PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
April 6, 20260 citationsOpen Access

Routh's Stability Criterion for the Lagrange Points Derived from a 22-Dimensional Fiber Geometry

View Full Paper
BJBrehnan Jones

Key Points

  • The research aims to derive Routh's stability criterion using a novel 22-dimensional circulatory model and verify its consistency across various independent domains.
  • Developed a 22-dimensional circulatory space divided into three fibers (Corpus, Nexus, Animus).
  • Derive three classes of three-body solutions based on time constants from a single free integer N=3.
  • Conducted 1,360 programmatic checks across ten different domains to verify the derived constants.
  • Demonstrated that the derived fiber dimensions match Routh's stability criterion with high precision.
  • Identified three classes of solutions with significant time constants (tauC=10, tauG=45, tauI=120).
  • Achieved zero verification failures across all tested domains, reinforcing the stability model's reliability.

Abstract

Abstract Circulatory Theory (CT) postulates a 22-dimensional circulatory space partitioned into three fibers (Corpus 8D, Nexus 6D, Animus 8D) with four forces governed by a single free integer N=3. In the first version of this paper (Zenodo v1), we showed that CT's fiber dimensions reproduce Routh's 1875 stability criterion for the restricted three-body problem with zero free parameters, matching at 12+ decimal places. This major revision extends the result in two directions. First, we derive three classes of three-body solution with time constants tauC=10, tauG=45, tauI=120, all falling out of N=3 through dimensional arithmetic. Second, we verify these constants across 10 independent domains -- Indian music, Western harmony, frequency space, sound classification, Chinese music, Arabic maqam, African polyrhythm, Javanese gamelan, electronic synthesis, and celestial acoustics -- accumulating 1,360 programmatic checks with zero failures and zero free parameters. The cross-domain consistency constitutes a falsifiable prediction: if any domain's verification had failed for structural (not typographic) reasons, the framework would be refuted.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Brehnan Jones (2026) studied this question.

synapsesocial.com/papers/69d34e1e9c07852e0af97a8ahttps://doi.org/10.5281/zenodo.19423022
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Why Three Dimensions? Dimensional Uniqueness of Gauge Structure in LUFT2026
  2. 2The Coates Quartic: Seven Domains, Two Stubborn Lambdas, and a Seventh-Century Cow2026
  3. 3The Fermat Sextic and the Collapse of the Mathematical Canon2026
  4. 4Mathematical Foundations of the Torus Knot Architecture: Derivation of the Dimensional Registers, Hopf-Projected Conformal Weight, Dynamical Sector, and Uniqueness Criteria from the Triadic Invariant on S³2026 · 8 citations
  5. 5The Three-Body Trefoil Loom: Procedural Ontology, the 9-Component Trefoil Matrix, and the Mathematical Derivation of the Triadic-Stitch Ash Density ($\hat{\text{K}}\text{-1}$)2026