01-EFT.WP.Core.Terms v1.0 | Chapter 1, Naming Principles and Notation Conventions

Home ／ Docs-Technical WhitePaper ／ 01-EFT.WP.Core.Terms v1.0

Chapter 1, Naming Principles and Notation Conventions

I. Chapter Objectives

• Unify EFT-wide naming syntax, prefix/suffix patterns, and notation rules so symbols are directly reusable across volumes without ambiguity.
• Fix axioms P10-1, P10-2, P10-3, P10-4, and provide a minimal example tied to implementation binding I10-2.
• This chapter governs names and notation only; equations are in Core.Equations, and metrology is in Core.Metrology.

II. Naming Axioms (P10- series)

1. P10-1 Notation Policy
   • All inline symbols are wrapped in backticks: phi(x,t), Xi(x,t), K, Q, T_fil, T_trans, n_eff.
   • Any expression with division, integration, or composite operators uses parentheses and explicitly shows the path gamma(ell) and the measure d ell.
2. P10-2 Explicit-Path Policy
   For line integrals and time-of-arrival expressions, write gamma(ell) and d ell explicitly, and state whether c_ref is constant.
3. P10-3 Unified Time-of-Arrival Convention
   • Constant factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
4. P10-4 Conflict-Name Safeguard
   Do not conflate T_fil (tension) with T_trans (transmission coefficient). Distinguish n (number density) from n_eff (effective refractive index).

III. Ten Naming Rules (Unified Syntax)

• Uniqueness and clarity: each concept maps to one canonical name canonical. Prefer intuitive English compounds or proper terms such as TensionPot, TensionGrad.
• Case semantics: use leading capitals for object names (e.g., Thread, Sea). Use lowercase with arguments or underscores for fields and functions (e.g., rho(x,t), n_eff(x,t)).
• Prefix pattern: dimensionless uses bar_, perturbation uses tilde_, estimate uses hat_. Examples: bar_T_fil, tilde_rho, hat_n_eff.
• Suffix pattern: use _ref and _eff for reference and effective; use _crit, _min, _max for thresholds and bounds; use _avg, _std for statistics.
• Constants: name physical and reference constants in lowercase with _ref or a clear semantic suffix, e.g., c_ref, m_ref, k_T. Bare c is forbidden.
• Vectors vs. scalars: write vectors as functions or indexed components, e.g., p(x,t) or p_i. Do not use bold or arrows.
• Path and measure: write the path as gamma(ell) and the measure as d ell. Any path change must explicitly declare the new path name.
• Operators: use grad[f], div[F], curl[F], lap[f] for gradient, divergence, curl, and Laplacian. Use avg_t[f; Δt], avg_V[f] for time and volume averages.
• Definition and approximation: first definitions use def=, approximations use approx, dimensional similarity uses sim. Use “identity” for identities.
• Aliases and normalization: controlled aliases may be registered, but only the canonical name is used in the main text. Alias resolution and canonical rewriting are handled by I10-2.

IV. Structured Prefixes and Examples

• bar_: bar_T_fil(x,t) denotes the dimensionless version of T_fil(x,t); the mapping is given in Chapter 6, Dimensions and Non-Dimensionalization.
• tilde_: tilde_rho(x,t) denotes the perturbation relative to a slowly varying background.
• hat_: hat_n_eff(x,t) denotes an estimator or a filtered estimate.
• _ref: c_ref is the reference propagation ceiling; its value and calibration are defined only in Core.Metrology.
• _eff: n_eff(x,t) is the effective refractive index; its use must state how it is obtained (model, measurement, or assimilation).
• _crit: K_crit is the locking threshold; formal definition and estimation workflow are provided in Core.Equations and Methods.Inference.

V. Notation and Writing Conventions

1. Fields and distributions: T_fil(x,t), rho(x,t), n(x,t), n_eff(x,t).
2. Orientation and topology: p(x,t) (unit-norm orientation), L (locked loop length), w (winding number).
3. Time-of-arrival templates:
   • T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • T_arr = ( ∫ ( n_eff / c_ref ) d ell )
4. Dimension tags: [L], [T], [M]; example: [T_arr] = [T].
5. Statistics and domains: avg_t[f; Δt], avg_V[f]; use explicit domain qualifiers, e.g., avg_V[f; V=Ω].

VI. Conflict and Prohibited List (Mandatory)

• Ambiguous symbols are forbidden: bare c, T, and n are not allowed. Write c_ref, T_fil, n_eff, or define the quantity inline.
• Reserved conflict pairs: T_fil / T_trans, n / n_eff; interchanging them is strictly prohibited.
• Semantic overloading is forbidden: within one context, a symbol must not represent different physical or statistical quantities.
• Path omission is forbidden: for any line integral or path-dependent quantity, do not omit gamma(ell) and d ell.

VII. Canonical Usage and Counterexamples

1. Time-of-arrival expression
   • Correct: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
   • Incorrect: T_arr = ∫ n_eff d ell / c (missing parentheses and undefined c_ref)
2. Path declaration
   • Correct: ∫_gamma n_eff d ell, where gamma(ell) is the observation path parameterized by arc length.
   • Incorrect: ∫ n_eff dl (path not named, measure not aligned)
3. Symbol uniqueness
   • Correct: T_fil denotes tension; T_trans denotes transmission coefficient.
   • Incorrect: using T in the same section to denote both.

VIII. Aliases and Normalization (I10-2 Example)

1. Objective: maintain a search-friendly alias table without polluting the main text, and rewrite to the canonical name during export and validation.
2. Operation sequence
   • Register alias: add_alias(canonical="n_eff", alias="n_effective")
   • Resolve to canonical: normalize_symbol(token="n_effective") -> "n_eff"
   • Review output: use n_eff in prose and figures; data dictionaries may list aliases to preserve compatibility with historical assets.

IX. Numbering and Cross-References

• Number families: axioms Pxx-?, equations Sxx-?, metrology Mx-?, implementations Ixx-?.
• Anchors in this chapter: P10-1, P10-2, P10-3, P10-4; implementation reference: I10-2.
• Citation format: “this volume, Chapter x, P/S/M/I…”. Cross-volume format: “companion white paper Energy Threads, Chapter x, S/P/M/I…”.

X. Quick Compliance Checklist

• Are all symbols in this section consistent with the parentheses and path rules for inline expressions?
• Are bare c, T, and n avoided, with clear distinctions among T_fil, T_trans, n, and n_eff?
• Are gamma(ell) and d ell provided wherever required?
• Are prefix and suffix conventions followed (bar_, tilde_, hat_, _ref, _eff, _crit, etc.)?
• Are the P10-* axioms enforced, with alias normalization verifiable through implementation layer I10-2?

Chapter Summary

This chapter presents four naming axioms, ten rules, and a controlled alias mechanism, together with explicit notation for paths and measures and a unified time-of-arrival convention. Any later chapter that introduces new symbols must first satisfy this chapter’s requirements and complete registration and validation at the implementation layer.