Λ Stationary, H₀ Local: A Phase-Lattice Correspondence for the Hubble Tension

Version 2 (2026 Jul). Second version of the 2026 Jan deposit under this concept DOI, rewritten rather than amended. v1 presented the 8.4% lattice step as the output of a proposed mechanism, a coherence-scale trigger at L_f = v_c^2/a_0. That trigger was pre-registered against 123 SPARC rotation curves and falsified, and the threshold program built on it is retired. v1's own stated falsifier, discrete clustering of local H_0 determinations, was separately examined and not detected. Both negative results are reported here against their registered criteria. What survives is an arithmetic correspondence, stated conditionally: under C(Θ) = 2 sin^2(π Θ), the ratio between adjacent bosonic positions at the H_0 well is 1.0837, carrying 67.4 to 73.04 km/s/Mpc, against 0.27% at Λ under the same step. That ratio is fixed once four choices are stipulated, all imported from the base framework rather than derived here, and H_0 is itself the framework's calibration anchor. Also corrected from v1: the title, since Λ is stationary to first order but not invariant under a finite step, moving by 0.27% rather than zero; the phase variable, renamed from α to Θ to avoid collision with the fine-structure constant; and the propagation prediction of intermediate H_0 values for geometric methods, withdrawn as numerically wrong. Latest derviation of this paper can be found at github.com/hubble-tension

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-30
DOI
https://doi.org/10.5281/zenodo.21710944
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Λ Stationary, H₀ Local: A Phase-Lattice Correspondence for the Hubble Tension

Blake Shatto
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Λ Stationary, H₀ Local: A Phase-Lattice Correspondence for the Hubble Tension

Blake Shatto
preprint en

Abstract

Version 2 (2026 Jul). Second version of the 2026 Jan deposit under this concept DOI, rewritten rather than amended. v1 presented the 8.4% lattice step as the output of a proposed mechanism, a coherence-scale trigger at L_f = v_c^2/a_0. That trigger was pre-registered against 123 SPARC rotation curves and falsified, and the threshold program built on it is retired. v1's own stated falsifier, discrete clustering of local H_0 determinations, was separately examined and not detected. Both negative results are reported here against their registered criteria. What survives is an arithmetic correspondence, stated conditionally: under C(Θ) = 2 sin^2(π Θ), the ratio between adjacent bosonic positions at the H_0 well is 1.0837, carrying 67.4 to 73.04 km/s/Mpc, against 0.27% at Λ under the same step. That ratio is fixed once four choices are stipulated, all imported from the base framework rather than derived here, and H_0 is itself the framework's calibration anchor. Also corrected from v1: the title, since Λ is stationary to first order but not invariant under a finite step, moving by 0.27% rather than zero; the phase variable, renamed from α to Θ to avoid collision with the fine-structure constant; and the propagation prediction of intermediate H_0 values for geometric methods, withdrawn as numerically wrong. Latest derviation of this paper can be found at github.com/hubble-tension

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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