Axiom-0

Collapse is generative.
Only what returns is real.

Collapsus generativus est; solum quod redit, reale est.

Explore the Kernel ↓ Try the Calculator →

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 20 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

14,565

Tests

Domains

Identities

Lemmas

181

Closures

Languages

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.

Primitive — computed directly from the trace vector

Derived — follows algebraically from a primitive

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.

The Spine

Every claim, validation, and discourse follows a fixed five-stop spine. Click each stop to see what happens there.

Three Regimes

Regime classification is derived from gates on (ω, F, S, C) — never asserted. Click to explore each regime.

Fisher Space Partition

12.5%

24.4%

63.1%

Stability is rare — 87.5% of the manifold lies outside it. Return from collapse to stability is what the axiom measures.

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.

Three-Tier Architecture

Every symbol, function, and artifact belongs to exactly one tier. Click to understand each layer.

One-Way Dependency (No Back-Edges)

Tier-1 → Tier-0 → Tier-2

No feedback from Tier-2 to Tier-1 or Tier-0 within a frozen run.

14,565 Tests

Not 14,565 separate assertions — compounding parametrized sweeps across 20 domains. ~800 base test functions expand 18× through domain × entity × configuration parametrization.

How Test Compounding Works

~800

Base test functions

Written once per pattern

~18×

Parametrization factor

Domain × entity × config

14,565

Collected test items

Every invariant, every domain

Example: One Tier-1 identity test compounds across 20 domains

# One parametrized test function:

@pytest.mark.parametrize("domain", ALL_20_DOMAINS)

def test_duality_identity(domain):

traces = domain.get_all_entities() # 12–118 entities each

for trace in traces:

F, ω = kernel(trace)

assert abs(F + ω - 1) == 0.0 # Exact to 0.0e+00

→ 1 function × 20 domains × 12–118 entities = hundreds of assertions from one test

Test Distribution by Domain

Click a tier to see its test domains.

172 test files, numbered test_000 through test_293

Proto

Core

Domains

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.

Explore all 44 identities in detail →

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

Python Domain closures · CLI · Dashboard · Fleet

C++17 Types · Validation · pybind11 zero-copy

C99 Raw math · Kernel · Seam · Pipeline

Same formulas, same frozen parameters — three layers of the same truth

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.