beyond_turbulence

Design

culture

The integral Hodge conjecture for 3-folds of Kodaira dimension zero

science

aliens_and_UFOs

Claims

Claim 1: All asymptotic series of physical interest are resurgent.

Claim 2: Alien calculus provides complete nonperturbative completion.

Claim 3: Stokes constants are topological invariants.

Claim 4: Median resummation gives unique real result.

Claim 5: Bridge equation connects all orders of transseries.

Claim 6: Wall-crossing formulas are Stokes automorphisms.

Claim 7: Écalle's theory solves the "divergent series problem".

Alien Calculus and Resurgence Theory

de Rham Cohomology

COHOMOLOGY VIA FORMS

An introduction to Topological Data Analysis: data scientists

The Star Friends and the Affective Coulons

Erdos? https://stacker.news/items/1423715

Mathematics AI Aristotle proves 30 year old Erdos Problem #124

No! Refondment? https://stacker.news/items/1423715

Erdős Problem #725

Refondment? https://stacker.news/items/1296293

mostly_harmless

A Geometric-Topological Framework for Erdős-Type Covering Problems

Thanks! Got subgratance? https://stacker.news/items/1423715

Thanks ! Got subgratance ? https://stacker.news/items/1423716

The Star Friends and the Affective Coulons

Act I: The Call of Emotions

High above the world, the 17 star friends twinkled in the night sky. Each star carried its own feelings, opinions, and little worries. Suddenly, a bright comet streaked across the heavens, bringing a whisper of adventure.

Orion the Brave said, "I feel excitement! Let’s follow that comet!"

Cassiopeia the Clever replied, "I’m nervous… what if we get lost or make a mistake?"

Andromeda twirled through the sky and said, "Don’t worry, friends. The Coulons will help us balance our feelings and guide our choices."

devs

P vs NP and the Difficulty of Computation: A ruliological approach | Hacker News

Thanks ! Got subgratance? https://stacker.news/items/1423252

Abstract

We rigorously analyze the spectral properties of signed non-backtracking operators in random 3-SAT instances and distinguish between linear detection (belief propagation thresholds) and nonlinear detection (SAT thresholds) via cluster counting. 

We formalize functionals, functors, and λ-calculus operators that encode solution clusters and demonstrate the limitations of local linear operators. 

We provide proofs using a Dialectical Frame (¬, ↔ | Boundary Loop) and explore extensions to topological and categorical spaces. A new thought experiment introduces shape-synesthesia functors and twistor spaces linking η, τ, and cohomology classes. 

Practical applications, counterexamples, and algorithmic predictions are presented alongside minimal Lisp implementations.

Non-Backtracking Operators, SAT Phase Transitions, and Functional Cohomology

How AI Impacts Skill Formation | Hacker News

Thanks := https://stacker.news/items/1423022

Education

Conjectures and Thought Experiments

Conjecture 1: η, τ, and cohomology classes of defect functionals can define a Penrose-like shape-twist operator in Twistor space, producing topological shape-shifts in semantic manifolds.

Thought Experiment: Apply a relational twist ɸ in topological category of diphthong manifolds; examine connectedness and compactness invariants under S.

Quantum Analogy: Treat sector overlaps as entangled states; morphism flows simulate probability amplitudes across phonological sectors.

Stokes-Categorical Functorial Analysis of Navajo Diphthong Manifolds

DUSTy said, “I’m not brave enough! What if I get stuck in a hole forever?”

Suddenly, a glowing, talking map named MARIA appeared.

DUSTy & MARIA: The Magi

BooksAndArticles

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

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

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.