Documentation Index
Fetch the complete documentation index at: https://mintlify.com/theislampill/orthemology/llms.txt
Use this file to discover all available pages before exploring further.
The notation registry is the single authoritative symbol table for all formal notation used in Orthemology. It lives in docs/notation-registry.yaml and was normalized by Decision 0005 (2026-07-20, registry version 1.0.0). The principle governing the table is: one symbol, one role. Semantic roles take precedence over glyph preference. The notation validator (scripts/validate_notation.py) enforces the current table across the corpus; historical documents under archive/ retain old symbols and are never rewritten, and the validator whitelists those archive contexts.
Every document in the current corpus MUST follow this table. Retired symbols must not appear in new work. If a retired symbol appears outside of archive/ or an explicitly annotated historical quotation, the notation validator will fail.
Active symbol table
Analysis and task
| Symbol | Glyph | Role |
|---|
A | A | Declared analysis (identifier + version). Never an actor index. |
T = task(A) | T | Task component of the analysis |
Universes and analysis-active domains
| Symbol | Glyph | Role |
|---|
M_univ, O_univ | 𝓜, 𝓞 | Universal occurrence and ortheme universes |
M_A, O_A | M_A, O_A | Analysis-active domain (M_A ⊆ 𝓜) and repertoire (O_A ⊆ 𝓞). Unsubscripted M, O are licensed scoped shorthand once one analysis is fixed |
Actors
| Symbol | Glyph | Role |
|---|
alpha, beta, ... | α, β, … | Actor indices. Formal actor indices are never A/B |
Instantiation and profiles
| Symbol | Glyph | Role |
|---|
Inst_A | Inst_A | Analysis-relative instantiation, Inst_A ⊆ M_A × O_A (the primitive) |
O*(m; A) | O*(m; A) | True (actual) profile of m under A |
Pi_A | Π_A | Complete-profile space under A (Π_T is scoped shorthand) |
Pi_A_partial | Π_A^∂ | Partial-profile space under A |
C_hat | Ĉ_(m) | Candidate set of complete profiles (equivalently the typed family C^profile) |
p_hat | p̂_(m) ∈ Π_A^∂ | Inferred (partial) profile — belief, never ground truth |
Observation
| Symbol | Glyph | Role |
|---|
Omega | Ω_ | Observation map, indexed where analysis/actor/time matter (Ω_α is scoped form) |
| Symbol | Glyph | Role |
|---|
mu | μ | Metaortheme type ⟨g, S_μ, select_μ, prov, ver⟩ |
pi_mu | π_μ | Paired meta-policy |
mu_bar | μ̄_ | The j-th metaorthemma (configuration token) in episode e |
MetaInst | MetaInst | Token typing MetaInst(μ̄_, μ) |
select_mu | select_μ | Metaortheme state-selecting evidence procedure |
estatus_e | estatus_e | Per-claim evidence-status map of episode e |
Episodes and governance
| Symbol | Glyph | Role |
|---|
Gamma_E | Γ_E = (E, ⇝) | Episode DAG (nodes = episodes, typed edges) |
e_Gamma | e_Γ = comp(Γ_E) | Composed boundary-level episode (when composition conditions hold) |
Q_e | 𝒬_e | Claim ledger of episode e |
delta_e | δ_e | Residual-disposition map of episode e |
ReqPath | ReqPath(e) | Governance-derived required pathway verdicts. The sole pathway requirement function |
Goal schemas and target sets
| Symbol | Glyph | Role |
|---|
GoalSchema | GoalSchema(α) | Parametric goal schema for actor α |
G_target | 𝒢_ | Actor-α’s grounded target profile set (𝒢_α is scoped shorthand) |
Representations and loss
| Symbol | Glyph | Role |
|---|
Rep_A | Rep_A | Representation family under A |
chi | χ | One representation, χ ∈ Rep_A |
L_A_star | L_A*(χ) | Best attainable loss/risk under representation χ |
Repertoires
| Symbol | Glyph | Role |
|---|
K_A | 𝒦_A | Cause repertoire (𝒦_T is scoped shorthand) |
R_A | ℛ_A | Route repertoire (ℛ_T is scoped shorthand) |
W_A | 𝒲_A | Warrant-state repertoire (𝒲_T is scoped shorthand) |
Tolerances and thresholds
| Symbol | Glyph | Role |
|---|
eps_A | ε_A | Accepted tolerance of the analysis |
theta_stop | θ_stop | ANDON stop/escalation risk threshold |
The scoped-shorthand rule
Task-subscripted forms (Inst_T, O*_T, Π_T, 𝒦_T, ℛ_T, 𝒲_T, ≢_T) and the unsubscripted M, O are licensed only after one analysis A with task(A) = T is explicitly fixed. They are forbidden in multi-analysis contexts: level-indexed audits, multi-actor evaluation, cross-version comparisons, and execution-vs-review comparisons.
Retired symbols
The following symbols are retired from normative use. They must not appear in new work. Historical documents under archive/ retain them and are never rewritten.
| Retired symbol | Reason | Replacement |
|---|
App(e) | Competed with ReqPath(e) as a requirement function; applicability is now expressed via ReqPath(e) plus recorded not-applicable reasons | ReqPath(e) |
W(·) | Collided with warrant repertoire | GoalSchema(·) |
G (bare, for the episode graph) | Collided with target sets | Γ_E |
G(α, T_α) | Target sets live in per-analysis profile spaces | 𝒢_{α,A_α} |
q / Q (representation / representation set) | Collided with claim ledger | χ ∈ Rep_A |
R*(q) | Collided with route repertoire and risk | L_A*(χ) |
ε_μ (epsilon_mu as selector) | Overloaded with tolerance and evidence status | select_μ |
ε (bare, as evidence-status map) | Overloaded | estatus_e |
τ (tau as ANDON threshold) | Replaced to free τ for generic time use | θ_stop |
I_T | Pre-D1 primitive; superseded by Inst_A | Inst_A (historical only) |
No definition changed meaning in Decision 0005’s normalization. Every rename is 1:1 role-preserving, recorded in the registry’s retired_symbols list. Semantic roles control over glyph preference throughout.
How to use this registry
Every new document must declare its analysis before using scoped shorthand. When writing:
- Use
O*(m; A) with the full analysis identifier at the definition site.
- After fixing one analysis,
O*_T(m) is permitted as local shorthand — but only within that single-analysis scope.
- Use
α, β, … for actors; never use A or B as actor variables.
- Use
ReqPath(e) as the sole pathway requirement function; App(e) is retired.
- When citing a retired symbol in a historical quotation, mark it explicitly as a historical form.