The Crossing in the Rival Plane

All-Fields programme paper (All-Fields Run, Batch 19 (AF)), November 2026. Written November 2026; publicly deposited 9 November 2026. The extremal gap's zero set as a function of ΛCDM's own point — the last of the configuration's points to be moved — is the boundary of a rectangle: ΛCDM w0 in [−1.00, −0.66], ΛCDM wa in [−1.3875, −0.1125], at the record centre and the current generation's uncertainties, with the frame standing at its own point and its minimum frozen at 2.125000, set by its w0 term. The gap — the rival's extremal distance less that frozen value — stands negative exactly inside the rectangle, at zero exactly on its boundary, and positive everywhere outside it: the candidate plane's closed boundary with its sign reversed, confirmed at every one of the plane's 2,793 graded points with zero exceptions. ΛCDM's banked point (−1.0, 0.0) stands outside the rectangle at the record gap +0.375000, and its standardized distance to the zero set is 0.375000 — the gap entire, the mirror of the candidate plane's banked distance — attained at the rectangle's corner (−1.00, −0.1125), the one point of the set that shares the banked point's w0. With this grading the four planes stand complete at the current generation:

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-09
DOI
https://doi.org/10.5281/zenodo.24089267
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

The Crossing in the Rival Plane

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

The Crossing in the Rival Plane

William Alexander Aldred
preprint en

Abstract

All-Fields programme paper (All-Fields Run, Batch 19 (AF)), November 2026. Written November 2026; publicly deposited 9 November 2026. The extremal gap's zero set as a function of ΛCDM's own point — the last of the configuration's points to be moved — is the boundary of a rectangle: ΛCDM w0 in [−1.00, −0.66], ΛCDM wa in [−1.3875, −0.1125], at the record centre and the current generation's uncertainties, with the frame standing at its own point and its minimum frozen at 2.125000, set by its w0 term. The gap — the rival's extremal distance less that frozen value — stands negative exactly inside the rectangle, at zero exactly on its boundary, and positive everywhere outside it: the candidate plane's closed boundary with its sign reversed, confirmed at every one of the plane's 2,793 graded points with zero exceptions. ΛCDM's banked point (−1.0, 0.0) stands outside the rectangle at the record gap +0.375000, and its standardized distance to the zero set is 0.375000 — the gap entire, the mirror of the candidate plane's banked distance — attained at the rectangle's corner (−1.00, −0.1125), the one point of the set that shares the banked point's w0. With this grading the four planes stand complete at the current generation:

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