II.1 Scope
This section applies to all Doctrine content that contains mathematical or symbolic notation. It applies, without exception, to every canonical entity whose identifier matches the schema TDY_COH-<Class>_<IndexOrTag> as defined in II.6, and to all accompanying prose (notes, descriptions, titles, captions, tables, Annex II-A, Annex II-B) and all cross-references. The Canonical Notation Matrix governs notational form and typesetting conventions only; semantic meaning, definitions, and inferential rules remain governed by the Formalisms Registry. Abbreviated or bare references (for example, a class-index token without the TDY_COH- prefix) are non-canonical and appear only for remediation per II.6 and II.7.
II.2 Binding to Other Sections
II.2.1 The Formalisms Registry SHALL reference symbols and operators only as defined in the CNM and SHALL NOT redefine typesetting.
II.2.2 Any section that includes mathematics SHALL conform to the CNM. Any deviation requires a recorded exception per II.11.
II.3 Canonicalization Policies
II.3.1 Variables that are single letters (Latin or Greek) SHALL be set in math italics by default.
II.3.2 Multi-letter named operators or functions SHALL be set with \operatorname{...}; any descriptive subscript SHALL be upright via \mathrm{...}.
II.3.3 Multi-letter acronyms used as symbols in math SHALL be set upright via \mathrm{...}; if used as an operator or mapping, \operatorname{...} SHALL be used.
II.3.4 Identifiers and labels (for example, TDY_COH-*) SHALL be typeset using \texttt{...}. When inside math mode, they SHALL be wrapped using \text{\texttt{...}}.
II.3.5 Standard LaTeX commands SHALL be preferred over Unicode characters for portability (for example, \sum not Σ when used as the summation operator).
II.3.6 Intervals SHALL use plain [ ] by default; \left ... \right MAY be used only when tall content requires scalable delimiters.
II.3.7 Unicode superscripts and subscripts SHALL NOT be used; canonical LaTeX ^{...} and _{...} SHALL be used instead.
II.3.8 The Telos manifold SHALL be set as T in math ($T$). \mathcal{T} is reserved for distinct families or spaces if introduced later.
II.3.9 Uppercase Greek macros that do not exist in base LaTeX SHALL NOT be invented (for example, \Alpha). Where LaTeX uses Latin glyphs for certain uppercase Greek letters, those Latin letters SHALL be used.
II.3.10 The indicator function SHALL be \mathbf{1}. Use of \mathbb{1} is permitted only if the package is explicitly declared.
II.3.11 Expectation SHALL be \mathbb{E}[\,\cdot\,]. Variance SHALL be \operatorname{Var}[\,\cdot\,].
II.3.12 Norms: canonical form is \| \cdot \|. Where \lVert is available (amsmath), \lVert \cdot \rVert MAY be used.
II.3.13 Descriptive subscripts (two or more letters, or snake_case) SHALL be upright via \mathrm{...}; single-letter or digit indices remain italic or numeric.
II.3.14 Words inside math SHALL be wrapped with \text{...}; literal underscores SHALL be written as \_ inside \text{...}.
II.3.15 Render Mode Conventions (Normative): Inline math SHALL use single-dollar delimiters: ＄...＄. Display math SHALL use double-dollar delimiters: ＄＄...＄＄. Agents SHALL NOT rewrite ＄...＄ to \(...\), nor ＄＄...＄＄ to \ [ ... \ ].
II.3.16 Operators and Limits: In inline math (＄...＄), operators MAY keep limits to the side (textstyle). Where under or over limits are essential inline, \displaystyle MAY be used locally. In display math (＄＄...＄＄), under or over limits SHALL render naturally; for operators that bind limits beneath or above (for example, argmin or argmax), \operatorname*{...} SHALL be used.
II.3.17 Primes SHALL be written as ^{\prime} and ^{\prime\prime}; Unicode prime characters MUST NOT be used.
II.3.18 Multi-line Display: Multi-line equations SHALL be wrapped once in ＄＄...＄＄ and MAY use aligned environments inside. Nested ＄＄ inside aligned environments is prohibited; a single outer ＄＄ wrapper SHALL be used.
II.3.19 Text and Literals: Prose inside math SHALL use \text{...}. Literal dollar signs in text SHALL be escaped as \$.
II.3.20 Punctuation: Inline math follows sentence punctuation conventions; punctuation appears outside the $...$ delimiters when it terminates the sentence. Display equations SHALL be punctuated as part of the surrounding prose; punctuation appears immediately after the closing $$.
II.3.21 Spacing: Visual spacing in math SHALL use LaTeX spacing commands (\,, \:, \;, \!), not repeated literal spaces.
II.3.22 Delimiters: Plain [ ] and ( ) SHALL be used by default; \left...\right MAY be used only when tall content requires scalable delimiters.
II.3.23 Interoperability: Agents SHALL preserve the Doctrine's $ and $$ delimiters during any transformation, migration, or lint-driven remediation.
II.4 Table Schema
Columns are: | Symbol Type | Notation Found in Source | Recommended Canonical LaTeX | Rationale or Notes |
This four-column schema is normative. Each row is a single normalized rule. When a specific token is not listed, apply II.3 policies and the closest matching row type below.
II.5 Canonical Notation Matrix
| Symbol Type | Notation Found in Source | Recommended Canonical LaTeX | Rationale or Notes |
| :--- | :--- | :--- | :--- |
| Set Notation | ℝ | \mathbb{R} | Blackboard bold; avoid Unicode dependency. |
| Set Notation | ℤ | \mathbb{Z} | Blackboard bold; avoid Unicode dependency. |
| Set Notation | ℕ | \mathbb{N} | Blackboard bold; avoid Unicode dependency. |
| Set Notation | ℚ | \mathbb{Q} | Blackboard bold; avoid Unicode dependency. |
| Set Notation | ℂ | \mathbb{C} | Blackboard bold; avoid Unicode dependency. |
| Script | ℳ | \mathcal{M} | Script M; use \mathcal. |
| Empty Set | ∅ | \varnothing | Prefer \varnothing; \emptyset allowed if AMS not available. |
| Summation | Σ (observed in TDY_COH-E_32) | \sum | Correct N-ary summation operator. |
| Greek Letter | Σ (symbol or name) | \Sigma | Use \Sigma when not the N-ary operator. |
| Integral | ∫ | \int | Standard integral operator. |
| Contour Integral | ∮ | \oint | Standard contour integral. |
| Differential | ∂ | \partial | Partial derivative symbol. |
| Vector Operator | ∇ | \nabla | Gradient, divergence, or curl context-dependent. |
| Arrows | → | \to | Rightwards arrow. |
| Arrows | ⇒ | \Rightarrow | Double-arrow implication. |
| Arrows | ⟶ | \longrightarrow | Long rightwards arrow. |
| Arrows | ⟵ | \longleftarrow | Long leftwards arrow. |
| Arrows | ⟹ | \Longrightarrow | Long double-arrow implication. |
| Mapping | ↦ | \mapsto | Maps-to arrow. |
| Relations | ≥ | \ge | Greater than or equal. |
| Relations | ≤ | \le | Less than or equal. |
| Relations | ≠ | \ne | Not equal. |
| Relations | ≈ | \approx | Approximately equal. |
| Relations | ≃ | \simeq | Asymptotically equal or similar. |
| Relations | ≅ | \cong | Congruent to or isomorphic. |
| Relations | ≡ | \equiv | Identically equal. |
| Proportionality | ∝ | \propto | Proportional to. |
| Set Membership | ∈ | \in | Element of. |
| Set Membership | ∉ | \notin | Not an element of. |
| Set Operators | ∩ | \cap | Intersection. |
| Set Operators | ∪ | \cup | Union. |
| Set Operators | ⊂ | \subset | Proper subset. |
| Set Operators | ⊃ | \supset | Proper superset. |
| Set Operators | ⊆ | \subseteq | Subset or equal. |
| Set Operators | ⊇ | \supseteq | Superset or equal. |
| Operators | × | \times | Cross product. |
| Operators | · | \cdot | Dot product; use only in math. |
| Operators | ⊗ | \otimes | Tensor product. |
| Operators | ∏ | \prod | N-ary product. |
| Operators | √ | \sqrt{} | Radicals. |
| Constants | ∞ | \infty | Infinity. |
| Greek (upper) | Δ | \Delta | Capital delta. |
| Greek (upper) | Ω | \Omega | Capital omega. |
| Greek (lower) | θ | \theta | Theta. |
| Greek (lower) | δ | \delta | Delta. |
| Greek (lower) | ε | \varepsilon | Prefer \varepsilon. |
| Greek (lower) | φ | \varphi | Prefer \varphi. |
| Greek (lower) | σ | \sigma | Sigma. |
| Greek (lower) | ω | \omega | Omega. |
| Greek (upper) | Ψ | \Psi | Psi. |
| Greek (lower) | ψ | \psi | Psi. |
| Indicator | 𝟙 | \mathbf{1} | Bold 1 as indicator function. |
| Expectation | \mathbb{E}[·] | \mathbb{E}[\,\cdot\,] | Blackboard bold E; disambiguates from variable E. |
| Variance | Var[·] | \operatorname{Var}[\,\cdot\,] | Named operator with correct spacing. |
| Heaviside | H(·) | \operatorname{H}(·) | Upright operator. |
| Dirac delta | \delta(·) | \delta(·) | Greek \delta; not a Latin d. |
| Norm | ||x|| | \|x\| (or \lVert x \rVert if amsmath available) | Canonical double bars; \lVert permitted when loaded. |
| Prime | ′ | ^{\prime} | Use superscript prime for derivatives and labels. |
| Double Prime | ″ | ^{\prime\prime} | Use superscript prime macros. |
| End of Proof | ∎ | \qed or \qedhere | Standard QED marker. |
| Interval | [0,1] | [0,1] (or \left[0{,}1\right]) | Use scalable delimiters only when tall content requires. |
| Interval | [0,∞) | [0,\infty) (or \left[0{,}\infty\right)) | As above. |
| Text in Math | epi_feasible | \text{epi\_feasible} | Snake_case prose label; render as text. |
| Text in Math | execution_constraints | \text{execution\_constraints} | Snake_case prose label; render as text. |
| Text in Math | formal_title | \text{formal\_title} | Snake_case prose label; render as text. |
| Text in Math | related_axioms | \text{related\_axioms} | Snake_case prose label; render as text. |
| Text in Math | related_occ | \text{related\_occ} | Snake_case prose label; render as text. |
| Operator Correction | int_0 | \int_{0} | Replace literal "int" token with integral operator plus limits. |
| Concept or Manifold | Telos (T or \mathcal{T}) | $T$ | Canonical is $T$; \mathcal{T} reserved for families or spaces. |
| Function or Operator | Dist | \operatorname{Dist} | Named operator; upright roman. |
| Function or Operator | Dist_Local | \operatorname{Dist}_{\mathrm{Local}} | Descriptive subscript upright via \mathrm{...}. |
| Function or Operator | Align | \operatorname{Align} | Named operator; upright roman. |
| Function or Operator | Align_ID | \operatorname{Align}_{\mathrm{ID}} | Descriptive subscript upright via \mathrm{...}. |
| Function or Operator | RCO | \operatorname{RCO} | Named operator; upright roman. |
| Function or Operator | RCO_epi | \operatorname{RCO}_{\mathrm{epi}} | Descriptive subscript upright via \mathrm{...}. |
| Function or Operator | RCO_phys | \operatorname{RCO}_{\mathrm{phys}} | Descriptive subscript upright via \mathrm{...}. |
| Function or Operator | EF | \operatorname{EF} | Named operator; upright roman. |
| Function or Operator | SDI | \operatorname{SDI} | Named operator; upright roman. |
| Function or Operator | SIV | \operatorname{SIV} | Named operator; upright roman. |
| Function or Operator | SRF | \operatorname{SRF} | Named operator; upright roman. |
| Function or Operator | SSS | \operatorname{SSS} | Named operator; upright roman. |
| Function or Operator | argmin | \operatorname*{argmin} | Limits beneath or above in display. |
| Function or Operator | argmax | \operatorname*{argmax} | Limits beneath or above in display. |
| Function or Operator | exp | \exp | Standard operator in upright roman. |
| Function or Operator | log | \log | Standard operator in upright roman. |
| Function or Operator | lim | \lim | Standard operator in upright roman. |
| Function or Operator | sup | \sup | Standard operator in upright roman. |
| Function or Operator | inf | \inf | Standard operator in upright roman. |
| Function or Operator | min | \min | Standard operator in upright roman. |
| Function or Operator | max | \max | Standard operator in upright roman. |
| Variable (Greek macro) | \Psi_0 | \Psi_{0} | Numeric index; standard subscript syntax. |
| Variable (Greek macro) | \theta_0 | \theta_{0} | Numeric index; standard subscript syntax. |
| Variable (Greek macro) | \theta_s | \theta_{s} | Single-letter index is a variable (italic). |
| Variable (Greek macro) | \sigma_i | \sigma_{i} | Single-letter index is a variable (italic). |
| Variable (Greek macro) | \varepsilon_h | \varepsilon_{h} | Single-letter index is a variable (italic). |
| Variable (Latin) | \lambda_d | \lambda_{d} | Single-letter index is a variable (italic). |
| Symbol with descriptor | ID_subspace | $\mathrm{ID}_{\mathrm{subspace}}$ | Multi-letter symbol plus descriptive subscript upright; use \operatorname{ID}_{\mathrm{subspace}} if mapping. |
| Variable or Other | R_d | \operatorname{R}_{\mathrm{d}} | Named operator R with descriptive subscript upright. |
| Variable or Other | S_Centurion | $S_{\mathrm{Centurion}}$ | Variable with descriptive subscript upright via \mathrm{...}. |
| Identifier or Label | TDY_COH-OCC_<n> | \texttt{TDY\_COH-OCC\_<n>} (or \text{\texttt{...}} in math) | Identifiers or labels are monospace; wrap with \text{...} in math. |
II.6 Identifier Schemas (Normative)
II.6.1 Canonical form. All Doctrine identifiers SHALL be rendered as \texttt{TDY\_COH-<Class>_<IndexOrTag>}. When used inside math mode, they SHALL be wrapped with \text{\texttt{...}} to preserve upright monospaced appearance.
II.6.1.1 The separator after TDY_COH SHALL be a hyphen "-". The separator between <Class> and <IndexOrTag> SHALL be an underscore "_".
II.6.1.2 <Class> SHALL be one or more uppercase ASCII letters [A-Z]+ with no internal punctuation or digits.
II.6.1.3 <IndexOrTag> SHALL be one or more ASCII letters, digits, or underscores [A-Za-z0-9_]+ and MAY contain underscores to express multi-word tags (for example, Centurion, subspace, id_min).
II.6.2 Abbreviations prohibited. Bare or abbreviated references lacking the \texttt{TDY\_COH-} prefix SHALL NOT be used anywhere in Doctrine text.
II.6.3 Separator correctness. Wrong-separator forms SHALL NOT be used (hyphen between <Class> and <IndexOrTag>, or underscore after TDY_COH). Use the canonical pattern per II.6.1.
II.6.4 Schema sufficiency. The schema in II.6.1 is normative for all present and future identifiers; Annex II-B provides a point-in-time list of class tokens observed in this release.
II.6.5 Disambiguation with mathematical variables. Symbols that resemble class-index forms (for example, $E_3$, $A_{12}$) MAY appear as mathematical variables; such usage SHALL NOT be used for cross-referencing Doctrine entities. When referring to a Doctrine entity, the canonical identifier in \texttt{...} MUST be used (for example, \texttt{TDY\_COH-E\_3}), not $E_3$.
II.7 Self-Verification and Snapshot Regeneration (Normative; No External References)
II.7.1 Purpose. This procedure permits any agent to regenerate and verify Annex II-A (identifiers) and Annex II-B (class tokens) directly from the current Doctrine text, using only the rules herein.
II.7.2 Extraction rules (apply to the entire Doctrine file, UTF-8, canonical LF newlines):
II.7.2.1 Canonical identifiers: use the regular expression \bTDY_COH-[A-Z]+_[A-Za-z0-9_]+\b to locate identifiers of the form TDY_COH-<Class>_<IndexOrTag>.
II.7.2.2 Legacy OCC_n notation: if encountered in legacy text, the regular expression \bOCC_[0-9]+\b MAY be used only to locate occurrences for remediation to the canonical form per II.6.1.
II.7.2.3 Matches SHALL be captured verbatim as they appear in the Doctrine. Trailing punctuation ) , . ; : SHALL be excluded. Internal hyphens and underscores SHALL be preserved.
II.7.3 Identifier Snapshot (Annex II-A). Remove duplicate matches from II.7.2.1, sort lexicographically by raw UTF-8 codepoint order, and serialize one identifier per line with LF endings and no trailing blank line.
II.7.4 Class-Token Snapshot (Annex II-B). From each identifier TDY_COH-<Class>_<IndexOrTag>, extract <Class>, de-duplicate, sort lexicographically by raw UTF-8 codepoint order, and serialize one class token per line with LF endings and no trailing blank line.
II.7.5 Acceptance criterion (no hashes). Recompute Annex II-A and Annex II-B via II.7.2 through II.7.4 from the current Doctrine text. The recomputed lists SHALL be byte-for-byte identical to the lines enclosed in the corresponding BEGIN and END markers. Any difference marks the annex as stale; it SHALL be regenerated and replaced in full between its markers.
II.8 Annex II-A: Identifier Snapshot (Informative, Sealed at v4.1)
NOTE: Annex II-A is a point-in-time snapshot of identifiers detected in the v4.0 corpus extruded to v4.1 via II.7. It is not forward-exhaustive; future identifiers are governed by II.6.
BEGIN SNAPSHOT: ANNEX II-A IDENTIFIERS (one per line; sorted; UTF-8; LF)
TDY_COH-A_1
TDY_COH-A_10
TDY_COH-A_11
TDY_COH-A_12
TDY_COH-A_13
TDY_COH-A_14
TDY_COH-A_15
TDY_COH-A_16
TDY_COH-A_17
TDY_COH-A_18
TDY_COH-A_19
TDY_COH-A_2
TDY_COH-A_20
TDY_COH-A_21
TDY_COH-A_22
TDY_COH-A_23
TDY_COH-A_24
TDY_COH-A_25
TDY_COH-A_26
TDY_COH-A_27
TDY_COH-A_28
TDY_COH-A_29
TDY_COH-A_3
TDY_COH-A_30
TDY_COH-A_31
TDY_COH-A_32
TDY_COH-A_33
TDY_COH-A_34
TDY_COH-A_35
TDY_COH-A_36
TDY_COH-A_37
TDY_COH-A_38
TDY_COH-A_39
TDY_COH-A_4
TDY_COH-A_40
TDY_COH-A_41
TDY_COH-A_42
TDY_COH-A_43
TDY_COH-A_44
TDY_COH-A_45
TDY_COH-A_46
TDY_COH-A_47
TDY_COH-A_48
TDY_COH-A_5
TDY_COH-A_6
TDY_COH-A_7
TDY_COH-A_8
TDY_COH-A_9
TDY_COH-CPM_1
TDY_COH-ECR_1
TDY_COH-ECR_2
TDY_COH-ECR_3
TDY_COH-ECR_4
TDY_COH-ERA_1
TDY_COH-ERA_2
TDY_COH-E_1
TDY_COH-E_10
TDY_COH-E_100
TDY_COH-E_101
TDY_COH-E_102
TDY_COH-E_103
TDY_COH-E_104
TDY_COH-E_105
TDY_COH-E_106
TDY_COH-E_107
TDY_COH-E_108
TDY_COH-E_109
TDY_COH-E_11
TDY_COH-E_110
TDY_COH-E_111
TDY_COH-E_112
TDY_COH-E_113
TDY_COH-E_114
TDY_COH-E_115
TDY_COH-E_116
TDY_COH-E_117
TDY_COH-E_12
TDY_COH-E_13
TDY_COH-E_14
TDY_COH-E_15
TDY_COH-E_16
TDY_COH-E_17
TDY_COH-E_18
TDY_COH-E_19
TDY_COH-E_20
TDY_COH-E_21
TDY_COH-E_22
TDY_COH-E_23
TDY_COH-E_24
TDY_COH-E_25
TDY_COH-E_26
TDY_COH-E_27
TDY_COH-E_28
TDY_COH-E_29
TDY_COH-E_2a
TDY_COH-E_2b
TDY_COH-E_3
TDY_COH-E_30
TDY_COH-E_31
TDY_COH-E_32
TDY_COH-E_33
TDY_COH-E_34
TDY_COH-E_35
TDY_COH-E_36
TDY_COH-E_37
TDY_COH-E_38
TDY_COH-E_39
TDY_COH-E_4
TDY_COH-E_40
TDY_COH-E_41
TDY_COH-E_42
TDY_COH-E_43
TDY_COH-E_44
TDY_COH-E_45
TDY_COH-E_46
TDY_COH-E_47
TDY_COH-E_48
TDY_COH-E_49
TDY_COH-E_5
TDY_COH-E_50
TDY_COH-E_51
TDY_COH-E_52
TDY_COH-E_53
TDY_COH-E_54
TDY_COH-E_55
TDY_COH-E_56
TDY_COH-E_57
TDY_COH-E_58
TDY_COH-E_59
TDY_COH-E_6
TDY_COH-E_60
TDY_COH-E_61
TDY_COH-E_62
TDY_COH-E_63
TDY_COH-E_64
TDY_COH-E_65
TDY_COH-E_66
TDY_COH-E_67
TDY_COH-E_68
TDY_COH-E_69
TDY_COH-E_7
TDY_COH-E_70
TDY_COH-E_71
TDY_COH-E_72
TDY_COH-E_73
TDY_COH-E_74
TDY_COH-E_75
TDY_COH-E_76
TDY_COH-E_77
TDY_COH-E_78
TDY_COH-E_79
TDY_COH-E_8
TDY_COH-E_80
TDY_COH-E_81
TDY_COH-E_82
TDY_COH-E_83
TDY_COH-E_84
TDY_COH-E_85
TDY_COH-E_86
TDY_COH-E_87
TDY_COH-E_88
TDY_COH-E_89
TDY_COH-E_9
TDY_COH-E_90
TDY_COH-E_91
TDY_COH-E_92
TDY_COH-E_93
TDY_COH-E_94
TDY_COH-E_95
TDY_COH-E_96
TDY_COH-E_97
TDY_COH-E_98
TDY_COH-E_99
TDY_COH-OCC_1
TDY_COH-OCC_10
TDY_COH-OCC_11
TDY_COH-OCC_12
TDY_COH-OCC_13
TDY_COH-OCC_14
TDY_COH-OCC_15
TDY_COH-OCC_16
TDY_COH-OCC_17
TDY_COH-OCC_18
TDY_COH-OCC_19
TDY_COH-OCC_2
TDY_COH-OCC_20
TDY_COH-OCC_21
TDY_COH-OCC_22
TDY_COH-OCC_23
TDY_COH-OCC_24
TDY_COH-OCC_25
TDY_COH-OCC_26
TDY_COH-OCC_27
TDY_COH-OCC_28
TDY_COH-OCC_29
TDY_COH-OCC_3
TDY_COH-OCC_30
TDY_COH-OCC_31
TDY_COH-OCC_32
TDY_COH-OCC_33
TDY_COH-OCC_34
TDY_COH-OCC_35
TDY_COH-OCC_36
TDY_COH-OCC_37
TDY_COH-OCC_38
TDY_COH-OCC_39
TDY_COH-OCC_4
TDY_COH-OCC_40
TDY_COH-OCC_41
TDY_COH-OCC_42
TDY_COH-OCC_43
TDY_COH-OCC_44
TDY_COH-OCC_45
TDY_COH-OCC_46
TDY_COH-OCC_47
TDY_COH-OCC_48
TDY_COH-OCC_49
TDY_COH-OCC_5
TDY_COH-OCC_50
TDY_COH-OCC_51
TDY_COH-OCC_52
TDY_COH-OCC_53
TDY_COH-OCC_6
TDY_COH-OCC_7
TDY_COH-OCC_8
TDY_COH-OCC_9
END SNAPSHOT
II.9 Annex II-B: Class-Token Snapshot (Informative, Sealed at v4.1)
NOTE: Annex II-B is a point-in-time snapshot of class tokens detected by applying II.7.4 to Annex II-A's identifiers. It is not forward-exhaustive. Future class tokens must conform to II.6.1.2 and are admitted semantically via the Formalisms Registry and II.11.
BEGIN SNAPSHOT: ANNEX II-B CLASS TOKENS (one per line; sorted; UTF-8; LF)
A
CPM
E
ECR
ERA
OCC
END SNAPSHOT
II.10 Enforcement (Normative)
II.10.1 Applicability (plain-text release). Enforcement SHALL be performed by the ingesting agent directly over this file; no external tools are assumed. Pre-merge lint SHALL flag the following:
II.10.1.1 Presence of Unicode math characters where a LaTeX command exists (for example, Σ used as sum instead of \sum).
II.10.1.2 Multi-letter operators set in italics instead of \operatorname{...}.
II.10.1.3 Words or snake_case inside math not wrapped with \text{...}.
II.10.1.4 Descriptive subscripts not set upright via \mathrm{...}, including underscores (for example, _{id_min}, _{noise_term}).
II.10.1.5 Use of \left...\right on short content where plain delimiters suffice.
II.10.1.6 Abbreviated identifiers (for example, a class-index token without the TDY_COH- prefix).
II.10.1.7 Non-canonical delimiter rewrites (＄ to \(...\), ＄＄ to \ [ ... \ ] ) inside Doctrine text.
II.10.1.8 Wrong separator in identifiers (for example, missing hyphen after TDY_COH or a hyphen between <Class> and <IndexOrTag>).
II.10.1.9 Unwrapped canonical identifiers in math. Occurrences of \bTDY_COH-[A-Z]+_[A-Za-z0-9_]+\b inside ＄...＄ or ＄＄...＄＄ not wrapped as \text{\texttt{...}} SHALL be flagged.
II.10.2 Detection patterns (implementation guidance):
II.10.2.1 Bare operator words: (?<!\\)\b(lim|sup|inf|min|max|argmin|argmax|Var)\b
II.10.2.2 Σ used as sum: (?<!\\)Σ(?![A-Za-z])
II.10.2.3 Unicode sub or superscripts: [₀-₉ₐₑₕₖₗₘₙₒₚₛₜₓ⁰¹²³⁴⁵⁶⁷⁸⁹]
II.10.2.4 Snake_case in math not in \text{...}: (?<=\$)(?:[^$]*)([A-Za-z]+_[A-Za-z0-9_]+)(?:[^$]*)(?=\$)
II.10.2.5 TDY_COH schema conformance: \bTDY_COH-[A-Z]+_[A-Za-z0-9_]+\b
II.11 Exceptions and Versioning (Normative)
II.11.1 PATCH: additive rows or clarifications that do not change a canonical mapping.
II.11.2 MINOR: new canonical rows for notations discovered by FCI; expanded schemas; policy clarifications that alter enforcement guidance without changing existing mappings.
II.11.3 MAJOR: change to an existing canonical mapping or reversal of a prior rule; requires rerun of FCI and Mirror Team approval per TDY_COH-OC_1.
II.12 Cross-References (Informative)
II.12.1 For the FCI procedural details, see TDY_COH-ECR_1.
II.12.2 For semantic definitions of the formal entities referenced here, see the Formalisms Registry. That section is bound to this one and SHALL NOT redefine notation.
II.13 Authority
This section is the single source of truth for notational form in Cohereon Doctrine. In any conflict between notations appearing elsewhere and this section, this section prevails.
