A registered result in its source context
Original ledger classification: phi0 leading term [E]/[C]/[O] (phibase = F/(g_car N_fam) c3 = 1/(6 pi); F/h = |Z2|/N_fam; Gauss-Bonnet consistent; puncture 48 c3^4 still analytic) -- combinatorial reinterpretation, not full phi0 closure
Recorded statement: THE phi0 LEADING TERM FROM ICOSAHEDRAL COMBINATORICS (2026-06-24, sharpening v312/v395): the tree-level retained seed phibase = 1/(6 pi) has a forced combinatorial reading on the icosahedral hypergraph; the puncture 48 c3^4 stays analytic.…
Statement, assumptions and sources
Paper context: Origin Theory
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HYP.PHI0.01
Original ledger classification: phi0 leading term [E]/[C]/[O] (phibase = F/(g_car N_fam) c3 = 1/(6 pi); F/h = |Z2|/N_fam; Gauss-Bonnet consistent; puncture 48 c3^4 still analytic) -- combinatorial reinterpretation, not full phi0 closure
Original claim text
THE phi0 LEADING TERM FROM ICOSAHEDRAL COMBINATORICS (2026-06-24, sharpening v312/v395): the tree-level retained seed phibase = 1/(6 pi) has a forced combinatorial reading on the icosahedral hypergraph; the puncture 48 c3^4 stays analytic. [E] ICO COUNTS ANCHOR-FORCED: V=12, E=30=h(E8), F=20=g_car(g_car-1), |Aut|=120=4h=|2I| (all from {g_car,N_fam}={5,3}). [E] LEADING TERM EXACT: phibase = 1/(6 pi) = (4/3) c3 = F/(4 h pi) = F/(|Aut| pi) = (F/(g_car N_fam)) c3. [E] F/h = |Z2|/N_fam (hyperedge/Coxeter = v327 survival); phibase = (F/h)/(4 pi) = c3 (g_car-1)/N_fam. [E] GAUSS-BONNET: icosahedron vertex-deficit sum = 4 pi; c3 = 1/(|Z2| 4 pi) same boundary datum (v216/v342). [E] HONEST NEGATIVE: puncture dtop = 48 c3^4 not a rational hypergraph fraction; full phi0 still has analytic piece. [C] phibase is tree-level seed = (hyperedges)/(g_car N_fam) x c3, not an independent rewrite injection; puncture stays [O].
Original classification detail
[E] exact combinatorial identities + Gauss-Bonnet + puncture negative; [C] tree-level seed reading; [O] puncture term. Sharpens v312/v395; does not close full phi0.
Dependencies as recorded
v312; v216; v342; v327; v395
Open the original ledger source, row 463Location recorded in the ledger
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- Origin Theory
Sections that explicitly cite this claim
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- 2026-06-24 ( [formula in source] leading term from icosahedral combinatorics: v396)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Navigation through a shared verification script
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- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The compiler: why [formula in source]TFPT — Introduction and reading guide
- The whole integer skeleton from one pair [formula in source]Origin Theory
- 2026-06-24 (Two new tracked targets + axion-branch consistency: v408, v409)Research changelog; TFPT — Introduction and reading guide
- The whole integer skeleton from one pair [formula in source]origin theory
Registered verification modules
- v396_phi0_icosahedral.pyRegistered verification module · frontier
Read the description recorded in the module registry
HYP.PHI0.01: the phi0 leading term from icosahedral combinatorics (sharpening v312/v395). [E] ICO COUNTS ANCHOR-FORCED: V=12, E=30=h(E8), F=20=g_car(g_car-1), |Aut|=120=4h=|2I|. [E] LEADING TERM EXACT: phibase=1/(6 pi)=(4/3)c3=F/(4h pi)=F/(|Aut| pi)=(F/(g_car N_fam))c3. [E] F/h=|Z2|/N_fam; phibase=(F/h)/(4 pi)=c3(g_car-1)/N_fam. [E] GAUSS-BONNET: icosahedron deficit sum 4 pi; c3=1/(|Z2| 4 pi) (v216/v342). [E] HONEST NEGATIVE: puncture 48 c3^4 not rational hypergraph fraction. [C] phibase = (hyperedges)/(g_car N_fam) x c3, not independent injection; puncture [O].
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