Single-Axiom Mathematical Framework

Generative Collapse
Dynamics

"Collapse is generative; only what returns is real."

Collapsus generativus est; solum quod redit, reale est.

A mathematical framework built from a single axiom — measuring what survives collapse and what returns, verified across 23 domains, 746+ theorems, and 44 structural identities.

The Kernel Function

K: [0,1]n × Δn → (F, ω, S, C, κ, IC)

Four equations, six outputs, three effective degrees of freedom — the complete measurement of collapse and return.

F
Fidelity
Σ wici
ω
Drift
1 − F
S
Entropy
Bernoulli field
C
Curvature
σ(ci)/0.5
κ
Log-integrity
Σ wi ln ci
IC
Integrity
exp(κ)

Every claim follows the same path

The Spine

Contract
Canon
Closures
Ledger
Stance
Tier-1 · Immutable

The Kernel

The mathematical function plus 3 algebraic identities, 44 structural identities, 47 lemmas, and 5 frozen constants.

Tier-0 · Protocol

The Implementation

Python + C99 + C++ implementations. Three-valued verdicts. Frozen parameters from the seam. The code is Tier-0; what it computes is Tier-1.

Tier-2 · Expansion

Domain Closures

23 domains select which real-world quantities become channels. 746+ theorems, 228 modules. Same kernel, different questions.

Client-side · No server required

Interactive Tools

From quarks to consciousness

23 Domain Closures

Each domain selects which real-world quantities become channels. The kernel stays the same — only the question changes.

Generative Collapse Dynamics

The axiom, the kernel, the spine.

11 modules · 37 theorems · Epistemology
Recursive Collapse Field Theory

Recursive field-theoretic structure of collapse.

13 modules · 30 theorems · Epistemology
Kinematics

Motion, phase space, and trajectory analysis.

11 modules · 34 theorems · Ontology
WEYL Cosmology

Modified gravity and cosmological structure.

7 modules · 10 theorems · Ontology
Standard Model

31 particles → 8-channel trace. 30 proven theorems.

14 modules · 30 theorems · Ontology
Nuclear Physics

Binding energy, decay, QGP, confinement.

14 modules · 51 theorems · Ontology
Quantum Mechanics

Wavefunction, entanglement, QDM, FQHE.

21 modules · 99 theorems · Phenomenology
Atomic Physics

118 elements — full periodic kernel.

12 modules · 26 theorems · Ontology
Materials Science

118 elements × 18 fields.

23 modules · 52 theorems · Ontology
Everyday Physics

Thermo, optics, E&M, waves, fluids.

8 modules · 29 theorems · Phenomenology
Finance

Portfolio continuity and market coherence.

5 modules · 22 theorems · Policy
Security & Audit

Input validation, audit, integrity.

18 modules · 22 theorems · Policy
Astronomy

Stellar classification, HR diagram, ages.

12 modules · 42 theorems · Ontology
Evolution & Neuroscience

40 organisms, 10-channel brain kernel.

9 modules · 22 theorems · History
Consciousness Coherence

20 systems, 28 theorems, altered states.

5 modules · 28 theorems · Phenomenology
Awareness & Cognition

5+5 channel awareness-aptitude kernel.

4 modules · 22 theorems · Phenomenology
Clinical Neuroscience

10-channel cortical kernel, neurotransmitters.

8 modules · 53 theorems · Phenomenology
Dynamic Semiotics

30 sign systems, 8-channel semiotic kernel.

8 modules · 40 theorems · Semiotics
Continuity Theory

Continuity law, topological persistence.

5 modules · 29 theorems · History
Spacetime Memory

40 entities, gravitational memory.

8 modules · 46 theorems · Ontology
Immunology

Immune cell kernel, cytokine networks, vaccine response.

6 modules · 36 theorems · Phenomenology
Ecology

12 ecological states, trophic cascades.

3 modules · 2 theorems · History
Information Theory

10 complexity classes, computability kernel.

3 modules · 2 theorems · Epistemology
1
Axiom
6
Invariants
3
DOF
23
Domains
44
Identities
47
Lemmas
228
Modules
20,337
Tests