A registered result in its source context
Original ledger classification: Sheet generator V is a binary compiler [E]/[C]: V^n closed form + V^n.1 binary spine + four bilinear families (6,7,9,11; 13,27,55,56); spine FORCED by Spec(V)={0,1,2}, Lie/theta readings audit-typed [C]
Recorded statement: The sheet generator V is a binary internal compiler (2026-06-24): the rank-2 sheet axis V=Q diag(0,1,1) of the centered cross (v95/v218) has powers that print the binary carrier spine. [E] CLOSED FORM (induction F(n)*V=F(n+1)):…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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Read the exact registered claim and its dependencies
SHEET.GEN.BINARY.01
Original ledger classification: Sheet generator V is a binary compiler [E]/[C]: V^n closed form + V^n.1 binary spine + four bilinear families (6,7,9,11; 13,27,55,56); spine FORCED by Spec(V)={0,1,2}, Lie/theta readings audit-typed [C]
Original claim text
The sheet generator V is a binary internal compiler (2026-06-24): the rank-2 sheet axis V=Q diag(0,1,1) of the centered cross (v95/v218) has powers that print the binary carrier spine. [E] CLOSED FORM (induction F(n)*V=F(n+1)): V^n={{0,2^(n-1),0},{0,2^n,0},{0,2^(n+1)-2,1}}, so V^n.1=(2^(n-1),2^n,2^(n+1)-1)=(1,2,3),(2,4,7),(4,8,15),(8,16,31),... [E] BILINEAR FAMILIES (exact in n, 1=(1,1,1), a=(1,1,2)): 1.V^n.1=7*2^(n-1)-1, 1.V^n.a=7*2^(n-1), a.V^n.a=11*2^(n-1), a.V^n.1=11*2^(n-1)-2; at n=1 = (6,7,9,11). [E] readouts 1.V^2.1=13=Delta_Q, 1.V^3.1=27=1.R.a, 1.V^4.1=55=quark numerator, 1.V^4.a=56=dim 56_E7; 11=a.V.a the anchor amplitude. [C] SPINE READING (audit, NOT promoted): the spine {2^(k-1),2^k,2^(k+1)-1} is FORCED by Spec(V)={0,1,2}; the matches (1,2,3)=A3 exponents, (2,4,7)=(|Z2|,|mu4|,7), (4,8,15)=(|mu4|,rank E8,dim A3), (8,16,31)=(rank E8,dim S+,2^g_car-1=248/8) are audit Lie/dimension matches (v95 typing). [C] THETA CROSS-LINK (audit raster): sigma3(2)=9=a.V.1=N_fam^2, sigma3(3)=28=1.V^3.a=det(I+R), sigma3(5)=126 = local E7 root shell (tfpt_3).
Original classification detail
Identity
Dependencies as recorded
FLAV.KQ.01; v95; v218; v135
Open the original ledger source, row 478Location 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.
- Standard Model and flavor structure
- 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.
- 2026-06-24 (The sheet generator [formula in source] as a binary internal compiler: v410– v414)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 Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- 2026-06-25 (The cyclotomic norm triple [formula in source] the carrier-5 clock: v418)Research changelog; TFPT — Introduction and reading guide
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Front matter / supportStandard Model and flavor structure
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Group-theoretic audits (optional)E8 audit and bootstrap
- 2026-06-25 (The Gaussian operator [formula in source] the atom trichotomy: v415, v416)Research changelog; TFPT — Introduction and reading guide
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
Registered verification modules
- v410_sheet_generator_binary.pyRegistered verification module · registry
Read the description recorded in the module registry
The sheet generator V = Q diag(0,1,1) (the rank-2 sheet axis of the centered cross, v95/v218) is a binary internal compiler: V^n = ((0,2^(n-1),0),(0,2^n,0),(0,2^(n+1)-2,1)) (induction F(n)V=F(n+1)), so V^n.1 = (2^(n-1),2^n,2^(n+1)-1) = (1,2,3),(2,4,7),(4,8,15),(8,16,31); the bilinears 1.V^n.1=7*2^(n-1)-1, 1.V^n.a=7*2^(n-1), a.V^n.a=11*2^(n-1), a.V^n.1=11*2^(n-1)-2 give (6,7,9,11) at n=1 and 13=Delta_Q, 27=1.R.a, 55, 56=dim 56_E7; the binary spine is FORCED by Spec(V)={0,1,2}, the carrier (rank E8=8, dim S+=16, 248/8=31) and theta (sigma3(2)=9=a.V.1, sigma3(3)=28=1.V^3.a=det(I+R), sigma3(5)=126) readings audit-typed.
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