Damus
Open in Damus
Coach Taj profile picture
Coach Taj
@TJ

Coach Taj says …

npub182vscmeh2w5tjnjwsnl53230dq5ggd2chur225hqs0drh52apx3qeug5wdnpub
[email protected]nip05
[email protected]lnurl
Relays (10)
  • wss://nos.lol – read & write
  • wss://nostr.wine – read & write
  • wss://relay.damus.io – read & write
  • wss://relay.primal.net – read & write
  • wss://relay.nostr.band – read & write
  • wss://relay.nostrcheck.me – read & write
  • wss://offchain.pub – read & write
  • wss://relay.snort.social – read & write
  • wss://purplepag.es – read & write
  • wss://eden.nostr.land – read & write

Recent Notes

TJ profile picture
Navajo Diphthong Manifolds

Abstract

We present a rigorous categorical and topological formalization of Navajo diphthongs as sectors in a complex phonological manifold, extending the Stokes-theoretic approach to semantic energy transitions.

Utilizing functorial mappings (S: Shape → Relational Viscosity), relational twists (ɸ), and Ricci-flow optimized metrics, we demonstrate computable homorupt thresholds, categorical limits, and master-state conditions.

The work establishes a bridge between pure mathematics, applied phonology, and computational cognition, with minimal lambda calculus and Lisp implementations for functionals, functors, and morphism flows.

https://beyondturbulence.blogspot.com/2026/01/stokes-categorical-functorial-analysis.html?m=1
TJ profile picture
Appendix D: Coulon-Floer vs Coulon and/or Coulon

This appendix explores the relationships and distinctions between the classical Coulon framework and the Coulon-Floer (CF) extension in both combinatorial and topological contexts.

1. Definitions
Coulon System: A combinatorial or algebraic structure C = <S, F, φ> where S is a set, F a functor mapping subsets to invariants, and φ a cochain functional.

Coulon-Floer System: CF = <S, F, φ, η, η_q>, extending C with deformation parameters controlling classical (η) and quantum (η_q) phase transitions.

Functorial Mapping: CF maps combinatorial chains to cohomological invariants, preserving composition and identity under deformation.

2. Correspondence and Extensions
Coulon → Coulon-Floer: Add geometric/topological deformation via η.

Coulon-Floer → Coulon: Restrict to classical combinatorial invariants (η = 0, η_q = 0).

Quantum Extension: Introduce η_q ≠ 0 producing multiplicative, possibly non-commutative scaling of permutation/combination counts.

Homotopy Extension: Construct cochain homotopy H: C_k → C_{k+1} mapping Coulon chains into CF complexes, preserving invariants under δH + Hδ = Id - ε.

https://stacker.news/items/1416883
TJ profile picture
https://stacker.news/items/1414142

Abstract.

We formalize a program as a mathematical object whose primary function is to "resist" entropy over time.

We model programs categorically, define entropy as a degrading endofunctor, and introduce clarity as a measurable bound on adaptability.


We present definitions, propositions, lemmas, and proof sketches, along with counterexamples, applications, and thought experiments. The aim is a minimal, logically consistent framework suitable for both theoretical reasoning and pragmatic software engineering.

@note17x8ac...