The ASH Model
The source cosmology — a mathematical framework that treats identity, pattern, meaning, topology, and artifact generation as connected parts of one deterministic system.
The ASH Model is the theory; Sigil is the first working software demonstrator that applies it.
Model vs. demonstrator. Sigil is not the ASH Model. The ASH Model is the theory and mathematics — a 9-dimensional binary state space, deterministic state, codeword/XOR transitions, and coherence constraints, expressed independently of any one program. Sigil is the point where that symbolic state becomes executable software. The ASH-Model Cosmology is published in full at ashcosmology.net.
A 9-bit state over GF(2)
The key motif is a 9-bit ASH state — a vector over the finite field GF(2), written F₂⁹. The initial state is derived from the 5D canonical vector: each feature is thresholded at 0.5 to set one bit.
F₂⁹
9-dimensional binary state
512
possible states (0…511)
16
doubly-even codewords
256
orbit-length cap
Doubly-even codewords and XOR
ASH does not mutate state freely. It advances by XOR with a codeword from a fixed operator set — extended_hamming_8_4_4_embed9_v1, 16 codewords, each doubly-even (Hamming weight divisible by 4).
// the transition rule x_next = x_current XOR codeword // weights are 0, 4, or 8 only; XOR of two doubly-even vectors // stays doubly-even -> a structured group action, not noise. // Orbit cap 256, loop detection (period >= 6), // SHA-256 orbit_digest recorded in the codex.
One state, read three ways
The creative layer is not decorative — symbolic meaning is computed from the same deterministic state, not bolted on afterward.
Deterministic identity
ASH is a deterministic identity and pattern model. User input becomes a reproducible PersonalCodex and sigil.
State & diagnostics
State, transition, guards, topology, and diagnostics — canonical vectors, ASH orbit, guarded grammar, mesh hash, quality report.
Symbolic meaning
ASH gives symbolic meaning to identity — planes, wolves, celestial names, WRW origin, gifts, burdens, thresholds.
The five axioms
ASH uses guarded transitions. The KripkeGuardEngine validates every geometry-affecting decision against five named axioms, each tied to a concrete property. Rejections fall back deterministically — never randomly.
A1 · Relational existence
Disconnected geometry is allowed only when strokes are genuinely independent — no synthetic inter-primitive bridges.
A2 · Compressibility
Transitions stay within a bounded modifier budget.
A3 · Multiscale persistence
The canonical WRW anchor survives across scales.
A4 · Erasure cost
Required motifs cannot be erased.
A5 · Self-reference
Recursion is permitted only when the orbit actually loops.
ASH as a software pattern
ASH is not only a fictional cosmology — it is a pattern for software that is:
Deterministic
Same input produces same state and output.
Explainable
Intermediate state, transitions, and diagnostics are inspectable.
Testable
Golden profiles and digest checks assert behavior.
Reproducible
Outputs reconstruct from canonical input and context.
Modular
State, lore, geometry, export, and diagnostics are separable contracts.
Guarded
Incoherent transitions are rejected before finalization.
Cross-domain
One state drives app UI, game systems, lore, and exports.
Not procgen noise
A canonicalized identity seed with meaning built into the state — not an arbitrary random seed.
From theory to running software
See how a profile travels through the model to become a reproducible artifact.
The generation pipeline ASH Cosmology ashcosmology.net