A registered result in its source context
Original ledger classification: Identity (exact index) [E]/[C]/[O]
Recorded statement: RIEMANN-ROCH INDEX GATE (2026-06-16): P2 as the mode space of a degree-4 seam divisor (bedrock LANGUAGE for P2, NOT a proof from nothing). deg D=4=|mu4| on P^1 => h0(O(D))=deg+1=5=g_car (Riemann-Roch, genus 0); rank H1(P^1 minus 4…
Statement, assumptions and sources
Paper context: Origin Theory
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Read the exact registered claim and its dependencies
QGEO.RR.01
Original ledger classification: Identity (exact index) [E]/[C]/[O]
Original claim text
RIEMANN-ROCH INDEX GATE (2026-06-16): P2 as the mode space of a degree-4 seam divisor (bedrock LANGUAGE for P2, NOT a proof from nothing). deg D=4=|mu4| on P^1 => h0(O(D))=deg+1=5=g_car (Riemann-Roch, genus 0); rank H1(P^1 minus 4 marks)=4-1=3=N_fam; h0+rank H1=8=rank E8, h0-rank H1=2=|Z2|, (h0+rank H1)/2=4=|mu4|; Lambda^even(C^5)=1+10+5=16=dim S^+ (the D5 half-spinor, ARCH.RRCAR.02). Negative controls: deg 3->(4,2), deg 5->(6,4), colliding marks lower H1 and break N_fam. Relocates P2 from '5 slots' to 'the genus-0 mode count of a 4-mark divisor', conditional on the raw seam producing the degree-4 divisor (=QGEO.SYM.01).
Original classification detail
[E] deg-4 divisor => (h0,rankH1)=(5,3)=(g_car,N_fam), sum 8=rank E8, even Clifford 16=dim S^+; mode-space reading [C], the seam->divisor step [O] (=QGEO.SYM.01)
Dependencies as recorded
ARCH.RR.01; ARCH.RRCAR.02; QGEO.SYM.01
Open the original ledger source, row 310Location recorded in the ledger
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- Origin Theory
Sections that explicitly cite this claim
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- 2026-06-16 (the icosahedral bedrock, CM-norm duality, and a structural-finds round)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- Front matter / supportResearch contracts
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The whole integer skeleton from one pair [formula in source]Origin Theory
- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-07-21 (IX) ( v499 — the P2 weight-typing postulate HARDENED: the anchor [formula in source] typed as the Birkhoff–Grothendieck splitting exponents of the Deligne canonical extension, so integrality/positivity/sum- [formula in source] become theorems given the \ anchors; the v491 check-9 residual sharpened, the tfpt_2 ``balanced'' selection typed as stability; Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves — AX.P2.01 stays a declared axiom, QGEO.SYM stays )Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
All 10 linked sections
- The whole integer skeleton from one pair [formula in source]
- 2026-07-20 (III) ( v491 — [formula in source] as the partition COROLLARY of the four marks: [formula in source] into exactly [formula in source] positive parts is uniquely [formula in source] , sharpening v53; the residual is the weight-typing postulate — AX.P2.01 stays a declared axiom; no gate closes, no marker moves)
Registered verification modules
- v228_rr_index_gate.pyRegistered verification module · core
Read the description recorded in the module registry
P2 as the mode space of a degree-4 seam divisor (a Riemann-Roch INDEX GATE; bedrock language for P2, not a proof from nothing). deg D=4=|μ₄| on P¹ ⇒ h⁰(O(D))=5=g_car (Riemann-Roch, genus 0); rank H₁(P¹ minus 4 marks)=3=N_fam; h⁰+rankH₁=8=rank E₈, h⁰−rankH₁=2=|Z₂|; Λᵉᵛᵉⁿ(C⁵)=1+10+5=16=dim S⁺. Conditional on the raw seam producing the degree-4 divisor (=QGEO.SYM.01).
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