A registered result in its source context
Original ledger classification: Correction calculus [E]/[C] (each sector's gap sets its first-correction size; (2/3)^6 family vs golden family; the harvest of v383)
Recorded statement: The practical harvest of v383 (2026-06-24): the same spectral gap that makes each sector parameter-free ALSO sets the SIZE of its first correction -- for a gapped operator the deviation from the attractor decays at the ratio…
Statement, assumptions and sources
Paper context: Origin Theory
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CORRECTIONS.GAP.01
Original ledger classification: Correction calculus [E]/[C] (each sector's gap sets its first-correction size; (2/3)^6 family vs golden family; the harvest of v383)
Original claim text
The practical harvest of v383 (2026-06-24): the same spectral gap that makes each sector parameter-free ALSO sets the SIZE of its first correction -- for a gapped operator the deviation from the attractor decays at the ratio lambda_2/lambda_1 per step, so that ratio IS the leading-correction size. [E] FLAVOR: lambda_1=1, lambda_2=(2/3)^6=64/729 => first Koide correction ~0.0878 (v56/v82). [E] RECOVERY: the seam QECC Petz rate is the same (2/3)^6 (v221). [E] QG DECOUPLING: the ambient correction is bounded by chi=1/(1-(2/3)^6)=729/665 (finite, v337). [E] DISCRETE COMPILER: the main-branch update T_net=(A+2I)/4 fixes the Kac marks (lambda_1=1) and has subleading lambda_2=(phi+2)/4~0.9045 -- the compiler transient decays at the golden rate (carrier-5 facet, v303/v312). [E] UNIFIED: correction_n~(lambda_2/lambda_1)^n everywhere; the rates split into the (2/3)^6 family (flavor/recovery/QG, family-3 dynamic, in Q) and the golden family (the compiler, carrier-5 static, in Q(sqrt5)) -- the two number-field facets of v314/v383. [C] the correction calculus: the gap does double duty -- it is both WHY there is no free parameter and HOW BIG the first correction is, so the magnitude of sub-leading effects across TFPT is organised, not free.
Original classification detail
[E] the four computed correction rates + the unified (lambda_2/lambda_1)^n form + the two-facet split (Q vs Q(sqrt5)); [C] the correction-calculus reading. A harvest/application of v383 (as v303/v337 are of v56); reuses established eigenvalues, introduces no new number.
Dependencies as recorded
v56; v82; v221; v303; v312; v314; v337; v383
Open the original ledger source, row 450Location recorded in the ledger
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- Origin Theory
Sections that explicitly cite this claim
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- 2026-06-24 (Harvesting the QFT/gravity machinery: v385 the UV-branch kill-test surface, v386 the graviton-exchange amplitude, v387 the gap-driven correction calculus)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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 unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-24 (Typed correction budget: v388 the gap correction is keyed to the mechanism class, not a uniform band)Research changelog; TFPT — Introduction and reading guide
- 2026-06-24 (Website: an animated ``Universal Gap Lab'' visualising v383– v391)Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-24 (Completing the Coxeter clock: v390 the prime-2 (Gaussian / [formula in source] -seam) facet of [formula in source] )Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointOrigin Theory
- 2026-06-24 (Lean 4: FORM.SPECTRALGAP.01 formalises the scalar core of the universal spectral-gap principle)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v387_corrections_gap.pyRegistered verification module · frontier
Read the description recorded in the module registry
CORRECTIONS.GAP.01: the practical harvest of v383 -- the same spectral gap that makes each sector parameter-free ALSO sets the SIZE of its first correction (correction_n ~ (lambda_2/lambda_1)^n). [E] FLAVOR: lambda_2=(2/3)^6=64/729 => first Koide correction ~0.088 (v56/v82). [E] RECOVERY: the same (2/3)^6 Petz rate (v221). [E] QG: capped by chi=1/(1-(2/3)^6)=729/665 (v337). [E] DISCRETE COMPILER: the update (A+2I)/4 fixes the Kac marks (lambda_1=1) and decays at the golden (phi+2)/4~0.905 (carrier-5 facet, v303/v312). [E] the rates split into the (2/3)^6 family (family-3, in Q) and the golden family (carrier-5, in Q(sqrt5)) -- the two facets of v314/v383. [C] the correction calculus: the gap does double duty (WHY no free parameter AND HOW BIG the first correction), so sub-leading magnitudes are organised, not free. No new number.
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