01-EFT.WP.Core.Terms v1.0 | Chapter 7, Ambiguity Avoidance & Conflict Checklist

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Chapter 7, Ambiguity Avoidance & Conflict Checklist

I. Chapter Goals & Scope

• Establish cross-volume rules to avoid ambiguity and a conflict checklist that is executable for validation, aligned with Chapters 1–6 and implementation layers I10-1 … I10-7.
• Publish mandatory axioms P70-* and six conflict-check rules covering symbols, paths, dimensions, statistics, naming, and citations; all symbols and definitions use plain-text notation and the parentheses conventions.

II. Conflict Matrix (Overview)

• Symbol-pair conflicts
  T_fil ↔ T_trans; n ↔ n_eff; c_like ↔ c_ref; p (vector) ↔ p_i (component)
• Structural conflicts
  Omitted path/measure: gamma(ell), d ell; misuse of statistical windows: avg_t[•; Δt], avg_V[•]
• Dimension & unit conflicts
  Unregistered units/dimensions; arrival-time integrand not closed: ( n_eff / c_ref ) * d ell
• Citation & numbering conflicts
  Misuse/omission of Pxx-? / Sxx-? / Mx-? / Ixx-?; incorrect cross-volume citation format

III. Mandatory Axioms (P70- series)

• P70-1 Symbol Exclusivity
  T_fil def= intrinsic tension field; T_trans def= transmission coefficient; semantics are mutually exclusive—no reuse or suffix omission.
• P70-2 Refractive Separation
  n_eff(x,t) def= effective refractive index; n(x,t) def= particle number density; only n_eff is permitted in any arrival-time expression.
• P70-3 Path Explicitness
  Every line integral must state gamma(ell) and d ell explicitly, and provide L_gamma = ∫_gamma 1 d ell.
• P70-4 Timing Canonicality
  T_arr(gamma) def= ( ∫_gamma ( n_eff / c_ref ) d ell ); constant-factored: T_arr = ( 1 / c_ref ) * ( ∫_gamma n_eff d ell ).
• P70-5 Dimensional Closure
  The integrand ( n_eff / c_ref ) * d ell is dimensionless; after path integration dim[T_arr] = [T]; all units must be registered in I10-3.
• P70-6 Windowed Statistics
  Statistical measures must declare window and measure: avg_t[f; Δt], avg_V[f; V=Ω]; implicit windows or default domains are forbidden.

IV. Conflict Pairs & Correction Rules (Wrong → Right)

1. C1: T_fil / T_trans
   • Wrong: T = ... (same context used for both tension and transmission)
   • Right: T_fil(x,t) = ...; T_trans(•) = ... (semantics separated)
2. C2: n / n_eff
   • Wrong: T_arr = ( ∫ ( n / c_ref ) d ell )
   • Right: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
3. C3: c_like / c_ref
   • Wrong: T_arr = ∫ n_eff d ell / c (bare c, missing parentheses)
   • Right: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
4. C4: Path omission
   • Wrong: ∫ n_eff dl
   • Right: ∫_gamma n_eff d ell, with gamma(ell) and L_gamma defined in context
5. C5: Vector marking
   • Wrong: using bold or arrows for vector p
   • Right: p(x,t) or component p_i, and declare |p| = 1
6. C6: Statistical conventions
   • Wrong: avg_t[f] (window not declared)
   • Right: avg_t[f; Δt]; volume mean as avg_V[f; V=Ω]

V. Dimensional & Unit Conflicts (Detection & Repair)

1. Detection points
   • check_dim("( n_eff / c_ref ) * d_ell") -> "[T^0]"; ∫_gamma (...) d ell -> "[T]".
   • dim[avg_t[f; Δt]] = dim[f]; dim[var_t[f; Δt]] = dim[f]^2.
2. Repair path
   • Missing registration → register_unit(...)
   • Integrand not closed → verify c_ref and d ell
   • Mixed non-dimensionalization → in one derivation domain keep a single coordinate family (e.g., bar_ell or ell)

VI. Citation & Numbering Ambiguity (Unified Convention)

1. Rules
   • Use Pxx-? for axioms; Sxx-? for equations; Mx-? for metrology; Ixx-? for implementation.
   • New anchors here: P70-1 … P70-6.
2. Examples
   • Arrival-time citation: see this volume, Chapter 3, T_arr definition; conforms to P70-4.
   • Metrology windows: see this volume, Chapter 5, statistics; conforms to P70-6.
   • Unit registry: see this volume, Chapter 6 and I10-3.

VII. Term Lifetime & Scope (Temporary Symbol Governance)

1. Rules
   • Temporary symbols use prefix tmp_ and expire at the end of the current subsection.
   • Cross-section quantities must be registered as formal terms via I10-1 register_term(...).
2. Examples
   • Right: tmp_alpha def= local smoothing factor (cleared at section end)
   • Wrong: using an unregistered alpha in later chapters

VIII. Automated Validation & Implementation Binding (I10- Interface Mapping)

1. Expressions & symbols
   • validate_expr(expr, allowed): forbid bare ambiguous symbols { T, c, n }; allow { T_fil, T_trans, n_eff, c_ref, gamma, d ell }.
   • normalize_symbol(token): normalize aliases to canonical names (e.g., n_effective -> n_eff), aligned with P70-2.
2. Conflict scanning (suggested)
   lint_conflicts(expr:str) -> list[code]
   • C1_TensionMix: T_fil and T_trans appear in the same scope
   • C2_RefracMix: n used in an arrival-time integrand
   • C3_PathOmitted: missing gamma(ell) or d ell
   • C4_DimOpen: check_dim not closed
   • C5_StatWindowMissing: missing Δt or Ω
   • C6_RawConstant: bare c used
3. Minimal working sequence
   • validate_expr("T_arr = ( ∫ ( n_eff / c_ref ) d ell )", allowed=...) -> True
   • validate_expr("T_arr = ∫ n d ell / c", allowed=...) -> False
   • lint_conflicts(...) returns {C2_RefracMix, C3_PathOmitted, C6_RawConstant}

IX. Six Executable Conflict-Check Rules

• R1: Tension–Transmission Isolation
  Assertion: symbols_in(ctx) ∩ {"T_fil","T_trans"} ≤ 1. Violation → C1_TensionMix.
• R2: Refractive Convention for Arrival Time
  Assertion: integrand contains only n_eff, and c_ref appears explicitly: match("∫ ( n_eff / c_ref ) d ell"). Violation → C2_RefracMix or C6_RawConstant.
• R3: Path Explicitness
  Assertion: all line integrals include gamma(ell) and d ell. Violation → C3_PathOmitted.
• R4: Dimensional Closure
  Assertion: check_dim("( n_eff / c_ref ) * d_ell") == "[T^0]" and dim[∫ ...] == "[T]". Violation → C4_DimOpen.
• R5: Statistical Window
  Assertion: avg_t, avg_V, var_t, cov_t, etc., declare a window or domain. Violation → C5_StatWindowMissing.
• R6: Coordinate-Family Consistency
  Assertion: do not mix bar_ell with ell, or bar_x with x within one derivation domain. Violation → unify to a single coordinate family and declare the mapping.

X. Pre-Publication Checklist

• Do P70-1 … P70-6 hold without triggering {C1 … C6}?
• Are all arrival-time expressions written as T_arr = ( ∫ ( n_eff / c_ref ) d ell ) or its constant-factored form?
• Are paths, windows, units, and dimensions registered in I10-3 and validated via check_dim?
• Are cross-volume citations in the fixed format and targeting the correct P/S/M/I anchors?
• Have all bare ambiguous symbols and unclosed integrands been eliminated?

Chapter Summary

Through P70-* axioms and six executable rules, this chapter systematically closes high-frequency ambiguities—T_fil/T_trans, n/n_eff, c_ref/c_like, path omission, statistical windows, and dimensional closure—and pairs them with I10-* interfaces to enable automated linting and review. Future authoring and peer review must treat this checklist as a hard gate to guarantee cross-volume consistency and verifiability across both text and implementation.