# Symbol Canon — Ordinative Sciences Programme (repository edition)

**Status:** v1.2 (register extended; v1.0 LOCKED ratified 2026-06-11 — v1.1 adds 𝕊 for the Controfase Treatise, ratified 2026-06 — v1.2 adds the Lyapunov-volume and Direction-Problem alignment batch, ratified 2026-08-19). This file is the repository-level condensation of the programme-wide Symbol Canon; it does not supersede the master, which lives with the framework modules. Nothing below is re-assignable without the reservation procedure.

## Tier order

```
OST  (Tier-0 — mathematical-ontological anchor: 𝓘 = ⟨Σ, R, Φ⟩)
 └─ TE Vol 1  (Tier-1 — applied physics of expressions: E = Φ(C, I, K))
     └─ PA, SA  (Tier-2 — this repository)
```

Canon flows downstream. Tier-2 renames before Tier-0/1 does; declared coexistence by operand distinction is legitimate (e.g. TE's pairwise κ(I_a, I_b) beside the coherence vectors 𝓚/𝓚⁵); enum labels do not collide with operators.

## Reserved programme-wide

| Symbol | Meaning | Owner |
|---|---|---|
| 𝓘 | Ordinative Set ⟨Σ, R, Φ⟩ | OST — never reassigned |
| Σ, σ | Singularities; singularity | OST (SA's σ aligned) |
| R | Relational Field | OST (SA aligned) |
| Φ | Emergent Function — with the declared TE exception: Collapse Function E = Φ(C, I, K) | OST / TE |
| C, K, E, D | Coherent Content, Context, Explicit Expression, Decoherent Space | TE primitives (PA aligned; 𝒟 ≡ D) |
| I | Identity | TE/PA — invariants use the ι-family |
| 𝒜 | Author | TE — reserved exclusively |
| ρ, θ | Resonance; threshold | TE/PA/SA aligned. Form resistance is ϱ, not ρ (resolved v1.2) |
| τ | Pulsational Function (bare); subscripted τ_• = thresholds (OST/OCT); SA phase label = τ_ph | per canon rule A5 |
| ι, ι₁…ι₁₀, ι_k | Invariant; the library; indexed invariants | programme-wide (this repo) |
| 𝓚 / 𝓚⁵ / ⟨𝓚⁵⟩ | Coherence vector (OST 3-dim) / PA 5-dim extension / aggregate | OST/PA family |
| ℛ(I) | Remir | TE/PA |
| S, π | Strip; Re-contextualisation (π_R = OST Ordinative Projection, distinct by subscript) | SA/PA |
| κ_c, P | Connotation co-operator; payload channel — S(E) = ⟨ι, P⟩ | SA (§6.8) |
| A/B/C/D | Shared state taxonomy: PA collapse types ↔ OCT admissibility states | PA/OCT |
| 𝕊 | State / Configuration Space — 𝔠 : 𝕊 → 𝕊 | Controfase Treatise (added v1.1). Bare S stays reserved for the Strip |
| 𝔸 / {𝔸ᵢ} / τ_𝔸 | Ordinative attractor (well) / multi-well landscape / temporal coordinate of the well | Lyapunov vol. + DP (v1.2). Replaces DP 𝒜-as-attractor — 𝒜 stays the Author |
| 𝕋 | Ordinative Space (navigable time; points (x, τ)) | Lyapunov vol. + DP (v1.2). Replaces DP 𝒯-as-ordinative-space — 𝒯 stays the Expressive Terminal |
| σ_𝔸 | Attractor-signal intensity, σ_𝔸 = κ/d^α | v1.2. Replaces DP bare-σ-as-signal; avoids collision with OST σ-singularity |
| ϱ | Form resistance (drag of coherent form against the attractor signal) | v1.2 — resolves the candidate open since v1.0. ρ stays Resonance |
| **d**(t) / **d̂**(t) | Expressed vector / projected vector (observer's estimate) | v1.2. Lyapunov vol.; hat = standard estimator notation |
| τ_c | Delivery (hand-over of dominance between wells) | v1.2. Subscripted per rule A5 — bare τ stays the Pulsational Function |

## What this repository renamed at v2.0

Full mapping tables with rationale: `PA/PA_BOOK/appendix_a_symbol_register.md` (Canon Alignment Note) and `SA/SA_BOOK/appendix_a_vocabulary.md` (Canon Alignment Note). Headline moves — PA: 𝒞→ℭ_h, space ℛ→𝕀, κ-family→𝓚⁵, I_k→ι_k, Α/Β/Γ/Δ→A/B/C/D, domains→𝔻. SA: Φ→𝔉, K→𝒦_p, K_real→𝒦_r, invariants→ι, Controphase→C_φ, Domain→𝔻, τ→τ_ph, λ→λ_L, ω→ω_att, gap→Δ_𝔉. Notation only; no semantic changes. The TE collapse equation is quoted in TE notation by design wherever it appears.