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Original ledger classification: Typed correction budget [E]/[C] (the gap correction is keyed to the mechanism class, not a uniform band; seam-gapped=(2/3)^6/golden, exact-identity=0, external-rate=external, fixed-point=explicit texture)

Recorded statement: The gap correction (v387) is a TYPED budget, NOT a uniform band on every prediction (2026-06-24): the (lambda_2/lambda_1)^n size is a property of the distance from a gapped operator's leading eigenvector, so it is only defined where a…

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Paper context: Origin Theory

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CORRECTIONS.BUDGET.01

Original ledger classification: Typed correction budget [E]/[C] (the gap correction is keyed to the mechanism class, not a uniform band; seam-gapped=(2/3)^6/golden, exact-identity=0, external-rate=external, fixed-point=explicit texture)

Original claim text

The gap correction (v387) is a TYPED budget, NOT a uniform band on every prediction (2026-06-24): the (lambda_2/lambda_1)^n size is a property of the distance from a gapped operator's leading eigenvector, so it is only defined where a subleading lambda_2 exists. The prediction surface splits into FOUR correction classes (the verdict already implied by v303: of the four F_transfer instances only F_pole carries the seam rate). [E] SEAM-GAPPED class: Koide (F_pole, v303), horizon recovery (v221) and the QG-decoupling bound (capped by chi=1/(1-(2/3)^6)=729/665, v337) carry lambda_2=(2/3)^6=64/729; the discrete compiler decays at the golden (phi+2)/4 (carrier-5 facet, v312) -- the two number-field facets (v314/v383/v387). [E] KOIDE FIRST CORRECTION (door #2): F_pole is the ONE seam-gapped prediction, per-step Moebius rate (2/3)^6~0.0878 (v371), while the source quotient Q_src=0.66446 sits 0.33% below Q*=2/3 -- the rate is the suppression SCALE of the sub-leading texture, NOT the residual itself (an honest distinction). [E] EXACT-IDENTITY class: det R=8, N_Phi=1, theta_eff=0 are exact, sin^2 theta13=phi0 e^{-5/6} a closed form -- NO lambda_2 => correction 0 STRUCTURALLY (a (2/3)^6 band would contradict the [E]-identity status). [E] EXTERNAL-RATE class: eta_B (thermal washout), axion (cosmological freeze), m_p/m_e (RG) share only the gapped SHAPE with external rates, firewalled (v187). [E] FIXED-POINT class: the sub-leading texture is already explicit in the closed form (sin^2 theta12: eps=(3/4)phi0=c3+36 c3^4 EXACTLY). [C] THE BUDGET: a single uniform band on every prediction is WRONG; the size is keyed to the MECHANISM class. A typing of v387 (as v384 is of v383), no new number.

Original classification detail

[E] the four-class classification + the seam (2/3)^6 and golden (phi+2)/4 rates + the exact-identity zero-correction facts (det R=8, N_Phi=1, theta_eff=0) + the explicit theta12 texture (eps=c3+36 c3^4); [C] the typed-correction-budget reading. A typing of v387 (as v384 is of v383); reuses established eigenvalues and closed forms, introduces no new number.

Dependencies as recorded

v303; v371; v383; v387; v314; v337; v221; v312; v187

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  • v388_corrections_budget.pyRegistered verification module · frontier
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    CORRECTIONS.BUDGET.01: the gap correction (v387) is a TYPED budget, NOT a uniform band on every prediction -- the (lambda_2/lambda_1)^n size is a property of the distance from a gapped operator's leading eigenvector, so it is only defined where lambda_2 exists. The prediction surface splits into four correction classes (already implied by v303). [E] SEAM-GAPPED: Koide (F_pole v303), recovery (v221), the QG bound (capped by chi=729/665, v337) carry (2/3)^6; the discrete compiler decays at the golden (phi+2)/4 (v312). [E] KOIDE FIRST CORRECTION (door #2): F_pole is the ONE seam-gapped prediction, rate (2/3)^6~0.0878 (v371), source quotient 0.33% below 2/3 -- the rate is the suppression SCALE, not the residual. [E] EXACT-IDENTITY class (det R=8, N_Phi=1, theta_eff=0, sin^2 theta13): no lambda_2 => correction 0 STRUCTURALLY (a band would contradict [E]). [E] EXTERNAL-RATE class (eta_B/axion/m_p,m_e): the gapped shape with external rates (only F_pole has the seam rate, v303), firewalled (v187). [E] FIXED-POINT class: the texture is already explicit (theta12 eps=c3+36 c3^4). [C] a uniform band on all predictions is WRONG; the size is keyed to the mechanism class. A typing of v387, no new number.

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