50-Parameter Registration Card Template v1.0 | Chapter 2 — Terms & Symbols (Minimal Registration Set)

Home ／ Docs-Technical WhitePaper ／ 50-Parameter Registration Card Template v1.0

Chapter 2 — Terms & Symbols (Minimal Registration Set)

I. Variables & Symbols (minimal set)

Wrap all inline symbols in backticks; for path-related parameters you must explicitly declare gamma(ell) and the measure d ell in text, and record delta_form ∈ {general, factored} in the card data.

• param_id: primary key (in snake_case), globally unique.
• symbol: physical/mathematical symbol (e.g., c_ref, λ_ref, τ_sys, n_eff).
• domain: value domain & datatype, including type / unit / range / default / precision.
• lineage: source/provenance (source_type, instrument, calib_run_id).
• freshness: validity window (valid_from/valid_to, policy{tau_calib_s_max, clock_state}).
• uncertainty: type(A/B), estimate, distribution, coverage{k or confidence}.
• constraints: dependencies & derived relation (depends_on[], derived control equation).
• cov_group: covariance grouping tag (for coordination with the Error Budget Card).
• status: lifecycle state (draft/stable/deprecated).
• see[]/references[]/version: citation anchors and version fields (volume+version+anchor, anchor coverage ≥ 90%).

II. Minimal UQ Notation

• u(x): standard uncertainty; u_c: combined standard uncertainty; U = k · u_c: expanded uncertainty.
• E[x], Var[x], Cov(x,y), ρ: expectation, variance, covariance, correlation coefficient.
• Interval types: confidence / credible / quantile (state coverage such as k=2 or [2.5%,97.5%]).

III. Constants & Reference Quantities

• c_ref: reference propagation limit, unit m/s.
• λ_ref: reference wavelength, unit m.
• k_ref = 2π / λ_ref: reference wavenumber, unit 1/m.
• σ_y(τ): Allan deviation, unit 1 (dimensionless).

IV. Units & Dimensions

• Base units & examples: m, s, rad, 1; SI derivatives Pa, N, J, Hz, etc.
• Arrival-time check:
  T_arr = ( ∫ ( n_eff / c_ref ) d ell ) ⇒ [1]/[m·s^-1]·[m] = [s].
• Phase check:
  Phi = ( 2π / λ_ref ) ( ∫ n_eff d ell ) ⇒ [1/m]·[m] = [rad].
• Registration requirement: all expressions pass I70-dim_check, p_dim = 1.0, and export includes check_dim_report.json.

V. Mandatory Conventions (writing & conflicts)

• Parentheses & precedence: any division/integral/composite operator must use parentheses; logs/exp/convolution use ln(·), log10(·), exp(·), conv(·).
• Explicit path: for any parameter linked to T_arr/Phi, the text must show gamma(ell) and d ell, and the card must record delta_form.
• Forbidden bare symbols: c, T, n; use c_ref, specific quantity names (e.g., T_arr), and n_eff (or n with explicit unit).
• Conflict names: T_fil (tension) ≠ T_trans (transmittance); n (number density) ≠ n_eff (effective refractive index); do not mix.
• Language: formulas, symbols, definitions must use international notation (no Chinese); headers in snake_case.

VI. Normative Examples (paste-ready)

• Arrival time (two equivalent):
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
  T_arr = ( ∫ ( n_eff / c_ref ) d ell )
• Phase accumulation:
  Phi = ( 2π / λ_ref ) * ( ∫ n_eff d ell )
• Freshness policy example:
  policy: { tau_calib_s_max: 86400, clock_state: "locked" }.
• Covariance grouping:
  cov_group: "timing", "optics", "medium", etc., for cross-card composition.

VII. Machine-Readable Registration (YAML, minimal snippet)

version: "1.0.0"

param_card:

param_id: "REF-c_ref"

name: "reference_speed"

symbol: "c_ref"

domain: { type: "real", unit: "m/s", range: [2.9e8, 3.1e8], default: 2.99792458e8, precision: "float64" }

lineage: { source_type: "constant", method: "SI", instrument: "—", calib_run_id: "—" }

freshness: { valid_from: "2025-01-01T00:00:00Z", valid_to: "9999-12-31T23:59:59Z", policy: { tau_calib_s_max: 86400, clock_state: "locked" } }

uncertainty: { type: "B", estimate: 0.0, distribution: "degenerate", coverage: { k: 2 } }

constraints: { depends_on: [], derived: "" }

cov_group: "timing"

status: "stable"

see: ["EFT.WP.Core.Terms v1.0:P10-3","EFT.WP.Core.Metrology v1.0:check_dim"]

version: "1.0.0"

VIII. Consistency for Publishing

• Text and data see[]/references[] use “volume + version + anchor (P/S/M/I)”, with anchor coverage ≥ 90%; no external links/aliases.
• For path-related parameters: explicit gamma(ell)/d ell in text; delta_form recorded; len(path) ≥ 2, Δell satisfies sampling constraints.
• In the registry and results page, list units/dimensions and coverage; align with the Error Budget Card’s cov_group and U = k·u_c composition.