Axiom-0
Collapse is generative.
Only what returns is real.
Collapsus generativus est; solum quod redit, reale est.
The Framework
What is GCD?
Generative Collapse Dynamics is a mathematical framework that measures what survives collapse and what returns. It begins from a single axiom — Axiom-0 — and derives a complete measurement protocol that works identically across 21 scientific domains, from particle physics to consciousness studies.
The framework is implemented as UMCP (Universal Measurement Contract Protocol), a reproducible validation system with frozen parameters that are seam-derived — discovered by the mathematics, not chosen by convention.
At a Glance
Six Invariants, Three DOF
The Kernel
The kernel function K: [0,1]ⁿ × Δⁿ → (F, ω, S, C, κ, IC) maps any trace vector to six invariants — but only 3 effective degrees of freedom.
Click any invariant to learn what it measures, why it exists, and how it connects to the others.
How the Six Invariants Relate
4 are primitive (computed directly), 2 are derived (follow algebraically). Together, they have only 3 effective degrees of freedom because S is asymptotically determined by F and C.
Every Claim Follows This Path
The Spine
Every claim, validation, and discourse follows a fixed five-stop spine. Click each stop to see what happens there.
Derived from Gates, Never Asserted
Three Regimes
Regime classification is derived from gates on (ω, F, S, C) — never asserted. Click to explore each regime.
Fisher Space Partition
Stability is rare — 87.5% of the manifold lies outside it. Return from collapse to stability is what the axiom measures.
Minimal Prose Vocabulary
The Five Words
The minimal prose vocabulary for telling the story of any collapse-return cycle. Click a word to see its ledger role and operational definition.
Immutable Dependency Structure
Three-Tier Architecture
Every symbol, function, and artifact belongs to exactly one tier. Click to understand each layer.
One-Way Dependency (No Back-Edges)
No feedback from Tier-2 to Tier-1 or Tier-0 within a frozen run.
Compounding Parametrized Sweeps
20,337 Tests
Not 20,337 separate assertions — compounding parametrized sweeps across 23 domains. ~800 base test functions expand 18× through domain × entity × configuration parametrization.
How Test Compounding Works
Example: One Tier-1 identity test compounds across 23 domains
Test Distribution by Domain
Click a tier to see its test domains.
231 test files, numbered test_000 through test_338
Verified to Machine Precision
44 Structural Identities
All derived from Axiom-0 and verified to machine precision. They fall into four series. Click a series to see its identities and what they prove.
6 Connection Clusters
The 44 identities form a connected network. These clusters reveal the deep structure.
Same Formulas, Three Implementations
Three Languages, One Kernel
The same kernel function K: [0,1]ⁿ × Δⁿ → (F, ω, S, C, κ, IC) is implemented in three languages — each serving a distinct architectural role. Click to explore each layer.
Three-Layer Sandwich Architecture
Same formulas, same frozen parameters — three layers of the same truth
Formal Foundation
47 Lemmas
The formal foundation beneath the kernel. Each lemma proves a property used by the implementation — tagged as OPT-* in the code. Click a category to explore.
Lemmas in Code
Every optimization in the kernel references its proving lemma via OPT-* tags:
Every speedup has a proof. Every optimization has a lemma number. Nothing is ad hoc.
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