A registered result in its source context
Original ledger classification: Named target [E]/[O] (the phi0 puncture 48 c3^4 as the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture, summed over Omega_adm=N_fam dim S+=48; a face of the seam boundary analysis, elevates v396's puncture residual to a citable target; no new gate)
Recorded statement: NAMES THE phi0 PUNCTURE TERM AS A TRACKED [O] HEAT-KERNEL TARGET (2026-06-24, v408): dtop = Omega_adm c3^4 = 48 c3^4 = 3/(256 pi^4) IS the order-4 (|mu4|) local boundary Seeley-DeWitt contact term of the mu4 puncture divisor, summed over…
Statement, assumptions and sources
Paper context: Origin Theory
The exact identifier, original classification and full claim are available below.
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HYP.PHI0.PUNCTURE.01
Original ledger classification: Named target [E]/[O] (the phi0 puncture 48 c3^4 as the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture, summed over Omega_adm=N_fam dim S+=48; a face of the seam boundary analysis, elevates v396's puncture residual to a citable target; no new gate)
Original claim text
NAMES THE phi0 PUNCTURE TERM AS A TRACKED [O] HEAT-KERNEL TARGET (2026-06-24, v408): dtop = Omega_adm c3^4 = 48 c3^4 = 3/(256 pi^4) IS the order-4 (|mu4|) local boundary Seeley-DeWitt contact term of the mu4 puncture divisor, summed over Omega_adm = N_fam dim S+ = 48 admissible fermion states -- the analytic complement of the icosahedral tree term phibase (v396, HYP.PHI0.01). Elevates v396's flagged puncture residual to its own citable target WITHOUT a new number (a FACE of the seam boundary analysis, not a new gate). [E] THE SPLIT IS EXACT: phi0 = phibase + dtop = 1/(6 pi) + 48 c3^4 (v396/ARCH.QUAD.01). [E] PUNCTURE COUNT = Omega_adm = N_fam dim S+ = 48, order = |mu4| = 4. [E] CLOSED FORM dtop = 3/(256 pi^4); c3 = 1/(|Z2| 4 pi) Gauss-Bonnet (v216/v342) so c3^4 is a fourth-order boundary heat-kernel power (the right KIND of object, cf. v391). [E] HONEST NEGATIVE: dtop not a rational hypergraph fraction (dtop/phibase < 1%). [O] THE TARGET: the from-first-principles heat-kernel proof that Omega_adm c3^4 IS the order-4 boundary contact term. [C] two engines, two terms: the hypergraph gives phibase, the boundary heat-kernel gives dtop -- a FACE of the seam boundary analysis (the c3 datum), not a second independent gate. No new number (reuses v396/ARCH.QUAD.01, Wolfram-mirrored under ARCH.QUAD.01/v37). UPDATE 2026-07-14 (v483/HYP.PHI0.GEOM.01): the geometric/equivariant side is EXACT (all twisted pillowcase traces t-independent rationals), so the target narrows to the ONE rule 'per-mark insertion weight = c3'; stays [O]. UPDATE 2026-07-14 (v484/SEAM.CONTACT.UNIT.01): the per-mark weight rule MERGES with ALPHA.QUILLEN.EXACT.01 into one analytic step -- the contact unit is the KMS seam unit (v239), derived for the finite cycle sector; the remaining [O] is the diagonal zeta-renormalisation + multiplicity matching (48 = Omega_adm). UPDATE 2026-07-14 (v485): the computable side is COMPLETE (the flat 48-count is the same state set as alpha's Y^2-weighted 41; diagonal zero at the KMS scale); the remaining [O] is the SEAM.EQUIV.01 face alone.
Original classification detail
[E] the exact split phi0 = 1/(6 pi) + 48 c3^4, the puncture count Omega_adm=N_fam dim S+=48, the closed form 3/(256 pi^4), the hypergraph negative (reused from v396/ARCH.QUAD.01, machine-checked); [O] the from-first-principles heat-kernel-contact-term proof (the named target); [C] a face of the seam boundary analysis, not a second independent gate. A typing/registration of v396's puncture residual; introduces no new number.
Dependencies as recorded
HYP.PHI0.01; ARCH.QUAD.01; v396; v312; v216; v342; v391
Open the original ledger source, row 464Location 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.
- Origin Theory
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.
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- 2026-07-14 (III) ( v484 — the two open analytic targets MERGE: the shared `` [formula in source] per boundary insertion'' rule of ALPHA.QUILLEN.EXACT.01 and HYP.PHI0.PUNCTURE.01 is the KMS seam unit [formula in source] with [formula in source] , derived on the seam circle for the finite cycle sector — no gate closes, no marker moves)Research changelog; TFPT — Introduction and reading guide
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- The whole integer skeleton from one pair [formula in source]Origin Theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)Architecture, E8 and the electromagnetic fixed point
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
All 13 linked sections
- 2026-06-24 (Two new tracked targets + axion-branch consistency: v408, v409)
- 2026-07-14 (IV) ( v485 — the merged analytic target's computable side COMPLETED: the diagonal self-energy is renormalised to ZERO exactly at the KMS seam scale, the mark contact calculus resums in closed form (BFK route), and the [formula in source] / [formula in source] multiplicities are ONE state set under two response weights — the residual collapses onto the SEAM.EQUIV.01 face alone; no gate closes, no marker moves)
- 2026-07-14 (II) ( v482– v483 — the deep-dive round: the [formula in source] -scale decision computation EXECUTED (the integer [formula in source] -rung excluded unstructured, the [formula in source] -proximate structure escape recorded and declined) and the [formula in source] puncture target HALVED (the geometric side proven exact: all twisted pillowcase heat traces are [formula in source] -independent rationals, so the [formula in source] must sit in the per-mark coupling weight) — no gate closes, no marker moves)
- 2026-07-14 ( v479– v481 — the bird's-eye ``overlooked tools'' round: R3's graph [formula in source] geometry bridge discharged to Kronheimer 1989; the four [formula in source] marks realised as the exactly solvable four-interval multilocal modular geometry with [formula in source] manifest; and the absolute [formula in source] -scale collapsed to a one-parameter, PS-window-bracketed candidate under the carrier normalisation [formula in source] — no gate closes, no marker moves)
- The whole integer skeleton from one pair [formula in source]
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.
- Appendix: computational verification (reproducibility)TFPT — Introduction and reading guide
- 2026-07-14 (website + figure refresh — the /verification journey views become live HTML (the stale timeline/residual-chain images replaced by interactive components wired to the in-browser reproducer), the prediction surface's empirical-audit wall of text restructured into dated, expandable rounds, and the generated timeline/residual-chain figures extended to the current suite — presentation only, no content or marker moves)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v408_phi0_puncture_heatkernel.pyRegistered verification module · frontier
Read the description recorded in the module registry
HYP.PHI0.PUNCTURE.01: name the phi0 puncture term dtop = 48 c3^4 as the order-4 local boundary heat-kernel (Seeley-DeWitt) contact term of the mu4 puncture divisor -- the analytic complement of the icosahedral tree term (v396, HYP.PHI0.01). [E] THE SPLIT IS EXACT: phi0 = phibase + dtop = 1/(6 pi) + 48 c3^4 (v396/ARCH.QUAD.01), a tree term plus a fourth-order boundary correction. [E] PUNCTURE COUNT = Omega_adm = N_fam dim S+ = 48, order = |mu4| = 4: dtop = Omega_adm c3^|mu4|. [E] CLOSED FORM dtop = 48 c3^4 = 3/(256 pi^4); c3 = 1/(|Z2| 4 pi) Gauss-Bonnet (v216/v342) so c3^4 is a fourth-order boundary heat-kernel power (cf. v391). [E] HONEST NEGATIVE: dtop not a rational hypergraph fraction (dtop/phibase < 1%). [O] THE TARGET: prove Omega_adm c3^4 IS the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture summed over the Omega_adm admissible states. [C] two engines, two terms; a FACE of the seam boundary analysis (the c3 datum), not a new gate. No new number.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.