Spatial Constancy Fails Too: The Weaker Reading of Paper #234's Second Requirement in a Perturbed Universe

Computes the one corner packet #506's QA left uncomputed for item D-220-237-61: the weaker, spatial-only reading of paper #234's response requirement R2 (the Hoyle-Narlikar half-sum constant at every place at fixed time) in a perturbed universe. Gate reproduces packet #234's exhibits digit-for-digit (retarded sum 0.500000; advanced sums 40.5 / 4900.5 / 499000.5 in both cosmologies; negative-mass price 50.000000%) and packet #506's exhibits at its DECLARED inputs (eta_infty = 4.3898/H0 finite, R1 closed in remainder; m(eta) varying by factor 1.960, R2's temporal half refuted). In Hawking's reduced form, a single DECLARED plane-wave density perturbation gives the half-sum a spatial variation eps cos(k.x) [(1 - cos k eta) + (1 - cos kD)] / (2 k^2), D the future conformal range: amplitude 1.3614 eps at k eta_0 = pi today (0.4607% of the background 2.9551 at eps = 0.01), retarded-half nodes at 2 pi and 4 pi filled by the advanced half, and no mode below 0.01 eps in a 4,000-mode scan. Exact spatial constancy fails for generic modes at linear order: the weaker reading does not rescue R2. Disposition: the item stands at packet #506's surviving price unchanged -- R2 at full strength, R3 untouched (zero of four classes), paper #234's Door two unworked. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-03
DOI
https://doi.org/10.5281/zenodo.23936584
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Spatial Constancy Fails Too: The Weaker Reading of Paper #234's Second Requirement in a Perturbed Universe

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

Spatial Constancy Fails Too: The Weaker Reading of Paper #234's Second Requirement in a Perturbed Universe

William Alexander Aldred
preprint en

Abstract

Computes the one corner packet #506's QA left uncomputed for item D-220-237-61: the weaker, spatial-only reading of paper #234's response requirement R2 (the Hoyle-Narlikar half-sum constant at every place at fixed time) in a perturbed universe. Gate reproduces packet #234's exhibits digit-for-digit (retarded sum 0.500000; advanced sums 40.5 / 4900.5 / 499000.5 in both cosmologies; negative-mass price 50.000000%) and packet #506's exhibits at its DECLARED inputs (eta_infty = 4.3898/H0 finite, R1 closed in remainder; m(eta) varying by factor 1.960, R2's temporal half refuted). In Hawking's reduced form, a single DECLARED plane-wave density perturbation gives the half-sum a spatial variation eps cos(k.x) [(1 - cos k eta) + (1 - cos kD)] / (2 k^2), D the future conformal range: amplitude 1.3614 eps at k eta_0 = pi today (0.4607% of the background 2.9551 at eps = 0.01), retarded-half nodes at 2 pi and 4 pi filled by the advanced half, and no mode below 0.01 eps in a 4,000-mode scan. Exact spatial constancy fails for generic modes at linear order: the weaker reading does not rescue R2. Disposition: the item stands at packet #506's surviving price unchanged -- R2 at full strength, R3 untouched (zero of four classes), paper #234's Door two unworked. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.

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