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A registered result in its source context

Original ledger classification: Identity [E] (RR arithmetic) + Physical [C] (carrier identification)

Recorded statement: THE RIEMANN-ROCH CARRIER READING (external-review proposal 2026-06-14): (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=mu4 on P^1. [E]: h^0(P^1,O(mu4))=deg+1=5 (function side) and rank…

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Paper context: Origin Theory

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ARCH.RRCAR.01

Original ledger classification: Identity [E] (RR arithmetic) + Physical [C] (carrier identification)

Original claim text

THE RIEMANN-ROCH CARRIER READING (external-review proposal 2026-06-14): (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=mu4 on P^1. [E]: h^0(P^1,O(mu4))=deg+1=5 (function side) and rank H_1(P^1\\mu4)=deg-1=3 (cycle side, already QGEO.COHOM.01/v177); g_car=5=rank(D5) (carrier=so(10) half-spinor, rank D5+rank A3=5+3=8=rank E8, v1), N_fam=3=(dim S+ -1)/g_car. [C]: the identification 'carrier = the meromorphic seam-mode space H^0(P^1,O(mu4))' is a geometric reading (less number, more geometry), matched by rank(D5)=5, but the physical identification is conjectural and does NOT replace the over-determined g_car=5 (Pascal v2, bootstrap v6, Lean FORM.LADDER.01) -- it is a fourth, geometric reading; h^0 and rank H_1 are both fixed by deg=4 (one object, two invariants: a unification, not extra over-determination). Exact; Wolfram-mirrored

Original classification detail

Identity [E] for h^0=5=rank(D5)=g_car and rankH1=3=N_fam from one mu4 divisor; [C] for the carrier=mode-space identification (does not replace the over-determined g_car=5)

Dependencies as recorded

ARCH.CORE.01; AX.P2.01; QGEO.COHOM.01; E8.GLU.01; v177_seam_marking_kernel.py; v1_e8_glue.py

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Registered verification modules

  • v189_riemann_roch_carrier.pyRegistered verification module · registry
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    the Riemann-Roch carrier reading: (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=µ₄ on P¹. [E] math: h⁰(P¹,O(µ₄))=deg+1=5 (function side) and rank H₁(P¹∖µ₄)=deg−1=3 (cycle side, already QGEO.COHOM.01/v177); g_car=5=rank(D₅) (carrier=so(10) half-spinor, rank D₅+rank A₃=5+3=8, v1), N_fam=3=(dim S⁺−1)/g_car. [C]: 'carrier = the meromorphic seam-mode space H⁰(P¹,O(µ₄))' is a geometric reading (less number, more geometry) matched by rank(D₅)=5, but the physical identification is conjectural and does NOT replace the over-determined g_car=5 (Pascal/bootstrap/Lean) — a fourth, geometric reading. h⁰ and rank H₁ are both fixed by deg=4 (one object, two invariants).

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