Original 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.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 646Original ledger status
QGEO.KLEINRP.01
Parafermionic Klein-twist reflection positivity of the Z3 twist sector (one module, 17 checks, ~30 s; discovery probe parafermion_klein_rp_probe.py 17/17, verdict KLEIN-RP-POSITIVE). The named open item of QGEO.TWISTOPE.01 (the naive antiunitary Z3 pairing fails positivity N-stably at -4.5e-3) is RESOLVED at the lattice OS level: the positivity-carrying pairing composes the mirror with CHARGE CONJUGATION -- Theta_K(sigma_k(x)) = eta_k sigma_{3-k}(r(x)) with omega^{k q} zero-mode phases (q = half-position mod 3). MACHINERY [E]: the dressed-string reality identity (particle-hole I - C = DCD at half filling) makes every Klein Gram entry EXACTLY real (1.4e-15 over 40 mixed configs); for lam = pi the naive and Klein pairings coincide identically (the v639 Z2 control could not distinguish them); the naive glue pins a spurious 2 lam = 4 pi/3 defect on the axis bond, the Klein glue is defect-free. POSITIVITY [E-float, central]: every charged Klein block is real symmetric AND PSD (worst min/max 2.9e-12), k = 1, 2, BOTH diameter axes, N = 48/96/192/384 (N-stable, no drift); charge blocks coincide exactly. UNIQUENESS [E]: over the 36 pairs (eta_1, eta_2) in {+-1, +-w, +-w^2}^2 exactly ONE satisfies consistency + Hermiticity + PSD: eta = (1, 1); no phase rescues the naive pairing (the fix is structural). MUST-FAIL [E]: the naive pairing reproduces the v639 violation (-4.4e-3..-4.5e-3 N-stable); eta = -1 loses PSD, eta = omega breaks Hermiticity. THE LATTICE OS STATEMENT [E-float]: the FULL mixed Gram over {1, sigma_1, sigma_2, dipoles} with NO sector projection is real symmetric and PSD at N = 48/96 (min/max -5e-17), stable at N = 192. HONEST TYPING [C]: continuum OS reconstruction, R/fermion-parity sectors (deck^3 = -1), modular invariance, chiral factorization, non-abelian content stay NAMED, not claimed; GATE.QGEO does not move. [2026-08-02 XLV: the modularity/assembly successors land -- v650 (S measured with a clean N^{-4} rate, T exact), v651 (the seam assembly is B, matching this row's Klein phase eta = (1,1)), v652 (Arf hardening; the half-twist tau sector is Klein-PSD too), v653 (bond defect = lattice theorem); the orbifold front is complete at the lattice level; GATE.QGEO does not move.]
Recorded status: Exact [E] reality/uniqueness/must-fail structure + [E-float] PSD Grams (N-stable) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: KLEIN-RP-POSITIVE: the Z3 twist sector is reflection positive on the seam-double lattice under the parafermionic Klein-twist pairing (mirror x charge conjugation, omega^{k q} phases, eta = (1,1) unique among 36), N-stable 48..384, both axes, including the full mixed OS Gram; the naive pairing keeps its N-stable violation (must-fail); continuum OS/modularity typed open; GATE.QGEO does not move.
Dependencies: QGEO.TWISTOPE.01; QGEO.ORBCAS.01; QGEO.COVERSEAM.01; v519; v622; v623; v628; v639
Scripts: v645_klein_rp.py
Location: tfpt_3
Original CSV, line 649Original ledger status
E8.ONEOBJECT.01
The d = 4 forcing census + the 60-line clock synchronization kill, one module from two probes (21/21 + 23/23 checks, ~5 s; discovery probes one_object_reduction_probe.py ONE-OBJECT-PARTIAL and clock_fiber_product_probe.py CLOCK-FIBER-DEAD, both 2026-08-05). THE FORCING CENSUS (exact Fraction arithmetic, d = 2..12): the TFPT glue pattern (cyclic isotropic glue, evenness q = 0 mod 2Z, unimodularity |H|^2 = 4d) admits an even unimodular DIAGONAL glue of A_{d-1} (+) D_{d+1} iff d = 4 -- at d = 4 the census reproduces v92 EXACTLY (precisely two even Lagrangian glues, the graphs of the anti-isometries k -> k and k -> 3k), the explicit glued lattice is E8 (Gram det 1, exactly 240 norm-2 vectors, all integral over the glued basis), d = 9 (the only other perfect-square candidate from |H|^2 = 4d) dies at isotropy (0 even Lagrangians in Z9 (+) Z2 x Z2), and both relaxation controls fire (dropping evenness opens d != 4; dropping unimodularity opens d != 4). COROLLARIES AT THE FORCED d (verified arithmetic): g_car = d+1 = 5, N_fam = d-1 = 3, rank = 2d = 8, glue index sqrt(4d) = 4 = d = |mu4| -- the boundary object with four marked points reads P2 and the family count as the two functor readouts of ONE object. HONESTY GATE (binding): c_3 = 1/(2 pi d)|_{d=4} = 1/(8 pi) is a corpus-legitimate REWRITING (c_3 = 1/(2 e_1(a) pi) with e_1(a) = 4 = |mu4|, tfpt_1 anchor-first refinement / v23), NOT a corpus derivation of P1 -- ONE-OBJECT-FORCED was predeclared unreachable and P1 stays a primitive postulate. THE CLOCK KILL (part 2): the hypothesized fiber-product action L_60 = Z12 x_{Z6} Z30 of the seam clock (order 12, c = J o sigma, v629/v634) and the Coxeter clock (order 30, Kostant census {30: 8}, w^15 = -1) on the 60 Gaussian lines is DEAD at three levels -- the Coxeter clock does not preserve the line partition; the FULL line-compatible group (the 11520 line-reflection image extended by conjugation) has order 23040 with maximum element order 12, so line orders 15/30/60 are absent for EVERY realization of the clocks; and the fiber product itself is cyclic Z60 (exact SNF arithmetic; the full product Z12 x Z30 has invariant factors (6,60)) which cannot embed. All three census controls fire (the CC2 sampler-widening correction disclosed and carried). ROOTCLASS-MIXED (v775) binding in both parts: no line/code -> matter semantics. No marker move, NO RH claim. NOTE (2026-08-06, v807 -- marker UNCHANGED): the BOUNDARY.NULLSELECTOR addendum -- a second, independent d = 4 selector on the same invariant: the functor vector v_d = (d+1, -(d-1), d) (honest RR/Serre arithmetic) has |v_d|^2_L = det M(v_d) = d(4-d), null/rank-one iff d = 4, with M_4 = 2(1,2)^T(1,2) the certified spinor square and g^2 - N^2 = 4d = |H|^2 identically -- null <=> glue index = d; the glue census forces {4} via evenness/unimodularity, the null selector via 4d = d^2: independent inputs, same output; the missing premise (why the boundary reading carries the functor vector) is typed OPEN in v807. Scope note (Prime Front separation): v807 supplies only its original S1 RR/Serre/null-spinor algebra here; no prime-window hypothesis or additional physical selector follows.
Recorded status: Exact [E] lattice/discriminant-form census results and an exact [E] group-theoretic kill, both behind explicit fences; the c_3 link stays typed INTERPRETATION (no P1 derivation); no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ONE-OBJECT-PARTIAL + CLOCK-FIBER-DEAD: even unimodular diagonal glue of A_{d-1}+D_{d+1} iff d = 4 (census 2..12, v92 reproduced, E8 certificate); g_car = 5 / N_fam = 3 / |mu4| = 4 as one-object corollaries; c3 = 1/(2 pi d)|_{d=4} typed corpus-legitimate rewriting, NOT a P1 derivation; the Z12 x_{Z6} Z30 clock action on the 60 lines dead at three levels (group order 23040, max element order 12); controls fire; no RH statement.
Dependencies: v1; v23; v53; v92; v623; v629; v633; v634; ARF.ROOTCLASS.01
Scripts: v781_one_object_clock_census.py, v807_lorentz_nullselector.py
Location: tfpt_1;tfpt_3
Original CSV, line 684Original ledger status
E8.SHELL.GLOBAL.01
THE GLOBAL GAUSSIAN SHELL THEOREM (2026-08-08 round 36, v875; discovery probe gaussian_shell_global_probe.py 15/15, verdict SHELL-GLOBAL-THEOREM) -- the census->theorem upgrade: the v857 value law 'Thetahat_u/Theta_L = -1/15 on odd shells' holds for ALL shells, no census cap. THEOREM: on V = L/(1+i)L of the Gaussian E8, for EVERY n >= 1: Theta_v(n) = (Theta_L(n) - Theta_0(n))/15 for all v != 0 (the division exact), Thetahat_u(n) = 16(16 1_{2|n} sigma_3(n/2) - sigma_3(n)) for every nontrivial character u, and at every ODD n: Thetahat_u(n) = -16 sigma_3(n), Thetahat_u(n)/Theta_L(n) = -1/15 EXACTLY. INPUTS (each warded): (i) LEMMA 1 -- every g in G31 is a norm-preserving bijection of L transporting classes ((4M)^T(4M) = 16I; complex linearity (4M)J = J(4M)); the induced group is Sp(4,2) (order 720, generated by the 60 symplectic transvections), TRANSITIVE on the 15 nonzero classes, and IDENTICAL to the shell-module class action (coordination verified on generators); (ii) LEMMA 2 -- (I+J)^T(I+J) = 2I and (1-J)/2 inverts (1+i) on L: Theta_0(2m) = Theta_L(m), Theta_0(odd) = 0 (from 2 = -i(1+i)^2); (iii) LEMMA 3 -- Theta_L(n) = 240 sigma_3(n) (classical Eisenstein E4; verified to n = 24 directly and via the v857 packet glue identity to n = 16500). The n <= 16500 census is RETAINED as the exact ward (matched everywhere, odd AND even). CONTROLS: the non-transitive subgroup <T_1> (11 orbits) admits an explicit invariant NON-uniform census with Walsh multiset {-48 x4, -16 x7, +16 x4} -- transitivity is load-bearing; the even-shell formula differs correctly (7/135 at n = 2: the -1/15 law is the ODD-shell statement only). This REPLACES the finite-census argument behind the v857 value theorem (dated note there); the consequence chain is kernel-checked in FORM.E8.SHELL.GLOBAL.01. NO physics claim beyond the audit statement.
Recorded status: Honest promotion of a proved shell law [typed evidence line: 15/15 checks, zero fails, verdict SHELL-GLOBAL-THEOREM; frozen spec SHA a4b2f6d9...]
Dependencies, status detail and source
Canonical status: SHELL-GLOBAL-THEOREM: Sp(4,2) transitivity + (1+i) doubling + Theta_L = 240 sigma_3 => Thetahat_u/Theta_L = -1/15 at ALL odd shells; census n <= 16500 retained as ward; non-transitive control breaks the law.
Dependencies: E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v857; v858; v868
Scripts: v875_shell_global_lean.py
Location: tfpt_1_architecture_e8;tfpt_3;tfpt_research_contracts
Original CSV, line 716Original ledger status
ALPHA.QUILLEN.FACES.01
THE TWO NAMED FACES OF ALPHA.QUILLEN.EXACT.01 CARRY COMPUTED WITNESSES (2026-08-27, seam/alpha promotion wave; probes seam_bfk_conical_det_probe 21/21 SPEC d06b3bbec70e7efc / laughlin_pump_em1_probe 20/20 SPEC f9b5cb0bf20d0293 / quillen_rigidity_chain_probe 18/18 SPEC b4ee0dd0141da6ab, embedded byte-exact in v974). [E] BFK FACE EXECUTED: the Mayer-Vietoris determinant gluing on the seam circle at the four mu4 marks -- C_glue = 2^-N EXACT (N = 1..4 symbolic, general lengths), det'_zeta(Delta_S1) = l^2 reassembled, R(m) = (G_m|_marks)^-1; at KMS R_0 = 16 c3 circ(2,-1,0,-1), det'R_0 = 2^16 c3^3, glued product (2 pi)^2; vs v484 channel-wise EXACT (same mu4 eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling, Tr B^k = 4^k + 2 2^k vs Tr C^k = 4^k + 2(-2)^k) but NOT globally proportional -- the kernel swap (gauge zero mode vs sign rep) is the sharpened diagonal-zeta face. [E] EM1 FACE COMPUTED: pumped charge == edge spectral flow == Streda == Chern == 1 on the v367 collar, single complex copy, sign-coherent conjugation mutant; 16-copy bookkeeping exact (c_- = 8, kY = 5/3, (1/kY) 41/6 = 41/10 = b1). [E] QUILLEN IDENTITY AT THE FINITE SHADOW: Berry integral == Poincare-Lelong divisor integral == +1 two-sided, difference an exact form, transition winding == Chern; anchor re-derived (alpha^-1 = 137.03599921684071, split residual 6.4e-58 at 50 digits, 8 b1 = 164/5 exact). [C] TYPED CONDITIONAL: IF the seam state is quasi-free (the rigidity premise, measured not forced in the strong form by SEAM.STATE.RPMIXING.01) THEN the identity applies literally to the seam det line. HONEST SCOPE: closes NOTHING on ALPHA.QUILLEN.EXACT.01 -- remaining content {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification}; the BFK face is Delta = |D|^2, not a |D|-level operator identity; the pump is a single-copy statement.
Recorded status: Exact/computed witnesses [E] + typed conditional [C]; the target row stays [O]
Dependencies, status detail and source
Canonical status: Exact witnesses for both faces; target stays open
Dependencies: ALPHA.QUILLEN.EXACT.01; SEAM.CONTACT.UNIT.01; SEAM.CONTACT.UNIT.02; EM.WARD.01; ALPHA.QUILLEN.INFLOW.01; SEAM.STATE.RPMIXING.01
Scripts: v974_alpha_faces_computed.py
Location: tfpt_1;origin_theory;tfpt_research_contracts
Original CSV, line 754Original ledger status
SEAM.SIMPLECURRENT.GENERATOR.01
THE SIMPLE-CURRENT GENERATOR CONTRACT [O] (registered 2026-08-27 from the external bird's-eye review; the seam-gap compression conjecture). CONTEXT: v973 carved the cited-theorem coverage of the seam target -- the so(16)_1 fermion-bilinear half is COVERED (strong convergence, Virasoro/correlator control, polynomial errors), the NAMED residual is N1 (the mu4/GSO extension SO(16)_1 -> (E8)_1 as a NET statement: the 128 spinor currents are not bilinears), N2 (the twist/spin-field sector), N3 (the one-sided chiral edge), N4 (the holomorphy selector det K = 1 vs 4). DEMAND (the compression): construct ONE normalized simple-current/spin-field intertwiner -- the generator of the index-4 Q-system extension (v125/v154) -- with proofs of (G1) convergence on the finite-particle core with energy bounds, (G2) locality relative to the bilinear net, (G3) the correct braiding/monodromy relation, (G4) Q-system closure, so that symmetry and fusion generate the ENTIRE 128-dimensional extension sector from the single generator -- collapsing N1 + N2 (and, via uniqueness of the extension, the N4 selector) onto ONE convergence theorem instead of 128 separate current controls. KILL TESTS: the generator is provably nonlocal relative to the bilinear net; the energy bounds fail on the core; the braiding closes on the WRONG extension (SO(16)_1 stays unextended); the convergence rate is incompatible with the measured bilinear collar rate (v973: p = 3.48 inside the preregistered band). DIMENSION TYPING (binding, per DIMENSION.UPLIFT.FIREWALL.01): hypotheses AND conclusion live in 1+1D -- closing this contract does NOT close SEAM.BULK4D.RECON.01 or any 3+1D claim. EXECUTED UPDATE (2026-08-28, v988): S3 crossed-product/tower exchange EXACT (naturality; non-equivariant mutant fails); S1 window convergence + sector collapse measured (rates ~N^{-1.85} on the large collar; qualitative law on a reduced collar); S2 quantitative: windowed HS bounded (Shale ~0.376) + global HS^2 = 3.605+0.203 log N (topological) vs saturation (trivial); matrix-element Cauchy on the phase-fixed band; energy bounds f_n < C^{n+1}(n!)^2 (probe C=2.86). VERDICT: the remaining lemma REDUCED to cited quasi-free theorems (Shale-Stinespring/Araki/Ruijsenaars) + the MMST identification -- REDUCTION, NOT CLOSURE. Open rest = the MMST identification. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-28, v993): [lambda]^2 = [v] EXACTLY -- the order-4 glue class squares to the fermion-parity / D5-vector class (lattice shadow of U^2 = (-1)^F); non-split (vector glue norm 7/4 not in 2Z). The FULL rank-8 ADE census selects (D5, A3) uniquely, so the D+A architecture is an OUTPUT of (rank 8 + cyclic Z4). Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-28, completeness wave, v994): 5 of 7 MMST identification criteria executed [E-measured] (c = 8.005, conformal spectrum, k = 1, det D8=4 -> det E8=1, (E8)_1 vacuum character [1,0,248,0,4124,0,34752] three orders deep). C6 is the written-out quasi-free convergence theorem (articles/2026-08-28/psi_lambda_convergence_theorem_en.tex; 2/pi^2 = 0.20264 vs measured 0.203, 0.18%) -- this IS the G1/C6 hand-off. C7 modular invariance stays cited/open. Display stays [O]. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-29, review wave 4, v998): the C7 arithmetic shadow of the MMST identification (Theta_E8=E4 exact, character four orders, two-edge HS 2.11) is now machine-checked; net-level C7 / G2/G3/G4 stay cited. Display stays [O].
Recorded status: Open [O] + lattice shadow [E] (v983) + quantitative S1/S2 skeleton [E-measured] + reduction-to-cited-class [C conditional] + MMST criteria 5/7 executed [E-measured] (v994) + C6 written-out [C]; open rest = C7 modular invariance + net-level G2/G3/G4; no closure
Dependencies, status detail and source
Canonical status: [E] (v983): lattice-arithmetic generator lambda = (omega_s, omega_f). [E-measured] (v988): S3 exact + S1/S2 quantitative skeleton on toy and v367 QWZ collar. [C conditional] (v988): lemma reduced to cited quasi-free class + MMST identification. [O] open rest = C7 modular invariance + net-level G2/G3/G4; no closure; 1+1D in and out. [E] (v993): [lambda]^2 = [v] parity shadow of U^2 = (-1)^F; rank-8 ADE census unique (D5, A3) -- D+A architecture is an OUTPUT. [E-measured] (v994): 5/7 MMST identification criteria (c=8.005, character [1,0,248,0,4124,0,34752], k=1, det D8=4->det E8=1). [C] (v994): C6 written-out in psi_lambda_convergence_theorem_en.tex (2/pi^2 vs 0.203).| 2026-08-29 v998: C7 arithmetic shadow exact (shared with SEAM.EQUIV.MMST.01); net-level C7 stays cited. Display unmoved. WAVE-5 (2026-08-29): parent scaling-limit theorem SEAM.MMST.TYPEIII.CHARGED.01 [O] named; G1-G4 analytic half still [O]. Display unmoved.
Dependencies: SEAM.EQUIV.01; SEAM.EQUIV.MMST.01 (the v973 N1-N4 carve); v125; v154; DIMENSION.UPLIFT.FIREWALL.01; v993
Scripts: v983_simple_current_generator.py, v988_psi_lambda_reduction.py, v993_minimal_defect_selector.py, v994_mmst_criteria_battery.py, v998_seam_modular_closure.py
Location: tfpt_research_contracts
Original CSV, line 756Original ledger status
E8.DIRECTED.READOUT.01
THE SEVEN EXACT E8 READOUT CELLS [E] Identity (round r609, promoted 2026-09-02; module v1018, re-derived, no probe imports). (1) Seifert/Euler: S+S^T=A_E8, charpoly(-S^{-1}S^T)=Phi_30, rank(S-S^T)=8, orientation-independent charpoly (exponents=totatives of 30; degrees {2,8,12,14,18,20,24,30}, sum(2m_i+1)=248). (2) Hamming H_8 enumerator 1+14 y^4+y^8, 240=16+14*16, S(3,4,8). (3) srg(120,56,28,24) eigenvalues 56/8/-4 with multiplicities 1/35/84. (4) Hecke N(n)=240 sigma_3(n) for n<=10 (theta of E8 = E_4). (5) Delta: A_P(n)/A_P(1)=tau(n) for n<=8 on three axes, degree-2/4/6 vanishing, E_4^3-E_6^2=1728 Delta. (6) (Z/30)^x cong C_2 x C_4 (orders {1,2,2,2,4,4,4,4}, not C_2^3); D_chi(s)=L(s,chi)L(s-3,chi) for n<=200. (7) E6 oplus A2 gluing: index 3, Smith (1^6,3,3), roots 72+6+162, glue classes 78/81/81. C7 Gauss-code transform NOT promoted: stays OPEN (note_e8_gaussian_code.tex rem:c7-audit). NOT evidence for or against the Riemann Hypothesis. NO RH CLAIM.
Recorded status: Proven finite statement [E] (Identity, exact over Z/Q via sympy); C7 Gauss-code transform stays OPEN (rem:c7-audit); NO RH claim
Dependencies, status detail and source
Canonical status: [E] Identity: seven exact E8 readout cells (Seifert/Phi_30, Hamming, srg(120,56,28,24), N(n)=240 sigma_3(n), tau, C2 x C4, E6 oplus A2 glue); C7 OPEN (rem:c7-audit); NO RH claim
Dependencies: v1018
Scripts: v1018_e8_directed_readout.py
Location: note_e8_gaussian_code;introduction;tfpt_4_frontier
Original CSV, line 771Established within the stated premises
finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection
Original minimization does not classify the minimal algebra/bimodule fiber. The joint discrete theorem imports Higgs rank2 and branch-Yukawa rank3; the master functional fixes d_disc*,P_adm and B_min before varying only ξ=(α,χ_geo,δ_ph,ρ_vac). The singleton fiber product presupposes discrete uniqueness with E3⊕E2,Y in the shared invariant tuple. Two exact conditional decoders exist: independent occupancy balance at g5 gives {b,s}={2,3}; independent Bγ=g/(g−1) with Y roots−1/b,+1/s gives s²=g−1, hence s2,b3. Their cited original proofs evaluate these equalities only on the fixed3+2 branch. Using them as upstream selectors adds a premise.
Scope: Source and logical dependency audit of the cited chain, not a universal impossibility theorem. An independent original derivation of the cross-identification or unique minimal algebra/bimodule classification could close the gap. E8 glue rank selection and fixed state for given transport are retained and not equated with local algebra selection.
Required premises and original source excerpts
- P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
premise:declared-p1-p2 - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection
Original explicitly contains SU3⊂SU4 via4=3+1. For supplied90degree family-vector rotation R,U=diag(R,1) preserves each of (16,4) and(bar16,bar4). Actual five E8 branches yield248 multiplicities(134,56,2,56) for(1,i,−1,−i),trace132,the already known root-quarter type. In fixed four-basis U induces only h1↔h2 on traceless Cartan,spectrum(1,1,−1),order2; this is not order4R on family vectors. Native glue clock has(60,64,60,64),trace0. Claimed spinlift selection m=(k,k,k,−2−3k),minimal mF/dual,was already proved exactly on22September under extra fixed irreducible parallelity; general covariance does not supply it. Actual mixed output is(E⊕E*)⊗D^(mi+mj+1),with dual pairing of complementary SU4-six indices. Candidate general single-Higgs exclusion ofmA therefore lacks actual physical field map. Later The reviewed dual exclusion from charged-triplet determinant also does not follow from SU3 flavor:forB_k=A+k a I3,tracefree part remainsA for everyk;fullSU4 beta part stays traceless for both natural duals.
Scope: Source-reviewed reuse and concrete representation distinction. Different original clocks need not be identical or incompatible from multiplicities alone. Whole native C12 conjugacy and supplied parallel representatives remain solved. FixedM preservation needs actual transitions,connection and domain; free M↦HMH⁻¹ is not automatic fixed-bundle automorphism for unequal D powers. Fourth-slot anomaly compensation is existing conditional index arithmetic,not a physical fourth generation. Bare E8-bracket/Weyl single-anchor class remains settled in its statistics scope. No original common source,state/R/time derived from this representation comparison. The reviewed I_mu4 identification of normal sphere with flavor base and four equal logarithmic poles is new expressly underived geometry. Conditional uniqueness for fixedO1/simple-pole data holds,but is not origin. Fuchs degree and monodromy need same∇d±a convention:res−1/4 for∇d+a gives+i;ODE+a gives−i withdegree−1. Explicit horizontal point map in original iA(iz)=UA(z)U^-1 convention usesU,notU^-1. Anti-linear coefficient symmetry proves neitherOS norunchanged singularL2 normal index. ActualC3/q-cover alternatives retained.
Required premises and original source excerpts
- Existing SU3 family-vector embedding into SU4 four
Use original SU3⊂SU4 embedding with4=3+1 and existing E8 branches (45,1),(1,15),(16,4),(bar16,bar4),(10,6). A supplied family-vector rotation R acts by U=diag(R,1), with actual tensor/exterior powers on these branches. This does not identify original v117 connection with physically used marked family connection or derive original joint operator source.
premise:given-original-su3-to-su4-family-vector-action - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape
The restricted D8 contains only20 of40 original D5 roots. An original grade-zero D5 zero mode gives the explicit cocycle-correct word into the missing carrier half, preserving glue grade2. Full original D5 action with the triplet seed closes to all240 roots; its Weyl orbit completes15 to30 complex target directions and adjoints to all60. No new O fermion or freely supplied full16 input is needed. Original marked glue lambda maps in the fixed chart exactly to C0 dagger, with its adjoint the minimal D8 escape pair. The D8 vacuum lattice VOA preserves its coset; distinguish its new Z2 parity from old mu4 grades.
Scope: Positive actual operator connection at the given P2/E8 current level; replaces the extra-carrier/O gate. Not primitive P1 realization, physical zero-mode history, geometric mu-to-current or simultaneous-QY consumer derivation. Original quarter twist still lacks the localized charged glue-vertex identification beyond its conditional neutral eight-copy kernel. Accept The reviewed independently matching D8/D5 step, not its further exchange/CP or normal-carrier-selection conjectures. Do not count existing total Hom character compensation twice.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Given original C/X current source with E8 cocycle and compact adjoint
Use the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection.
premise:given-original-e8-cx-current-cocycle-and-compact-adjoint - Original D5 base-current action on supplied P2 and E8 carrier
Original D5_1 x A3_1 base net and explicit P2 Clifford carrier supply full45-dimensional D5 operator action including20 non-U5 roots. Its zero modes act with the existing Chevalley cocycle on the supplied compact E8 currents; no primitive P1 preparation or history selecting a word is presumed.
premise:original-d5-base-current-action-on-given-p2-e8-source
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action
ActualmarkedColorL0=ker tmod3equalsE6_perpColor orthogonalsumA2_Colorbyinclusionandequalindex3,forALLlatticevectors. WholefixedpointVOAretainsalloscillatorsandchargedV1,V2;weight1split86/81/81,actualcolorweights3x27withnorms2/3,4/3. E6commutesColor,notoldD5(4not40intersectionroots). OriginalWardtriality1andwholeweak24blocktriality0;allfieldcoefficientsPrYqPsonlyforr=s+tq. Balancedwordsretainneutralendpointsandchargedpaths;adjointWardnorm1iskilledonlybyfactorwiseP0. Existingproperlysupportedlocalcurrentgivesneutralbounded(I+A*A)^-1inthesamelocalfixedpointnet.
Scope: GivenstipulatedE8branchandoriginalmarks;genericE6glueandoldJtheoremreused. NophysicalPadm/OS/96CARidentity,HweightornewYderivation. Dimensionsarenotparticlecounts. CenterandglobalSU3fixedpointsretainc8;affinecommutanthasc6. FixedcolorbranchnotnativeJclosed;retainwholeclocks/fields.
Required premises and original source excerpts
- Original marked color center on whole stipulated E8 lattice field source
ExistingstipulatedunitaryE8_1lattice/currentnetinactualD5+A3targetframe,ColorA2=e1-e2,e2-e3,originalcentert=p1+p2-2p3mod3andneutraloscillators. GivenoldWardlambdaA=e3+e6andwholeweak(10,6)block;retainY/Flavor/Alpha,wholefields/clocks. ExecutePsingonTHISbranch,assumenoP1/OS/Padm/P_F/96CARintertwiner. Properlysupportedlocalcurrentswithactualdomains/adjoints. Extensiontheoremonlyintegrallattice/superlatticewithSAMEconformalvector. ReusenativeJboundarywithoutidentifyingJwithsourcequarterfoldorphysicaltime.
premise:original-marked-color-center-on-whole-e8-lattice-current-source - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Stipulated E8 H8 module with original color-center selector
Retain stipulated E8 lattice extension with H8=8K_alpha,alpha=1/4 or3/4,actual rational Weyl dictionary M and original marked color center on first three carrier slots. Apply its P_sing after the carrier theorem. No intertwiner to the primitive P1/OS space is assumed.
premise:stipulated-e8-h8-with-original-color-center-selector - Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
premise:local-e8-current-response-realization - Original D5+A3 compiler split and established seed
Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.
premise:fixed-native-d5-a3-compiler-split-and-seed - Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-COLOR-SECTORS-PROOF.txt, lines 1–198
Source SHA256: 9cd6d5a71c47a68af94b4720a2066bbcbd74d18969877c3fe12f63ec787b9df6
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_original_color_sectors.py, lines 1–135
Source SHA256: 947dd4f6547081bc1d953abdacb82e7f052baeac71990e38242717302bd6e4eb
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-COLOR-SECTORS.json, lines 1–200
Source SHA256: 64f8e2b753f44c45749dadb8fbca73836bc7019b254dca0d1980a8d979aa8697
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-COLOR-SECTORS.json, lines 201–359
Source SHA256: 64f8e2b753f44c45749dadb8fbca73836bc7019b254dca0d1980a8d979aa8697
bounded-excerpt · current-at-snapshot
- verification/v1_e8_glue.py, lines 1–40
Source SHA256: 1978d66a85974e5fa189cf4dec507f9be4c4dcc113e90eb1b33a9aae9259a0d7
bounded-sanitized-excerpt · current-at-snapshot · 1 administrative lines explicitly omitted
- verification/v1018_e8_directed_readout.py, lines 710–780
Source SHA256: 25f541903f01621990cf317372f1349be22a495b1594eb12c77c64db151dc9db
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/bracket_process_origin_20261028/closure/WARD-U5-CREATION-CHANNEL.txt, lines 1–86
Source SHA256: 03adbed045f9269eb4e4ca2c534426ee8066aa9d12b765bde482528eef238ec7
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/CLUSTERING-ADMISSIBLE-SECTOR.txt, lines 65–120
Source SHA256: 349e5a149d34078da67775e56f25e3aebf2c55111798a86d58322aa61cd380bc
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/e-series-quarter-clock-20261023/PROOF.txt, lines 64–91
Source SHA256: ac3e95975adb14c82815731b3d8aa0f6e1caf72d25fb749250a5b1bbcd269884
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex, lines 314–343
Source SHA256: 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DYNAMICAL-HIGGS-SOURCE-PROOF.txt, lines 1–38
Source SHA256: eda5bb664b1fb20370e59b39dbd5e3cb04d79864a8d1d0a0eb6c791cdaf98f49
bounded-excerpt · current-at-snapshot
Established within the stated premises
finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension
CompleteZ3²discriminantq=(2k²+l²)/3mod1hasdistribution5/2/2at0,1/3,2/3andno1/2. OriginalE8isotropicZ3gluehaschargedh1. ALLintegraloverlatticeswithSAMEconformalvectorareeven:det9forcesindex1or3,whereasoddnormkernelwouldforceevenindex. RenamingchargedbosonicE8currentsasquarkCARundertheunchangedinheritedchiralgradingisnotanoriginmap.
Scope: Onlyspecifiedintegrallattice/superlatticeclasswithinheritedstress. Noprohibitionofphysical3+1fermions,primitiveCAR,nonlocalintertwiners,actualsourcecovers/gradedmapsorTFPT. Nofreeexternalfermionsectorrequired. Distinguishconformalweight,internalSpin10indexandphysicalLorentzspin.
Required premises and original source excerpts
- Original marked color center on whole stipulated E8 lattice field source
ExistingstipulatedunitaryE8_1lattice/currentnetinactualD5+A3targetframe,ColorA2=e1-e2,e2-e3,originalcentert=p1+p2-2p3mod3andneutraloscillators. GivenoldWardlambdaA=e3+e6andwholeweak(10,6)block;retainY/Flavor/Alpha,wholefields/clocks. ExecutePsingonTHISbranch,assumenoP1/OS/Padm/P_F/96CARintertwiner. Properlysupportedlocalcurrentswithactualdomains/adjoints. Extensiontheoremonlyintegrallattice/superlatticewithSAMEconformalvector. ReusenativeJboundarywithoutidentifyingJwithsourcequarterfoldorphysicaltime.
premise:original-marked-color-center-on-whole-e8-lattice-current-source - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Stipulated E8 H8 module with original color-center selector
Retain stipulated E8 lattice extension with H8=8K_alpha,alpha=1/4 or3/4,actual rational Weyl dictionary M and original marked color center on first three carrier slots. Apply its P_sing after the carrier theorem. No intertwiner to the primitive P1/OS space is assumed.
premise:stipulated-e8-h8-with-original-color-center-selector - Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
premise:local-e8-current-response-realization - Original D5+A3 compiler split and established seed
Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.
premise:fixed-native-d5-a3-compiler-split-and-seed - Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-COLOR-SECTORS-PROOF.txt, lines 1–198
Source SHA256: 9cd6d5a71c47a68af94b4720a2066bbcbd74d18969877c3fe12f63ec787b9df6
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_original_color_sectors.py, lines 1–135
Source SHA256: 947dd4f6547081bc1d953abdacb82e7f052baeac71990e38242717302bd6e4eb
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-COLOR-SECTORS.json, lines 1–200
Source SHA256: 64f8e2b753f44c45749dadb8fbca73836bc7019b254dca0d1980a8d979aa8697
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-COLOR-SECTORS.json, lines 201–359
Source SHA256: 64f8e2b753f44c45749dadb8fbca73836bc7019b254dca0d1980a8d979aa8697
bounded-excerpt · current-at-snapshot
- verification/v1_e8_glue.py, lines 1–40
Source SHA256: 1978d66a85974e5fa189cf4dec507f9be4c4dcc113e90eb1b33a9aae9259a0d7
bounded-sanitized-excerpt · current-at-snapshot · 1 administrative lines explicitly omitted
- verification/v1018_e8_directed_readout.py, lines 710–780
Source SHA256: 25f541903f01621990cf317372f1349be22a495b1594eb12c77c64db151dc9db
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/bracket_process_origin_20261028/closure/WARD-U5-CREATION-CHANNEL.txt, lines 1–86
Source SHA256: 03adbed045f9269eb4e4ca2c534426ee8066aa9d12b765bde482528eef238ec7
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/CLUSTERING-ADMISSIBLE-SECTOR.txt, lines 65–120
Source SHA256: 349e5a149d34078da67775e56f25e3aebf2c55111798a86d58322aa61cd380bc
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/e-series-quarter-clock-20261023/PROOF.txt, lines 64–91
Source SHA256: ac3e95975adb14c82815731b3d8aa0f6e1caf72d25fb749250a5b1bbcd269884
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex, lines 314–343
Source SHA256: 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DYNAMICAL-HIGGS-SOURCE-PROOF.txt, lines 1–38
Source SHA256: eda5bb664b1fb20370e59b39dbd5e3cb04d79864a8d1d0a0eb6c791cdaf98f49
bounded-excerpt · current-at-snapshot
Established within the stated premises
finding:finite-carrier-glue-elements-orbits-and-halfway
In Fin4 x Fin4 with qZ=(5x^2+3y^2) mod8, named Lean declarations classify all six isotropic elements and four odd-coordinate isotropic generators. Explicit orbit identities give H1 and H2; klein_not_isotropic gives the nonisotropic Klein witness, spinor_swap_exchanges swaps the two orbits, and unique_halfway_stage classifies the only nonzero isotropic order-two element (2,2). Index and sector arithmetic are additional separate declarations.
Scope: The concrete element/orbit and arithmetic statements are available. No fresh kernel run, nor a newly checked single Lean theorem about all abstract subgroups or lattice isomorphisms. The general subgroup conclusion also uses finite group theory; concrete E8 basis embedding and physical carrier selection are separate.
Required premises and original source excerpts
Established within the stated premises
finding:e-series-integral-glue-and-normalization-nonidentifiability
The native E8 quotients for D6+A1+A1, E7+A1, E6+A2 and D5+A3 are C2²,C2,C3,C4. The E7-pair index4 is not cyclic C4 glue. Conditional continuations1/(pi*r) and1/(2pi*m), with selected exceptional rank r and lattice extension index m, agree at E6/E8 but differ at E7:1/(7pi) versus1/(4pi). The anchors do not determine the continuation. Complete conformal windows retain total rank and central charge8.
Scope: Exact lattice quotients and non-identifiability of an extra normalization map. No identification of original modular index I with m in each projection, no selection of a law or E7 coupling/scale prediction. The historical7pi window is no independent measurement. The established P1/P2→D5+A3→E8 construction and phi_base=(4/3)c3 remain intact. This comparison concerns only an additionally proposed E7 continuation and is not a missing step in the existing compiler.
Required premises and original source excerpts
- Active purely mathematical marked-seam program
Within the stated mathematical scope, marked pairs, lattice transport systems, reflections, clocks and cohomology are independent mathematical objects. Earlier origin/completion tasks are historical, not active. Distinguish new definitions, derived theorems and optional markings.
premise:marked-seam-pure-mathematical-program - Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension
Established within the stated premises
finding:marked-c4-glue-unique-local-e8-vacuum-source
In exactly Ext_H(U) there is one VOA and normalized local Q system class over U, represented by V_E8. q_D5(s)=5/8 and q_A3(f)=3/8 make H Lagrangian; the full abelian associator/braiding class trivializes only on H. H2(C4,C*)=H2(C4,U1)=0 gives uniqueness, with residual automorphisms Hom(C4,U1)=C4. The actual weight1 branching is60+64+60+64=248. Lattice vacuum, Sugawara vector, L0=N+Norm(alpha)/2, all vacuum correlators, unitary structure over U and associated local conformal net are determined in this class.
Scope: Complete conditional mathematical reconstruction for the specified U module and local unitary conformal extension. No derivation of primitive P1 membership or physical time/state/spacetime identification. H3(C4,U1) is not asserted zero; the original nonsplit G31 character extension is not replaced by scalar coefficients.
Required premises and original source excerpts
- Original D5+A3 compiler split and established seed
Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.
premise:fixed-native-d5-a3-compiler-split-and-seed - Exact local reconstruction class of the marked C4 glue
Mathematical object class Ext_H(U): U=V_D5 tensor V_A3 with fixed embedding and sector chart, H=<(s,f)>=C4. Objects are connected local unitary conformal VOA extensions with the same conformal vector and underlying labelled U module exactly the sum of M_h for h in H, each once. Isomorphisms fix U and sector labels. This is an explicit mathematical reconstruction class; membership of primitive P1 is neither assumed nor derived.
premise:marked-c4-unitary-local-extension-reconstruction-class
Established within the stated premises
finding:double-scalar-quarter-is-marked-glue-with-two-step-index
F(2q)=lambda is an actual lattice identity, not only equal norm. s=2q has order4 modulo D5+D3 and order2 modulo D8. The tower U to V_D8 to V_E8 has indices2,2 and mu-indices16,4,1. The older SO16 base with index4 mixes two different inclusions.
Scope: Given eight-channel chart and marked lattice generator. Squaring a finite disorder operator is not identified with the local vertex field.
Required premises and original source excerpts
- Given scalar quarter twist and explicit charge chart
Compare the given eight complex current channels, q=(1/4)^8, standard D5+D3 lattice and F=I5+T with T(x,y,z)=(x+y+z,x-y-z,-x+y-z,-x-y+z)/2. Eight channels and their normalization are not derived here from P1. Distinguish a local charged field, scalar monodromy character, flux register and native clock.
premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart
Established within the stated premises
finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags
Five-carrier parity kappa=exp(2pi i v(0)), v=(1/2^5,0^3), acts on the four U glue sectors as1,i,-1,-i and fixes precisely U. Among all65536 torus points modulo4 exactly15120 match actual Jhat; they form one actual W(E8) orbit. Thus C kappa C^-1=Jhat for a full VOA automorphism C. Each two inverse primitive characters share a fixed root lattice D5+A3; the7560 kernels are equivariantly the actual7560 compiler/tetrahedron flags.
Scope: Complete torus and Weyl classification plus compact E8 conjugacy, not mere matching spectra. C is not preferred and retains other marks only through their joint transport.
Required premises and original source excerpts
- Full unitary E8 field conjugacy with transported marks
Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator.
premise:full-unitary-e8-field-conjugacy-with-transported-marks
Established within the stated premises
finding:e-series-operational-role-review-and-source-time-centralizer
In the fixed original D5+A3 cut, each of the six pairs among the four E6 systems generates precisely its unique E7:104 union roots close to126, with a common40-root D5. Orthogonal root/Cartan projectors onto E6 and E7 are not Lie homomorphisms, as removed opposite-root pairs with nonzero projected coroot show. For the existing H8=8L0-rho_A7.a0+(2a-1)Q/2, Q-neutral E7 membership is not full horizontal energy symmetry: [H8,J_(e0-e1,0)]=-J_(e0-e1,0). At a=1/4 and3/4 exactly8 ordinary n=0 root modes commute, of type4A1; with8 Cartan modes this horizontal centralizer has dimension16. Complete conformal E7+A1 and E6+A2 windows retain their complements and glued modules. A cut sequence is not a derived physical breaking or time history.
Scope: Exactly the fixed native root chart and the given eight-channel time operator. The tetrahedron covers four of1120 E6 and six of120 E7. The Q-neutral E7 has a half-root normal and is not one of those six; Q is not automatically Y. Only ordinary horizontal n=0 modes are classified, not all affine conserved modes. Existing shifted p* sl2 modes and the solved color-center-neutral vacuum selection remain valid. The projector counterexample does not exclude genuine subalgebra inclusions, state restrictions or separately justified physical reductions.
Required premises and original source excerpts
- Original D5+A3 compiler split and established seed
Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.
premise:fixed-native-d5-a3-compiler-split-and-seed - Exact local reconstruction class of the marked C4 glue
Mathematical object class Ext_H(U): U=V_D5 tensor V_A3 with fixed embedding and sector chart, H=<(s,f)>=C4. Objects are connected local unitary conformal VOA extensions with the same conformal vector and underlying labelled U module exactly the sum of M_h for h in H, each once. Isomorphisms fix U and sector labels. This is an explicit mathematical reconstruction class; membership of primitive P1 is neither assumed nor derived.
premise:marked-c4-unitary-local-extension-reconstruction-class - Four D8 source modules with fixed affine time
Mathematical parent of the four D8*/D8 modules 0,v,s,c with eight identical Heisenberg oscillators, source charge chart p and N≥0. H=8(N+|p|²/2+delta.p),delta_j=(j+a)/8−1/2,0<a<1,Q=sum p_j. Original quarter cases are a1/4,3/4. Conformal L0, individual Cartan charges and totalQ remain distinct. This mathematical completion does not assume a physical P1 realization of the Ramond space or a local field map.
premise:four-d8-sectors-with-fixed-affine-source-time
Established within the stated premises
finding:glue-clock-twisted-sectors-share-marked-quadratic-module
A_Q=C4², q=(5a²+3b²)/8, describes E8 extensions, D8 and four clock sectors; flux=a−b=−r. (i,j)↦(3i+j,2i+j) gives type4{2}; ground spaces1,4,16,4 have the specified actual representations. Level8, T order24; no transverse isotropic complement to H+.
Scope: Given same-conformal E8 class/marks. A_Q≠A_J; modular phase is neither base cover nor physical time; H± remain allowed.
Required premises and original source excerpts
- Exact local reconstruction class of the marked C4 glue
Mathematical object class Ext_H(U): U=V_D5 tensor V_A3 with fixed embedding and sector chart, H=<(s,f)>=C4. Objects are connected local unitary conformal VOA extensions with the same conformal vector and underlying labelled U module exactly the sum of M_h for h in H, each once. Isomorphisms fix U and sector labels. This is an explicit mathematical reconstruction class; membership of primitive P1 is neither assumed nor derived.
premise:marked-c4-unitary-local-extension-reconstruction-class - Full unitary E8 field conjugacy with transported marks
Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator.
premise:full-unitary-e8-field-conjugacy-with-transported-marks