55-Decision & Change Log Template v1.0 | Chapter 12 Unified Symbols & Metrology

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Chapter 12 Unified Symbols & Metrology

I. Chapter Goals & Scope (Mandatory)

• Fix unified rules for symbols, units, dimensions, and statistical caliber across this volume and companion white papers, ensuring cross-chapter/cross-volume consistency, reproducibility, and auditability.
• Applies to: DR prose, human sign-off pages, machine-readable lists (YAML/JSON), API/Schema, verification and replay reports.

II. Core Symbols (minimal unified set, Mandatory)

• Fields & quantities: phi(x,t) (scalar field), Xi(x,t) (tensor/structural tensor), K, Q.
• Medium & propagation: c_ref (reference propagation limit), n_eff (effective refractive index).
• Arrival time: T_arr; path gamma(ell), measure d ell.
• Tension/Transmittance: T_fil (tension), T_trans (transmittance).
• Compatibility: compat_rate (replay/prod compatibility pass rate).
• Gate naming: gate_<metric><comparator><threshold>@<window> (e.g., gate_accuracy>=0.99@7d).

III. No-Mix & Naming Conflicts (Mandatory)

• Do not mix: T_fil ≠ T_trans; n ≠ n_eff; c ≠ c_ref.
• Any expression with division, integral, or composite operators must use parentheses; on first occurrence, explicitly give path gamma(ell) and measure d ell.
• No Chinese in formulas, symbols, or definitions; variables/parameters use Latin/Greek letters with underscore style.

IV. Unified Arrival-Time Caliber (Mandatory)

• Constant factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
• General form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
• Whenever T_arr appears, the same or adjacent paragraph must give both gamma(ell) and d ell, and record delta_form in machine lists (general|factored).

V. Units & Dimensions (Mandatory)

• Base units: time s, length m, mass kg, charge C, temperature K, count 1 (dimensionless).
• Derived units: velocity m·s^-1, density m^-3 or kg·m^-3 (contextual), energy J, power W.
• Dimension tags: use dim, e.g., dim: "T", dim: "L", dim: "L T^-1".
• Dimensional consistency: all formulas in verification/reports must provide check_dim=true.

VI. Statistics & Uncertainty (Mandatory)

• Confidence/interval: default CI_95%; method recorded at stats.method (e.g., bootstrap).
• Notation: point estimate μ̂ (write as mu_hat in text), standard deviation σ (write as sigma), interval [lo, hi].
• Uncertainty discount: in scoring/comparison use s' = clamp(s - k·sigma, 0, 1), default k=1.

VII. In-Text Typesetting (Mandatory)

• Inline math always wrapped in backticks, e.g., T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Fixed citation style: “See 《 vX.Y》 Ch.x S/P/M/I…” (anchors preferred).
• Lists use “- space”; numbered lists use “1. space”; subsection titles use bold Roman numerals.

VIII. Symbols—Units—Dimensions Overview (copy-ready)

IX. Machine-Readable Snippets (YAML; JSON equivalent, Mandatory)

units:

base: { T: "s", L: "m", M: "kg", Q: "C", K: "K", One: "1" }

derived:

velocity: { unit: "m·s^-1", dim: "L T^-1" }

density: { unit: "m^-3", dim: "L^-3" }

symbols:

c_ref: { unit: "m·s^-1", dim: "L T^-1", desc: "reference propagation limit" }

n_eff: { unit: "1", dim: "1", desc: "effective refractive index" }

T_arr:

unit: "s"

dim: "T"

caliber:

forms:

- { name: "factored", expr: "( 1 / c_ref ) * ( ∫ n_eff d ell )" }

- { name: "general", expr: "( ∫ ( n_eff / c_ref ) d ell )" }

required_context: ["gamma(ell)","d ell"]

T_fil: { unit: "N", dim: "M L T^-2", desc: "tension" }

T_trans: { unit: "1", dim: "1", desc: "transmittance" }

compat_rate: { unit: "1", dim: "1" }

stats:

method: "bootstrap"

ci: "95%"

discount:

k_sigma: 1.0

formula: "s' = clamp(s - k*sigma, 0, 1)"

dim_checks:

check_dim: true

anchors:

- "EFT.WP.Core.Equations v1.1:S20-1"

- "EFT.WP.Core.Metrology v1.0:check_dim"

X. Arrival-Time Fill Example (Human × Machine aligned, Mandatory)

1. Human text:
   • Use the general form: T_arr = ( ∫ ( n_eff / c_ref ) d ell ); path gamma(ell) is the observation segment; measure d ell is arc-length element.
   • Dimensional check: dim(T_arr)=T; check_dim=true.
2. Machine snippet:

arrival_time:

form: "general"

path: "gamma(ell)"

measure: "d ell"

c_ref: "ref:L2"

n_eff_profile: "dataset:cmb_set_v3@v3"

check_dim: true

XI. Unified Gates & Metrics (Mandatory)

1. Unified names and directions:
   • Accuracy: gate_accuracy>=0.99@7d (higher is better)
   • Latency: gate_latency<=2h@7d (lower is better)
   • Compatibility: compat_rate>=0.995@replay (higher is better)
2. Each gate in reports must include: data source, statistical method, CI, script locator (script@commit).

XII. Human × Machine Alignment (Mandatory)

XIII. Anti-Example & Fix (Mandatory)

• Anti-example: T_arr = ∫ n / c d ell — issues: bare n and c; missing gamma(ell)/d ell; no dimensional check.
• Fix: T_arr = ( ∫ ( n_eff / c_ref ) d ell ), and in the same paragraph provide gamma(ell), d ell, and check_dim=true.

XIV. Cross-Reference Style (Mandatory)

1. Fixed in-text format: “See 《 vX.Y》 Ch.x S/P/M/I…”, anchors preferred over whole volumes.
2. Provide a machine-readable list in the DR’s references.see (examples):
   • "EFT.WP.Core.Terms v1.0:P10-3"
   • "EFT.WP.Core.Equations v1.1:S20-1"
   • "EFT.WP.Core.Metrology v1.0:check_dim"
   • "EFT.WP.Core.DataSpec v1.0:I30-2"