30-EFT.WP.Propagation.TensionPotential v1.0 | Preface

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Preface

I. Overview
One-sentence abstract: Within the Energy Sea framework, this volume defines the Tension Potential Phi_T(x,t), establishes its properties and metrology, and specifies propagation gauges and arrival-time conventions via n_eff(x,t,f). It also provides implementation bindings and verification paths to support cross-volume, consistent propagation modeling and engineering reuse.

II. Background & Problem Statement

• Problem focus: In observations, arrival time, phase, and energy distribution show superposed “path terms” and “common terms.” Without a unified tension-potential gauge, comparable metrology across layers of media, frequency bands, and geometric paths is difficult.
• Theoretical gap: Prior volumes (Tension, Energy Sea, Metrology) define T_fil, the layered structure of the Sea, and metrological semantics separately, but a complete technical linkage from these to “effective refractive index n_eff and arrival-time gauges” is still missing.
• Engineering pain points: Different projects implement n_eff and path integrals independently, causing inconsistencies in units, references, error composition, and interfaces, which undermines reproducibility and portability.

III. Objectives & Contributions

• Definitions & conventions: Formally define Phi_T(x,t) and its relationship to T_fil(x,t); provide minimal equations, integrability, boundary conditions, and practical gauge choices.
• Propagation gauges: Construct n_eff(x,t,f) from Phi_T and grad_Phi_T; separate the frequency-independent common term from the path term; provide two equivalent arrival-time gauges.
• Metrology & calibration: Establish traceable calibration flows for n_eff and Phi_T, reference path sets, and uncertainty composition rules.
• Implementation binding: Offer standard APIs (I-layer) and numerical constraints to enable cross-project reuse and auditability.
• Validation & falsification: Provide datasets, benchmark metrics, and falsification lines to ensure consistent terminology, units, interfaces, and testability.

IV. Intended Audience & Prerequisites

• Audience: Theory and algorithm researchers, metrology and systems engineers, data and simulation engineers.
• Prerequisites: Familiarity with foundational terms, minimal equations, and metrological semantics from EFT.WP.Core.Terms v1.0, EFT.WP.Core.Tension v1.0, EFT.WP.Core.Sea v1.0, EFT.WP.Core.Equations v1.1, EFT.WP.Core.Metrology v1.0, and EFT.WP.Core.Errors v1.0.

V. Cross-References
Throughout, use the fixed convention “volume name + version + anchor,” e.g.:

• EFT.WP.Core.Tension v1.0 S12-*
• EFT.WP.Core.Sea v1.0 S08-*
• EFT.WP.Core.Equations v1.1 S06-*
• EFT.WP.Core.Metrology v1.0 M05-, M10-
• EFT.WP.Core.Errors v1.0 M20-*

VI. Control Equations (two arrival-time gauges; unified exemplar for cross-volume reuse)

• Constant factored out: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
• General gauge: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

Notes: The path is gamma(ell) with line element d ell; always write the reference speed as c_ref; the construction n_eff = F( Phi_T, grad_Phi_T, … ) is specified in later chapters; wrap all inline symbols in backticks.

VII. Non-Goals & Scope Boundaries

• No discussion of cosmological origins, early-universe events, or macroscopic statistical explanations; this volume provides engineering gauges at the propagation and tension-potential layers only.
• Do not conflate T_fil with transmission coefficient T_trans; do not replace the theoretical structure of n_eff with empirical refractive indices.
• No mechanical or electrical design details for specific apparatus; only metrology and interface specifications are provided.
• Avoid phrases like “wavelength is stretched”; describe spectral changes uniformly as “arrival-time or spectral-distribution changes induced by the tension-potential mapping.”

VIII. Reading Map

• Chapter 1 — Terms & Preliminaries: Minimal terms and symbols; unit and dimensional checks; mathematical notation; constraints on c_ref and path gamma(ell).
• Chapter 2 — Axioms & Applicability: Axiom set P20-*, applicable scales and default boundary conditions, gauge choices, and integrability prerequisites.
• Chapter 3 — Minimal Equations & Derivation Overview: Minimal equations S20-*; the functional skeleton for n_eff; two total forms for arrival time; full derivations relegated to appendices.
• Chapter 4 — Building the Tension-Potential Field & Its Properties: Definition, boundary behavior, smoothness, far-field behavior, superposition; discretization caveats.
• Chapter 5 — Effective Refractive Index & Propagation Limits: Construction n_eff = F(Phi_T, grad_Phi_T, rho, f); physical meaning and calibration of c_ref; asymptotic expansions and limiting cases.
• Chapter 6 — Path Formulation & Arrival-Time Gauges: Paths and measures; conditions of applicability for the two gauges; numerical implementation and convergence.
• Chapter 7 — Metrology & Calibration Flows: Reference-path design, inversion flows, traceability chains, and uncertainty composition; reporting format.
• Chapter 8 — Boundary Conditions & Inter-Layer Interfaces: Matching conditions for layered Sea; handling jumps in n_eff and T_arr at interfaces; name isolation for T_trans.
• Chapter 9 — Modeling Methods & Numerical Implementation: Solver choices, step-size control, error estimation, benchmark tasks and datasets, reproducibility requirements.
• Chapter 10 — Implementation Binding & API Specification: I10-* interface prototypes, units and coordinates, random sources, logging, versioning, and compatibility.
• Chapter 11 — Validation Experiments & Benchmark Datasets: Experimental design, benchmark metrics, falsification lines, and proposals for open reproducibility tests.
• Chapter 12 — Error Budget & Systematic-Error Safeguards: Inclusion of TBN, discretization error, ill-posedness, regularization, and confidence intervals.
• Chapter 13 — Applications & Case Studies: Arrival-time imaging, path comparison and inversion, and deployment guidance for multi-layer media propagation estimation.
• Chapter 14 — Consistency, Cross-Volume Alignment & Open Questions: Consistency checks with core volumes, limitations and open questions, and the roadmap.
• Chapter 15 — Version Notes & Change Log v1.0: Freeze points, compatibility, deprecations and migration advice, state of reference implementations.

IX. Version Note
This volume adopts White Paper Layout v1.1. Use “#” heading levels; only leading labels such as “one-sentence abstract,” “control equations,” “key points,” “cross-references,” “notes,” “limitations,” and “version note” may be boldfaced. All formulas and symbols are plain text; inline symbols are wrapped in backticks. Tables are disallowed; use bullets and numbering for matrices or comparisons. Cross-volume references must follow the fixed “volume name + version + anchor” convention.