48-Experimental Protocol Card Template v1.0 | Chapter 2 — Terms & Symbols (Minimal Set for the Protocol Card)

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Chapter 2 — Terms & Symbols (Minimal Set for the Protocol Card)

I. Variables (execution minimal set)

Wrap all inline symbols in backticks; for any path-dependent quantity, explicitly declare gamma(ell) and the measure d ell.

• T_arr: arrival time; unit s; path quantity—must co-appear with gamma(ell), d ell, n_eff, c_ref, and record delta_form.
• Phi: accumulated phase; unit rad; paired with lambda_ref.
• n_eff(ell): effective refractive index along path; dimensionless.
• gamma(ell): parametrized propagation path; unit m.
• d ell: path measure element; unit m.
• r_hat: unit pointing vector; dimensionless.
• Q: robust quality metric; dimensionless, in [0,1].
• ε_flux: paraxial conservation error; dimensionless.
• ΔT_arr: arrival-time residual (observed − reference); unit s.
• r_phi: correlation coefficient between Phi_ref and Phi_obs; dimensionless.

II. Constants & Reference Quantities

• c_ref: reference propagation limit; unit m/s.
• λ_ref: reference wavelength; unit m.
• k_ref: reference wavenumber = 2π / λ_ref; unit 1/m.

III. Units & Dimensions

• Base units: m, s, rad, 1.
• Arrival-time dimensional check (unified form):
  T_arr = ( ∫ ( n_eff / c_ref ) d ell ) ⇒ [1]/[m·s^-1]·[m] = [s].
• Phase dimensional check (unified form):
  Phi = ( 2π / λ_ref ) ( ∫ n_eff d ell ) ⇒ [1/m]·[m] = [rad].
• Results and reports must include a dimensional-closure report (check_dim).

IV. Mandatory Conventions (writing & conflict names)

1. Explicit path: whenever T_arr/Phi appear, the text must also show gamma(ell) and d ell, and data/metadata must record delta_form ∈ {general, factored}.
2. Two equivalent forms for arrival time (unified examples):
   • Constant factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
3. Forbidden bare symbols: c, T, n; use c_ref, specific quantity names (e.g., T_arr / T_fil), and n_eff (or n with explicit units).
4. Conflict names: T_fil (tension) ≠ T_trans (transmittance); n (number density) ≠ n_eff (effective refractive index); do not mix.
5. Parentheses & precedence: any expression with division/integrals/composite operators must use parentheses; specify ln(·), log10(·), exp(·) explicitly.
6. Language: formulas, symbols, and definitions must not use Chinese.

V. Normative Examples (paste-ready)

• Arrival time (general form): T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Phase accumulation: Phi = ( 2π / λ_ref ) ( ∫ n_eff d ell ).
• Correlation: r_phi = corr( Phi_ref , Phi_obs ) (interval via Fisher–z and back-transform).
• Conservation error: ε_flux → 0 @ O(θ^2) (under paraxial assumption).

VI. Machine-Readable Registry (YAML, minimal snippet)

version: "1.0.0"

symbols:

- name: T_arr

kind: variable

unit: s

desc: arrival time

requires: { path: "gamma(ell)", measure: "d ell", delta_form: "general|factored" }

- name: Phi

kind: variable

unit: rad

desc: accumulated phase

requires: { lambda_ref: m, path: "gamma(ell)", measure: "d ell" }

- name: n_eff

kind: variable

unit: "1"

desc: effective refractive index along path

- name: c_ref

kind: constant

unit: m/s

desc: reference propagation limit

- name: lambda_ref

kind: constant

unit: m

desc: reference wavelength

VII. Minimal Consistency Requirements (results page & data side)

• In-text and data see[]/references[] must use “volume + version + anchor (P/S/M/I)”, with anchor coverage ≥ 90%.
• Export manifests include version and the dimensional report; path expressions explicitly show gamma(ell) and d ell, and record delta_form.
• List metrics with units on the results page: ΔT_arr (s), r_phi (1), ε_flux (1), p_dim (1), Q (1).