PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
March 30, 20260 citationsOpen Access

Fibre Admissibility and Resolution of the Capacity Exponent Discrepancy

View Full Paper
JBJérôme Beau

Key Points

  • To resolve the discrepancy in the Weil-block capacity exponent related to admissibility in fibres.
  • Identified misidentification of relevant observable
  • Analyzed the non-injectivity of projection under Born--Infeld constraint
  • Investigated pair-level observable based on fibre organization
  • Confirmed a clean power law with exponent approximately 7.44
  • Achieved a factor-of-six reduction in slope variance
  • Numerical confirmation with R^2 greater than 0.9999

Abstract

The O-series has established that the Weil-block capacity exponent ₄ₗ₀₂ₓ 3. 72 0. 06 falls systematically below the phenomenological target range 7. 4, 10. 6, and that this discrepancy is structural: no reweighting of block data can raise the exponent (O15, Corollary~4. 8). The present paper resolves the discrepancy by identifying a misidentification of the physically relevant observable. The non-injectivity of the projection~, established from the Born--Infeld constraint, implies that admissibility is a property of complete fibres of~, not of individual preimage configurations. In the Weil realisation of Heis₃ (Z/qZ), these fibres are organised as conjugate pairs \c, q-c\ under the exact identity ₐ-₂ = c. The pair-level observable ₏₀₈ₑ (n) = c (n) \, ₐ-₂ (n) follows a clean power law with exponent ₏₀₈ₑ = 2\, c 7. 44 0. 12, confirmed numerically with R² > 0. 9999 and a factor-of-six reduction in slope variance. This result does not modify the underlying model; it identifies the correct unit of observation.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Jérôme Beau (2026) studied this question.

synapsesocial.com/papers/69c9c57ff8fdd13afe0bd7a6https://doi.org/10.5281/zenodo.19298427
Ask AI
Helpful
Bookmark
Share
View Full Paper