A registered result in its source context
Original ledger classification: Unification [E] (chi_E8=j^{1/3}, tau=i shared) + [C] (count 2->1) + [O] (one premise)
Recorded statement: THE E8-AT-tau=i UNIFICATION: TWO OBLIGATIONS -> ONE OBJECT (2026-06-18): the candidate simplification. The (E8)_1 character as a modular function of the seam torus modulus tau is chi_E8(tau)=Theta_E8/eta^8=E4/eta^8=j(tau)^{1/3} (since…
Statement, assumptions and sources
Paper context: tfpt research contracts
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QGAMB.UNIFY.01
Original ledger classification: Unification [E] (chi_E8=j^{1/3}, tau=i shared) + [C] (count 2->1) + [O] (one premise)
Original claim text
THE E8-AT-tau=i UNIFICATION: TWO OBLIGATIONS -> ONE OBJECT (2026-06-18): the candidate simplification. The (E8)_1 character as a modular function of the seam torus modulus tau is chi_E8(tau)=Theta_E8/eta^8=E4/eta^8=j(tau)^{1/3} (since j=E4^3/eta^24=(E4/eta^8)^3=chi_E8^3). [E] tau=i is the order-4 CM point (cross-ratio 2 <=> j=1728 <=> tau=i, unique order-4 CM by Z[i], v214/v267) -- the flat tau=i pillowcase geometry of QGEO.SYM.01. [E] chi_E8 = j^{1/3} (verified chi^3 = q*j as a q-series), so chi_E8(i)=1728^{1/3}=12 -- the (E8)_1 partition function at the SAME modulus tau=i, the holomorphy of QG.AMB.01. [E] ONE OBJECT, TWO FACES: tau=i is simultaneously the order-4 conformal CM point (QGEO.SYM.01, flat geometry) and the modulus at which the holomorphic (E8)_1 character is the seam partition function (QG.AMB.01, holomorphy). [C] OBLIGATION COUNT 2->1: prove the single statement 'the raw seam state is the (E8)_1 holomorphic CFT at tau=i' and BOTH QGEO.SYM.01 (flat tau=i, order-4 CM) AND QG.AMB.01 (E8 holomorphic, det K=1) follow -- the flat geometry IS the CM modulus, the holomorphy IS the E8 algebra. [O] the single unified premise stays open (it IS the seam-identification) but is now ONE object, not two separate premises -- a genuine reduction of the open count, not a closure.
Original classification detail
[E] tau=i the order-4 CM point + chi_E8=j^{1/3} (chi_E8(i)=12) + the one-object identification; [C] the obligation count drops 2->1; [O] the single unified premise stays open. The candidate simplification of the two math obligations. Exact core mirrored in Wolfram.
Dependencies as recorded
QGEO.SYM.03; QGEO.OBLIG.01; QGAMB.TIERB.01; QGAMB.MODULAR.01; QGEO.PILLOW.01
Open the original ledger source, row 377Location recorded in the ledger
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- Research contracts
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.
- 2026-06-18 (self-investigation round: pillowcase DtN, modular data, the E8-at- [formula in source] unification, live scorecard, v280– v283)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
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 closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- 2026-06-18 (the two proof routes decomposed: Route (i) and Route (ii) into lemma chains, v284/ v285)Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-24 (The arithmetic hull + the [formula in source] -character CM duality: v403, v404)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (closing sprint: the Seam Equivalence Theorem named + both routes attacked, v286– v288)Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-24 (Completing the Coxeter clock: v390 the prime-2 (Gaussian / [formula in source] -seam) facet of [formula in source] )Research changelog; TFPT — Introduction and reading guide
All 9 linked sections
Registered verification modules
- v282_e8_tau_i_unification.pyRegistered verification module · frontier
Read the description recorded in the module registry
QGAMB.UNIFY.01 — the E8-at-τ=i unification: the candidate SIMPLIFICATION reducing the two open obligations to ONE object (the raw seam is the (E8)₁ holomorphic CFT at τ=i). χ_E8(τ)=Θ_E8/η⁸=j^{1/3}. [E] τ=i is the order-4 CM point (j=1728, the QGEO.SYM.01 flat geometry); [E] χ_E8=j^{1/3} (χ³=q·j as q-series), so χ_E8(i)=1728^{1/3}=12 (the (E8)₁ character at the SAME τ=i, the QG.AMB.01 holomorphy); [E] one object, two faces — τ=i is both the order-4 CM point and the (E8)₁ partition-function modulus; [C] obligation count 2→1: prove 'the raw seam is (E8)₁ at τ=i' and BOTH QGEO.SYM.01 and QG.AMB.01 follow; [O] the unified premise stays open but is now ONE object. A genuine reduction of the open count, not a closure.
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