A registered result in its source context
Original ledger classification: Identity (exact)
Recorded statement: SPECTRAL RAMIFICATION LADDER (2026-06-15): for Q,K,C,F the characteristic polynomial splits as (t-r)(t^2-bt+c) with r rational, and the full cubic discriminant factors as Disc(chi)=q(r)^2 Disc(q): squares |q(r)| in…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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DIAMOND.SPECTRAL.01
Original ledger classification: Identity (exact)
Original claim text
SPECTRAL RAMIFICATION LADDER (2026-06-15): for Q,K,C,F the characteristic polynomial splits as (t-r)(t^2-bt+c) with r rational, and the full cubic discriminant factors as Disc(chi)=q(r)^2 Disc(q): squares |q(r)| in {1,3,4,6}=(N_Phi,N_fam,|mu4|,|R^+(A_3)|), kernels Disc(q) in {13,48,65,105}=(Delta_Q, Omega_adm, g_car Delta_Q, N_fam g_car 7), with Delta_Q=13=b^2+s^2=|R(A_3)|+1 the carrier-split norm (v14). The missing corner F carries the kernel 105=3*5*7=family*carrier*scalaron. Exact identity. (Audit blocks in the same module: the anchor-defect spectrum Delta_a(Q,K,R,C,L,F)=(8,16,18,21,24,26) and the pair-sum atlas/determinant staircase are AUDIT fingerprints -- the 28=2 dim G_2, 52=dim F_4 labels stay audit-only, not spine; F as transfer-completion corner is a HEURISTIC, not a hard filter)
Original classification detail
[E] Disc(chi)=q(r)^2 Disc(q) for Q,K,C,F: squares (1,3,4,6), kernels (13,48,65,105); audit/heuristic blocks honestly typed
Dependencies as recorded
v14_carrier_uniqueness.py; v94_sheet_diamond.py
Open the original ledger source, row 305Location recorded in the ledger
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- Standard Model and flavor structure
Sections that explicitly cite this claim
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- 2026-06-15 (the diamond axis geometry — two axes + the transfer corner)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- How to read this documenttfpt 1 architecture e8
- How to read this documentArchitecture, E8 and the electromagnetic fixed point
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- 2026-06-24 (The sheet generator [formula in source] as a binary internal compiler: v410– v414)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportStandard Model and flavor structure
- How to read this documenttfpt 1 architecture e8
- Front matter / supportStandard Model and flavor structure
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v218_diamond_axis_geometry.pyRegistered verification module · registry
Read the description recorded in the module registry
Diamond axis geometry: the Sheet Diamond (v94) is a discrete geometry with two axes around the centered cross (v95: C center, U winding, V sheet), and the missing corner F is the transfer completion. Three exact [E] lemmas + honest audit/heuristic typing, no new numbers. [E] AXIS CURVATURE: det(C+xU)=14+6x linear (winding flat, slope 6=|R⁺(A₃)|), det(C+yV)=14+14y+4y² quadratic with 2nd difference 8=rank E₈; det B(C+xU)=2 det(C+xU), anchor-block sheet 2nd difference 6=|R⁺(A₃)| — curvatures (8,6)=(rank E₈, |R⁺(A₃)|). [E] PLÜCKER TRANSFER LADDER: Pl(K)=(−1,6,4)→Pl(C)=(0,14,14)→Pl(F)=(1,22,30); C−K=(1,8,10)=(N_Φ,rank E₈,A_Λ), F−C=(1,8,16)=(N_Φ,rank E₈,dim S⁺) — decuple 10 then full generation 16 (identity [E], transfer reading [C]). [E] SPECTRAL RAMIFICATION: for Q,K,C,F the cubic discriminant=q(r)²·Disc(q); squares (1,3,4,6)=(N_Φ,N_fam,|μ₄|,|R⁺(A₃)|), kernels (13,48,65,105)=(Δ_Q,Ω_adm,g_car·Δ_Q,N_fam·g_car·7), F carries 105=3·5·7. [I] audit anchor-defect spectrum Δ_a(Q,K,R,C,L,F)=(8,16,18,21,24,26); [I] audit pair-sum atlas {12,24,28,36,40,52} total 64, staircase sum 81=N_fam⁴ — 28=2 dim G₂, 52=dim F₄ audit-only, not spine. [C] heuristic: F the transfer-completion corner, a search principle not a hard filter.
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