RSIT Relational Paths Package — Completed: Four Conditioned Trajectories, Scale-Relative Measure, and Equation Translation (2 November 2026)

Working package, not a journal paper. Not a detection. Not a joint MCMC. Does not revise the locked core. Prior deposits are not replaced. Four agents begin back-to-back at a common origin with identical initial momentum. Each successive step is the retention of a discrete option from the locked geometric set (φ-power or 36° family activation) that local conditions allow and do not reject. The resulting trajectories are relational and non-mirrored. The underlying option set is the golden spiral construction and regular pentagon that freeze w₀ = −φ/2 and wₐ = −1/φ. Residual class A ≈ 0.040 keeps a positive remainder at every finite stage so the relative measure never closes. Ultimate reference sits outside the residual centre. Equation translation: w₀ = −φ/2 = −cos 36° wₐ = −1/φ = −2 sin 18° z = 1/√5 A ≈ 0.040 (window [0.03, 0.05]) Retained = Select(Options | Conditions) Zero extra free parameters. No fourth door. Companion to the geometric construction package (10.5281/zenodo.23888446). Assembly and algebra check: Grok (xAI), editor line only. Not a co-author claim.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23890569
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
Field-Weighted Citation Impact
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article

RSIT Relational Paths Package — Completed: Four Conditioned Trajectories, Scale-Relative Measure, and Equation Translation (2 November 2026)

Daryl Jacobs
5 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
article

RSIT Relational Paths Package — Completed: Four Conditioned Trajectories, Scale-Relative Measure, and Equation Translation (2 November 2026)

Daryl Jacobs
article en

Abstract

Working package, not a journal paper. Not a detection. Not a joint MCMC. Does not revise the locked core. Prior deposits are not replaced. Four agents begin back-to-back at a common origin with identical initial momentum. Each successive step is the retention of a discrete option from the locked geometric set (φ-power or 36° family activation) that local conditions allow and do not reject. The resulting trajectories are relational and non-mirrored. The underlying option set is the golden spiral construction and regular pentagon that freeze w₀ = −φ/2 and wₐ = −1/φ. Residual class A ≈ 0.040 keeps a positive remainder at every finite stage so the relative measure never closes. Ultimate reference sits outside the residual centre. Equation translation: w₀ = −φ/2 = −cos 36° wₐ = −1/φ = −2 sin 18° z = 1/√5 A ≈ 0.040 (window [0.03, 0.05]) Retained = Select(Options | Conditions) Zero extra free parameters. No fourth door. Companion to the geometric construction package (10.5281/zenodo.23888446). Assembly and algebra check: Grok (xAI), editor line only. Not a co-author claim.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 16%
Advanced Mathematical Theories and Applications
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