The Hubble Ladder: Complete Self-Referential Classification of H0 Measurements and the φ-Rung Spectrum of the R12 Rendering Algebra
Abstract
We present a zero-parameter resolution of the Hubble tension within the Array Cosmology (AC) framework. The R12 rendering algebra predicts a true expansion rate Htrue 0 = 66.6 km/s/Mpc from the Friedmann equation with axiom-derived density parameters, consistent with Planck CMB (67.36±0.54, 1.5σ). We identify a systematic bias in Cepheid-calibrated distance ladder measurements arising from rendering friction: the irreducible Landauer erasure cost Znoise = (π−3) ln 2 ≈ 0.098 of
the discrete 12-axis substrate. This friction biases periodic pulsation measurements by a factor (1+Znoise), yielding H Cepheid
0 = 66.6×1.098 = 73.1 km/s/Mpc, matching SH0ES (73.04±1.04, 0.05σ). Snapshot-type measurements (CMB, BAO, TRGB) are
immune because angular ratios cancel the friction. The ratio H0(SH0ES)/H0(AC) = 1 + Znoise holds to 0.07% precision. Six falsifiable predictions are presented.
The Hubble tension is not a measurement error but the thermodynamic cost of computing a periodic process on a discrete circular lattice.
Related
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- Self-Referential Fixed Points and the Physical Horizon of NP-Complete Computation: A Structural Analog of Gödel–Löb Incompleteness in Resource-Bounded Computation
- The Barbero–Immirzi Parameter, Black-Hole Entropy, and the Area Gap from the R12 Rendering Algebra: McKayFolding, the SU(2)4 Horizon Category, and the Complete Entropy Expansion
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BibTeX
@misc{lim2026hubble,
title = {{The Hubble Ladder: Complete Self-Referential Classification of H0 Measurements and the φ-Rung Spectrum of the R12 Rendering Algebra}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603880},
url = {https://zenodo.org/records/23603880},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Hubble Ladder: Complete Self-Referential Classification of H0 Measurements and the φ-Rung Spectrum of the R12 Rendering Algebra
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603880
UR - https://zenodo.org/records/23603880
AB - We present a zero-parameter resolution of the Hubble tension within the Array Cosmology (AC) framework. The R12 rendering algebra predicts a true expansion rate Htrue 0 = 66.6 km/s/Mpc from the Friedmann equation with axiom-derived density parameters, consistent with Planck CMB (67.36±0.54, 1.5σ). We identify a systematic bias in Cepheid-calibrated distance ladder measurements arising from rendering friction: the irreducible Landauer erasure cost Znoise = (π−3) ln 2 ≈ 0.098 of the discrete 12-axis substrate. This friction biases periodic pulsation measurements by a factor (1+Znoise), yielding H Cepheid 0 = 66.6×1.098 = 73.1 km/s/Mpc, matching SH0ES (73.04±1.04, 0.05σ). Snapshot-type measurements (CMB, BAO, TRGB) are immune because angular ratios cancel the friction. The ratio H0(SH0ES)/H0(AC) = 1 + Znoise holds to 0.07% precision. Six falsifiable predictions are presented. The Hubble tension is not a measurement error but the thermodynamic cost of computing a periodic process on a discrete circular lattice.
ER -