01-EFT.WP.Core.Terms v1.0 | Chapter 2, Basic Objects & Roles

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Chapter 2, Basic Objects & Roles

I. Chapter Objectives & Structure

• Clarify the normative definitions, attributes, and usage boundaries of Thread, Sea, Density, and Tension. All definitions use def= in English. All symbols and formulas use plain-text notation and the established convention.
• Fix the minimum fields of each terminology entry, namely name, code, type, unit, def=, constraints, see, aligned with implementation binding I10-1.
• Cross-references follow P10-1, P10-2, P10-3, P10-4 (see this volume, Chapter 1).

II. Object Overview & Relations (prose)

1. Sea provides the propagation and phase reference. The key quantities are n_eff(x,t) and c_ref.
2. Thread is a locally phase-ordered conduit embedded in Sea. Its near field is constrained by T_fil(x,t) and orientation p(x,t).
3. Density uses rho(x,t) to describe how distributions influence paths and statistical terms.
4. Tension denotes the intrinsic tension field T_fil(x,t). Its TensionGrad and TensionPot govern propagation ceilings and path effects.
5. Unified time-of-arrival convention:
   • T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • T_arr = ( ∫ ( n_eff / c_ref ) d ell ) (see this volume, Chapter 1, P10-3)

III. Thread (Energy Thread)

• Definition (def=)
  Thread def= a locally phase-ordered energy conduit embedded in Sea; in the stable case it corresponds to a closed weave ring characterized by ring length L, winding number w, and orientation p(x,t).
• Type & fields
  type = object; core fields: p(x,t), L, w, T_fil(x,t).
• Domain & range
  Spatial domain is the neighborhood of gamma(ell); temporal domain t ∈ R; p(x,t) has unit norm.
• Units & dimensions
  L → [L]; w is dimensionless; p(x,t) is dimensionless; units of T_fil(x,t) are specified in Core.Metrology.
• Usage boundaries (constraints)
  Must provide both p(x,t) and (L,w); do not substitute an arbitrarily high-gradient region for a Thread.
• See
  see = ["Core.Equations","Core.Metrology","Methods.Inference"]

IV. Sea (Energy Sea)

• Definition (def=)
  Sea def= the background medium providing propagation and phase reference, effectively parameterized by n_eff(x,t) with reference limit c_ref.
• Type & fields
  type = medium; core fields: n_eff(x,t), gamma(ell).
• Domain & range
  n_eff(x,t) > 0; it may vary over space and time and couple to near-field structure.
• Units & dimensions
  n_eff(x,t) is dimensionless; T_arr → [T].
• Usage boundaries (constraints)
  Bare c is forbidden; any line integral must explicitly show gamma(ell) and d ell (see P10-2).
• See
  see = ["Core.Metrology","Metrology.PathCorrection","Propagation.PathRedshift"]

V. Density (Density)

• Definition (def=)
  rho(x,t) def= a field describing matter/energy distribution whose statistics act as sources or constraints for path- and gravity-like effects.
• Type & fields
  type = field; core fields: rho(x,t), avg_t[rho; Δt], avg_V[rho].
• Domain & range
  rho(x,t) ≥ 0; domains may be local or cosmological in scale.
• Units & dimensions
  rho(x,t) → [M L^-3] (dimension and unit registration see I10-3).
• Usage boundaries (constraints)
  Strictly do not conflate with n_eff(x,t); statistical averages must label their window and measure.
• See
  see = ["STG.Dynamics","Core.Errors","Methods.Falsification"]

VI. Tension (Tension)

• Definition (def=)
  T_fil(x,t) def= the intrinsic tension field of the medium–weave system; TensionGrad def= grad[T_fil]; TensionPot def= an effective potential governing propagation limits via mappings defined in Core.Equations.
• Type & fields
  type = field; core fields: T_fil(x,t), TensionGrad(x,t), TensionPot(x,t).
• Domain & range
  T_fil(x,t) is continuous and differentiable; its gradients and potentials enter propagation and imaging criteria.
• Units & dimensions
  Units and mappings are specified in Core.Metrology; consistency is verified by check_dim(expr).
• Usage boundaries (constraints)
  Do not confuse with T_trans; T_fil must not be used as a symbol for temperature or time (see P10-4).
• See
  see = ["Propagation.TensionPotential","EDX.OrientedTension","BH.TensionWall"]

VII. Derived Objects & Interoperation

1. WavePacket
   • Definition (def=) WavePacket def= a propagation unit within a coherence window whose delay and dispersion are governed by n_eff(x,t) and the TensionGrad/TensionPot mappings.
   • Interoperation: when entering time-of-arrival expressions, use the T_arr common-term convention.
2. STG
   • Definition (def=) STG def= a protocol family attributing gravity-like observations to statistics of unstable constituents and tension-field terms, constrained by rho(x,t) and T_fil(x,t).
   • Interoperation: source terms use avg_t[•; Δt], avg_V[•].
3. TBN
   • Definition (def=) TBN def= a background noise component associated with fluctuations of T_fil and n_eff that enters metrology budgets and mitigation strategies.
   • Interoperation: realized on the metrology side via Mx-* entries.

VIII. Typical Paths & Time-of-Arrival Interfacing

1. Path naming and measure: ∫_gamma (...) d ell, where gamma(ell) is parameterized by arc length.
2. Unified time-of-arrival forms:
   • T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • T_arr = ( ∫ ( n_eff / c_ref ) d ell )
3. Mapping to tension: the mappings and applicability domains between n_eff and TensionPot/TensionGrad are defined in Core.Equations.

IX. Implementation Binding & Registry List (I10-1 Use Cases)

• register_term(name="Thread", code="thread", type="object", unit=None, definition="a locally phase-ordered energy conduit embedded in Sea; closed weave ring with (L,w,p)", constraints=["must specify p(x,t), L, w"], see=["Core.Equations"])
• register_term(name="Sea", code="sea", type="medium", unit=None, definition="background medium with n_eff(x,t) and c_ref", constraints=["explicit gamma(ell), d ell in line integrals"], see=["Core.Metrology"])
• register_term(name="Density", code="rho", type="field", unit="[M L^-3]", definition="matter/energy distribution field with explicit temporal and spatial averages", constraints=["use avg_t and avg_V with windows"], see=["STG.Dynamics"])
• register_term(name="Tension", code="T_fil", type="field", unit="see Core.Metrology", definition="intrinsic tension field; mappings to n_eff defined elsewhere", constraints=["must not be confused with T_trans"], see=["Propagation.TensionPotential"])

Chapter Summary

This chapter provides harmonized def= entries in English, plain-text symbols and formulas for the four core objects, and clear rules for interoperation and boundaries. Subsequent chapters build on this foundation to specify fields and paths, constants and baselines, operators and statistics, and the full specification of implementation-binding interfaces.