (S1)+(S2) locus det(M + 2U) = 20 = det L holds for ALL 12 candidates - the fourth quartet determinant is NOT an independent selector but a consequence: the quartet (3,4,8,20) carries redundancy, the compiler's overdetermination pattern. (4) RESIDUE [P] (recorded): H2 reduces to the establishment of the selectors themselves (n and the diamond determinants - pre-existing inventoried objects); the address question introduces NO new residual class. FIREWALL: n, quartet, R, L, words frozen in v4/v18/v20/v71/v94 - nothing fitted
Recorded status: Identity [I] (exact census on frozen selectors) + Physical [P] (selector establishment)
Dependencies, status detail and source
Canonical status: Theorem: established selectors (n-annihilator + det R = 8 + det K = 4) pin R uniquely; margins + anchor column + sum rules = consequences; det L = 20 automatic
Dependencies: FLAV.H2.04; FLAV.DIAMOND.01-02; v71 (quartet); v94 (annihilator); CONTRACT.U.01
Scripts: v122_margin_theorem.py
Location: tfpt_research_contracts
Original CSV, line 206