Two Objects, One Name: The DESI Fork Reconciled — a Theorem About Λ_int, Two Imported Laws, and the Clock Schedule That Can Carry the Data's Sign

Discharges debt D-001-040-74, the internal reconciliation house paper #28 (The DESI Fork, Scored) left as its third debt. In the frame's rate variables (house paper #7: w + 1 = (2/3) Gamma, Gamma'(1) = -(3/2) w_a) the integration-constant theorem is the branch Gamma = 0 identically, while Laws C and D recompute to Gamma(1) = 0.172353 (Law C) and 0.045980 / 0.177353 / 0.413824 (Law D), all with Gamma'(1) <= 0. The category check: the theorem constrains Lambda_int, whose density has d rho/d ln a = 0 identically, while each law requires d ln rho_DE/d ln a = -3(1+w0) != 0 at a = 1 (-0.344705 for Law C; -0.091962 to -0.827646 for Law D). Identified with Lambda_int the laws contradict d_mu Lambda = 0 by those amounts: as derivations of the frame's cosmological constant they are wrong, because their premises are imported ansatze (Law C's evolution equation is Li's 2004 event-horizon holographic postulate, imported by the Link-3 attack as its T1 postulate; the EC+HT action contains no horizon functional) — the frame's owned machinery selects the theorem uniquely for its own Lambda sector. As effective descriptions under a trivial clock schedule the laws are instead bounded by the theorem's sector (Gamma'(1) <= 0, w_a >= 0, theorem point as boundary), which is the domain #28 scored and excluded. The third object, the parent clock schedule, is formalised for the first time: with the true universe exactly LambdaCDM, an observer schedule ln m = mu1 ln a + mu2 (ln a)^2/2 reconstructs all four DESI DR2 central pairs of #28 exactly (mu1, mu2) = (0.5960, 2.5978), (0.1665, 0.9262), (0.3422, 1.6590), (0.2548, 1.3055), while a one-parameter schedule m = a^mu provably cannot reach the freezing quadrant with w0 > -1 (sign lock, scanned). The schedule is fitted input, not a prediction: debt D-001-040-73 (a definite pre-registered parent-schedule prediction) stands, sharpened by the curvature condition. #28's scoring is untouched; the vacuum conversion remains NOT SOLVED. Graded DERIVED-INDEPENDENT, with the EXTENSION border argued in the QA.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23926593
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Two Objects, One Name: The DESI Fork Reconciled — a Theorem About Λ_int, Two Imported Laws, and the Clock Schedule That Can Carry the Data's Sign

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Two Objects, One Name: The DESI Fork Reconciled — a Theorem About Λ_int, Two Imported Laws, and the Clock Schedule That Can Carry the Data's Sign

William Alexander Aldred
preprint en

Abstract

Discharges debt D-001-040-74, the internal reconciliation house paper #28 (The DESI Fork, Scored) left as its third debt. In the frame's rate variables (house paper #7: w + 1 = (2/3) Gamma, Gamma'(1) = -(3/2) w_a) the integration-constant theorem is the branch Gamma = 0 identically, while Laws C and D recompute to Gamma(1) = 0.172353 (Law C) and 0.045980 / 0.177353 / 0.413824 (Law D), all with Gamma'(1) <= 0. The category check: the theorem constrains Lambda_int, whose density has d rho/d ln a = 0 identically, while each law requires d ln rho_DE/d ln a = -3(1+w0) != 0 at a = 1 (-0.344705 for Law C; -0.091962 to -0.827646 for Law D). Identified with Lambda_int the laws contradict d_mu Lambda = 0 by those amounts: as derivations of the frame's cosmological constant they are wrong, because their premises are imported ansatze (Law C's evolution equation is Li's 2004 event-horizon holographic postulate, imported by the Link-3 attack as its T1 postulate; the EC+HT action contains no horizon functional) — the frame's owned machinery selects the theorem uniquely for its own Lambda sector. As effective descriptions under a trivial clock schedule the laws are instead bounded by the theorem's sector (Gamma'(1) <= 0, w_a >= 0, theorem point as boundary), which is the domain #28 scored and excluded. The third object, the parent clock schedule, is formalised for the first time: with the true universe exactly LambdaCDM, an observer schedule ln m = mu1 ln a + mu2 (ln a)^2/2 reconstructs all four DESI DR2 central pairs of #28 exactly (mu1, mu2) = (0.5960, 2.5978), (0.1665, 0.9262), (0.3422, 1.6590), (0.2548, 1.3055), while a one-parameter schedule m = a^mu provably cannot reach the freezing quadrant with w0 > -1 (sign lock, scanned). The schedule is fitted input, not a prediction: debt D-001-040-73 (a definite pre-registered parent-schedule prediction) stands, sharpened by the curvature condition. #28's scoring is untouched; the vacuum conversion remains NOT SOLVED. Graded DERIVED-INDEPENDENT, with the EXTENSION border argued in the QA.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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