A registered result in its source context
Original ledger classification: Identity [I] (cusp-frame anchor reading + equivalences) + [P] (the one assignment)
Recorded statement: BOTH DUAL NORMALS ARE ANCHOR DATA (R4' at one discrete assignment): the pairings of the torsion normal n = (5,-9,6) with the cusp eigenbasis (v98) are EXACTLY (n.e1, n.e2, n.e3) = (6,3,5) = (p_2(a), p_0(a), e_2(a)) - the anchor's second…
Statement, assumptions and sources
Paper context: Research contracts
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GATE.UWALL.14
Original ledger classification: Identity [I] (cusp-frame anchor reading + equivalences) + [P] (the one assignment)
Original claim text
BOTH DUAL NORMALS ARE ANCHOR DATA (R4' at one discrete assignment): the pairings of the torsion normal n = (5,-9,6) with the cusp eigenbasis (v98) are EXACTLY (n.e1, n.e2, n.e3) = (6,3,5) = (p_2(a), p_0(a), e_2(a)) - the anchor's second power sum, zeroth power sum and second elementary symmetric function, one per Q_+ degree; the cusp matrix is unimodular so the three pairings determine n uniquely. With d = (3/2)a - 2*1 (v139) the dual normal PAIR (v134) is anchor data through and through - one normal per frame. Equivalences exact: cusp data (6,3,5) <=> frame pairings (2,8,121) (v139/v142) <=> the w0-lift (v145). AUDIT (not promoted): sigma -> cusp (5,1,2); alternate reading (6,3,5) = (|R+(A3)|, N_fam, g_car); sum 14 = dim G2. STATUS: R4' = derive the ASSIGNMENT (why degrees (1,2,3) carry (p_2, p_0, e_2) in that order) - one discrete assignment, zero continuous freedom, all values anchor invariants
Original classification detail
Identity [I]: n = (p2,p0,e2)(a) in the cusp frame; R4' = one assignment
Dependencies as recorded
GATE.UWALL.13; GATE.UWALL.12; FLAV.DUAL.01; v98; v139; v145
Open the original ledger source, row 234Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
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- 2026-06-12 (third round: both normals anchor data; the R3 mechanism exists, v149– v150)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- Research Contract 1 — [formula in source]tfpt research contracts
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v149_cusp_normal.pyRegistered verification module · registry
Read the description recorded in the module registry
both dual normals are ANCHOR DATA (R4′): in the cusp frame n pairs to (6,3,5) = (p₂,p₀,e₂)(a) — one anchor invariant per Q₊ line (d = (3/2)a−2·1 in the generation frame); equivalent to (2,8,121) and the w₀-lift; residue = ONE assignment (which invariant on which line)
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