01-EFT.WP.Core.Terms v1.0 | Preface

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Preface

I. Goals & Scope

• This volume defines EFT-wide terminology, symbols, and writing conventions, providing a unified citation base for all companion volumes.
• It introduces no new minimal equations Sxx-? and no new metrology processes Mx-?. Formal definitions of equations and processes are delegated to the corresponding volumes, such as Core.Equations and Core.Metrology.
• The preface locks the minimally necessary prior axioms and representative formulas, and sets the numbering scheme and cross-reference rules to ensure later chapters and other volumes remain consistent and reusable.

II. Audience & Use Cases

• Theoretical and observational researchers: when drafting models and decision criteria, cite symbols and conventions defined here.
• Numerical and data engineers: when implementing, validating, and exporting glossaries, units, and dimensions, follow this volume’s interfaces and field conventions.
• Review and release teams: use this volume as a checklist to verify whether other volumes conform to the unified terminology and writing standards.

III. Prior Axioms & Representative Formulas

1. P10-1 Notation Policy
   • Enclose all inline symbols in backticks, e.g., phi(x,t), Xi(x,t), K, Q, T_fil, T_trans, n_eff.
   • Any expression with division, integration, or composite operators must use parentheses and must explicitly show 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).
5. Representative marks and conventions
   • Definition: def=; approximation: approx; dimensional similarity: sim.
   • Statistical averages: avg_t[f; Δt], avg_V[f]; differential operators: grad[f], div[F], curl[F], lap[f].
   • Dimension tags: [L], [T], [M]; example: [T_arr] = [T].
   • Dimensionless prefixes: bar_ (scaling), tilde_ (perturbation), hat_ (estimate).

IV. Unified Symbols & Minimal Set (Forward Citation Base)

1. Core objects and sets
   • Thread, Sea, Density, Tension, TensionGrad, TensionPot
   • WavePacket, STG (statistical tension gravity), TBN (tension background noise)
2. Scalar constants and baselines
   c_ref (reference propagation ceiling), k_T (tension–mass conversion), e (unit charge), m_ref (reference mass)
3. Fields and distributions
   • T_fil(x,t) (tension field), rho(x,t) (density field), n(x,t) (number density), n_eff(x,t) (effective refractive index)
   • p(x,t) (unit-norm orientation), L (locked loop length), w (winding number)
4. Path and measure
   gamma(ell) (integration path, parameterized by arc length), d ell (path measure)

V. Numbering System & Cross-Reference Rules

1. Numbering families: axioms Pxx-?, minimal equations Sxx-?, metrology flows Mx-?, implementation bindings Ixx-?.
2. Fixed cross-volume format: “see companion white paper Energy Threads, Chapter x, S/P/M/I…”.
3. In-volume example citations:
   • Axioms: see this volume, Chapter 1, P10-1 … P10-4.
   • Time-of-arrival convention: see this volume, Chapter 3, T_arr definition. Method implementation: see Methods.Repro I* (fill with actual identifiers).

VI. Dependencies & Applicability Boundaries

• Numerical implementations and metrology for time-of-arrival and any path-dependent expressions are governed by Core.Metrology, Metrology.PathCorrection, and Metrology.Sync.
• Equation-level details and boundary conditions are governed by Core.Equations. This volume defines no new Sxx-?.
• Error taxonomy and pass/falsification criteria are governed by Core.Errors and Methods.Falsification. This volume standardizes symbols and notation only.

VII. How to Use (Minimal Three Steps)

• Select terms and symbols: choose name, code, unit, and the writing convention from this volume’s lists.
• Bind to implementations: register and validate via interfaces such as register_term(...), check_dim(...), validate_expr(...).
• Generate and review: export the glossary (e.g., export_terms("yaml")), and cite terms in other volumes following this volume’s conventions.

VIII. Terminology Governance & Versioning

• Register and approve new terms and aliases via standardized interfaces: register_term(...), add_alias(...), normalize_symbol(...).
• Unify dimensions and units after registration: register_unit(...), check_dim(...).
• From v1.0 onward, adopt backward-compatible minor increments. Any change must list impact scope and replacement options in the appendices.

IX. Quick Reference (Core Reusable Expressions)

• Time of arrival, constant factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
• Time of arrival, general: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
• Statistical average (time window): avg_t[f; Δt]
• Common operators: grad[f], div[F], curl[F], lap[f]
• Conflict pairs: T_fil / T_trans, n / n_eff

X. Relationship to Other Volumes (Navigation)

• Concepts → Equations: see Core.Equations (mapping from symbols to Sxx-?).
• Concepts → Metrology: see Core.Metrology (mapping from symbols to Mx-? calibration and traceability).
• Concepts → Implementation: see Methods.Repro and this volume’s implementation bindings I10-*.
• Concepts → Applications: see STG. , Propagation. , EDX. for domain and engineering instantiations.

Closing

This volume provides a minimal yet complete layer of terminology and notation to ensure that text, formulas, and implementations remain consistent and reusable across volumes. Subsequent chapters proceed under the axioms and rules above, delivering the full glossary, operators, units, and implementation-binding specifications.