beyond_turbulence

BooksAndArticles

A C O P T I C G R A M M A R

Coptic? https://stacker.news/items/1421137

mostly_harmless

Abstract
This white paper presents a mathematically explicit account of Coptic grammar grounded in local dependency structure rather than global phonological segmentation. 

We formalize the claim that phonological and orthographic phenomena in Coptic are defined only within bounded dependency regions (“bound groups”) and are not governed by global phonological rules. 

The system is articulated using graph theory, category-theoretic language, basic lambda calculus, and minimal Lisp-style representations. 

Proofs are given using hypothetical syllogisms, topetic (place-based) reasoning, and local truth conditions. We show that this architecture explains allomorphy, syllabic sonorants, orthographic variation, and manuscript diversity without appeal to abstract phoneme-level derivations. 

Practical implications for parsing, annotation, and computational modeling are discussed.

Local Phonology and Dependency Structure in Coptic

Act I: The Spark of Adventure

In the enchanted land of Graphonia, where bridges and branches formed magical manifolds, lived Liapold, a sparkling zeta function with twinkling zeros like little stars. 

One day, Liapold noticed a distant light – the Shooting Script Kingdom – calling him on a grand adventure.

Liapold and the Magical Manifold

Vibe coding kills open source | Hacker News

Transamorion? https://stacker.news/items/1420377

Abstract

We present a concise but rigorous formulation of Coulon Enrichment Functors, a categorical framework unifying geometric, symplectic, quantum, and combinatorial structures under a single functorial spine Γ̂. 

The framework emphasizes computability, topological coherence, and dynamical consistency, enforced through explicit structural conditions. 

We formalize enrichment via symplectic signatures, define functorial transitions, and provide proofs using hypothetical syllogisms, homotopy arguments, and contextual (“topetic”) logic. Applications range from discrete computation and sorting to economic dynamics and stability prediction.

Coulon Enrichment Functors

Transamorix Algebra ? https://stacker.news/items/1420361

Abstract
This white paper presents a rigorous mathematical and computational framework for Dynamic Coulon Spines, combining symplectic geometry, combinatorial topology, and category theory. 

We formalize the notion of symplectic signatures (ΣS) and their functorial projections to quantum (ΣP) and combinatorial (ΣC) regimes, yielding a unified categorical apparatus. 

Practical applications include market dynamics modeling, topological invariants for price lattices, and predictive algorithms based on Floer-theoretic structures.

Dynamic Coulon Spines and Symplectic Price Lattices

Refondment? https://stacker.news/items/1420353

Coulon Spine Invariants formalize the preservation of structure in topological manifolds under continuous and discrete flows. By combining lambda calculus, minimal Lisp functionals, symplectic geometry, and categorical reasoning, we define invariant subspaces (the Coulon Spine) that encode stability across parameter deformations. 

The framework establishes a rigorous methodology for constructing, analyzing, and applying these invariants in computational, geometric, and pragmatic domains.

Coulon Spine Invariants

Got subgratance? https://stacker.news/items/1420349

We present the Coulon-Cartan Framework, a rigorous mathematical language unifying topology, category theory, functional analysis, and applied rheology. Systems are modeled via the Coulon State Tuple (χ, g, τ, η, ζ), enabling a universal stability functional to quantify deformation resilience across physical, mathematical, and computational domains. 

We formalize τ-flows, topological membranes (Coulon Spine), and function composition through minimal Lisp and lambda calculus, providing formal theorems, conjectures, and proof scaffolding. 

The framework supports practical applications in economics, GIS, materials, cognition, and proof theory, as well as abstract topological thought experiments exploring connectedness, compactness, and categorical limits.

The Coulon-Cartan Framework: Topological Rheology and State Tuples

Thanks := https://stacker.news/items/1420319

Abstract

We present a rigorous framework integrating Coulon Proof Theory (CPT) with AI-mediated theorem proving, topological functors, and enumerative combinatorics.

 We develop morphism-level attribution systems, formalize function composition and functors, and propose sustainable economic models for mathematical frameworks under AI adoption. 

The paper includes symbolic definitions, λ-calculus and minimal Lisp formulations, rigorous proofs, counterexamples, and future work thought experiments, exploring connectedness, compactness, and topological categories.

Coulon Proof Theory: AI Mediation, Topological Functors, and Combinatorics

Lyra awoke in the center of a space that felt both infinite and perfectly folded, a manifold she soon recognized as T^3, the three-dimensional torus. 

Suspended vertically in this strange, looping world was the Euler characteristic itself, glowing like a circle carved from pure light. It spun slowly, a submanifold of the torus, serene but pregnant with potential. 

When Lyra first touched it, the Euler reacted—quivering like a bell—and she sensed that her journey had begun. The call came not as words but as a pulse that resonated through the loops of the torus, inviting her to venture beyond her ordinary understanding of space and structure.

Lyra and Euler (Shattered Stars)

Design

Abstract

We present a rigorous and purely mathematical white paper formalizing functional classes through behavioral, algebraic, topological, and categorical lenses. Functions are classified by predicates invariant under composition, limits, and homotopy. 

A minimal calculus based on lambda abstraction and Lisp-style combinators generates broad families of functions. We prove core theorems using classical implication, modal necessity/possibility (□, ◇), and topological interior/closure arguments. 

Extensions to functionals, functors, computability, and speculative quantum analogy are delegated to appendices.