A registered result in its source context
Original ledger classification: Identity [E, audit-only] (exact integer/q-series arithmetic incl. the j-series recomputation and all controls -- sympy exact, Wolfram-mirrored); explicitly NON-exclusive (D16 control passes); the fingerprint feeds no derivation (no-free-pattern rule honoured)
Recorded statement: THE E8 DUAL-DEGREE MODULAR CHECKSUM 744 + THE PRIME-TOTATIVE FINGERPRINT (2026-07-23; AUDIT-TYPED under the no-free-pattern rule -- feeds no derivation, kills no alternative alone, registered with its own negative controls; 11 checks, ~2…
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
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E8.DEGREE.MODULAR.01
Original ledger classification: Identity [E, audit-only] (exact integer/q-series arithmetic incl. the j-series recomputation and all controls -- sympy exact, Wolfram-mirrored); explicitly NON-exclusive (D16 control passes); the fingerprint feeds no derivation (no-free-pattern rule honoured)
Original claim text
THE E8 DUAL-DEGREE MODULAR CHECKSUM 744 + THE PRIME-TOTATIVE FINGERPRINT (2026-07-23; AUDIT-TYPED under the no-free-pattern rule -- feeds no derivation, kills no alternative alone, registered with its own negative controls; 11 checks, ~2 s, sympy exact): [E] the E8 invariant degrees (2,8,12,14,18,20,24,30) (v66) pair dually d_i + d_{9-i} = 32 = h+2; the four dual products (2*30, 8*24, 12*20, 14*18) = (60,192,240,252) satisfy SIMULTANEOUSLY sum = 744 = 3*248 = 3 dim E8, product = 696729600 = |W(E8)|, gcd = 12 = dim g_SM, and normalised (5,16,20,21) = (g_car, dim S^+, det L, N_fam*7). [E] MODULAR ANCHOR: 744 recomputed from scratch as the constant coefficient of the modular j-function, j = E4^3/Delta = q^-1 + 744 + 196884 q + ... (the cube of the (E8)_1 character, v496) -- a finite-to-affine checksum from the finite invariant degrees to the first regular coefficient of chi^3 = j. [E] NEGATIVE CONTROL (the checksum is NOT E8-exclusive -- the mandatory fence): D16 (same h = 30, rank 16) passes with dual-product sum 1488 = 3*496 = 2*744, exactly the heterotic dimension equality 496 = dim(E8xE8) = dim SO(32) (the tfpt_1 audit box); the checksum measures the common rank-16/Coxeter-30 heterotic structure. The non-heterotic controls ALL fail the 3*dim rule (half-pair convention): A8 100/240, D8 200/360, E6 117/234, E7 316/399, F4 72/156, G2 12/42. [E, audit] PRIME-TOTATIVE FINGERPRINT: {2,3,5} u (Exp(E8) minus {1}) = {2,3,5,7,11,13,17,19,23,29} = ALL primes below 30; every totative of 30 except 1 is prime; and 30 is the LARGEST integer with this property (exact scan to 10^4; full list {1,2,3,4,6,8,12,18,24,30}) -- h(E8) = 30 = |Z2| N_fam g_car is the maximal prime-totative Coxeter number. Complements the prime-facet arithmetic (COXETER.PRIME2.01, ARITH.HULL.01, ARITH.TRICHOTOMY.01) at the fingerprint level; per the no-free-pattern rule NONE of this becomes load-bearing. Discovery provenance: center_quotient_coxeter_modular_disc7_probe.py (76/76) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves.
Original classification detail
[E, audit] dual-degree checksum: (60,192,240,252) -> sum 744 = 3*248 (= j constant coefficient, recomputed), prod |W(E8)|, gcd 12, /12 = (5,16,20,21); D16 control 1488 = 3*496 (NOT E8-exclusive); primes-below-30 totative fingerprint with maximality scan; audit-only, no marker moves
Dependencies as recorded
E8.DEG.01 (v66); CELEST.WP4.01 (v496); COXETER.PRIME2.01; ARITH.HULL.01
Open the original ledger source, row 600Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- Architecture, E8 and the electromagnetic fixed point
- E8 audit and bootstrap
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- =150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- The Möbius origin of the irreducible [formula in source]input 5 tfpt 3 e8 audit bootstrap
- Level 2.5 — the even-flip transition atlas (a falsifiable program)tfpt 1 architecture e8
- Level 2.5 — the even-flip transition atlas (a falsifiable program)Architecture, E8 and the electromagnetic fixed point
- Level 2.5 — the even-flip transition atlas (a falsifiable program)tfpt 1 architecture e8
- The Möbius origin of the irreducible [formula in source]E8 audit and bootstrap
- The Möbius origin of the irreducible [formula in source]input 5 tfpt 3 e8 audit bootstrap
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v532_e8_degree_modular_checksum.pyRegistered verification module · core
Read the description recorded in the module registry
Dual-degree checksum: (60,192,240,252) → 744=3·248, |W(E8)|, gcd 12; j = q⁻¹+744+…; D16 control 1488=3·496; primes<30 fingerprint [audit]
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.