52-Dataset Card Template v1.0 | Chapter 2 — Terms, Symbols & Units (Dataset Minimal Set)

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Chapter 2 — Terms, Symbols & Units (Dataset Minimal Set)

I. Terms

• sample: the minimal record unit in the dataset.
• feature: a field usable for modeling/statistics.
• label: target/supervision field.
• metadata: auxiliary information describing the data and its generation process.
• split: dataset subsets train/val/test/holdout/slice_k.
• window/partition: aggregation unit in time/space/entity.
• contract/schema: declaration of fields, types, units, dimensions, and constraints.
• coverage: k-coverage / alpha significance / quantile[p_lo,p_hi].
• lineage: provenance chain & dependency DAG.

II. Symbols (minimal)

• Scale: N (samples), M (features), |split| (split size).
• Time & sampling: f_s (sampling rate), T_win (window), ts_start/ts_end (ISO-8601).
• Path quantities: gamma(ell) (path), d ell (measure), n_eff(ell) (effective refractive index), c_ref (reference propagation limit), λ_ref (reference wavelength), T_arr (arrival time), Phi (phase).
• Quality & uncertainty: Q_res, u(x), u_c, U = k·u_c, Σ (covariance), p_dim.
• Sync health: δt_abs (absolute time offset), Δτ_ch (inter-channel skew), σ_y(τ) (Allan deviation).
• Resource/perf (if applicable): Latency_P95, Throughput, ρ (utilization).

III. Units & Dimensions

• SI/international symbols: m, s, rad, 1, m/s, 1/m, Pa, N, J, Hz.
• Field tables must provide unit and/or declare dim in the contract.
• Dimensional closure: before publication, pass I70-dim_check, require p_dim = 1.0, and attach check_dim_report.json.

IV. Normative Path Forms

• Arrival time (two equivalent forms):
  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 )

In text, explicitly show gamma(ell) and d ell; record delta_form ∈ {general, factored} on the data side; arrays satisfy len(gamma_ell)=len(d_ell)=len(n_eff)≥2.

V. Mandatory Conventions

• Wrap inline symbols with backticks (e.g., T_arr, Phi, n_eff, c_ref).
• Parentheses required for any expression with division/integrals/composites; use ln/exp/conv in functional form.
• Conflict names: T_fil (tension) ≠ T_trans (transmittance); n (number density) ≠ n_eff (effective refractive index).
• Forbidden bare symbols: c, T, n.
• Coverage consistency: choose one of k/alpha/quantile and keep consistent between data and publication.

VI. Field Table (minimal template)

VII. Machine-Readable Contracts (excerpts)
A. schema.json

{

"$schema": "https://json-schema.org/draft/2020-12/schema",

"title": "Dataset v1.0.0 (minimal)",

"type": "object",

"required": ["record_id","acq","path","medium","ref","see","version"],

"properties": {

"record_id": { "type": "string" },

"acq": {

"type": "object",

"required": ["ts_start","ts_end"],

"properties": {

"ts_start": { "type": "string", "format": "date-time" },

"ts_end": { "type": "string", "format": "date-time" }

}

},

"path": {

"type": "object",

"required": ["gamma_ell","d_ell"],

"properties": {

"gamma_ell": { "type": "array", "items": { "type": "number" }, "minItems": 2 },

"d_ell": { "type": "array", "items": { "type": "number" }, "minItems": 2 }

}

},

"medium": {

"type": "object",

"required": ["n_eff_profile"],

"properties": {

"n_eff_profile": { "type": "array", "items": { "type": "number" }, "minItems": 2 }

}

},

"ref": {

"type": "object",

"properties": {

"c_ref": { "type": "number" },

"lambda_ref": { "type": "number" }

}

},

"see": { "type": "array", "items": { "type": "string" }, "minItems": 1 },

"version": { "type": "string" }

}

}

B. contract.yaml (path & coverage)

version: "1.0.0"

path:

required: true

gamma: "gamma(ell)"

measure: "d ell"

delta_form: "general" # or "factored"

coverage:

mode: "k" # k | alpha | quantile

k: 2

units:

T_arr: "s"

Phi: "rad"

c_ref: "m/s"

lambda_ref: "m"

VIII. Normative Examples

• Path consistency check:
  len(gamma_ell)=len(d_ell)=len(n_eff)≥2; Δell ≤ ( c_ref / f_s ) / max(n_eff).
• Phase interval reporting: use Fisher–z in z-space, back-transform to r_phi, report [LB, UB].
• Dimensional validation:
  T_arr = ( ∫ ( n_eff / c_ref ) d ell ) ⇒ [1]/[m·s^-1]·[m] = [s].

IX. Anti-Patterns & Fixes

• Anti: T_arr = ∫ n_eff / c_ref d ell (missing parentheses) → Fix: T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Anti: declaring only gamma(ell) without d ell/delta_form → Fix: add both and align with n_eff.
• Anti: unit % as text → Fix: use unit 1 and note “percent” in comments.
• Anti: references without version/anchor → Fix: See "EFT.WP.Core.Equations v1.1" Ch.2 S20-1.

X. Checklist

• Field table consistent with schema.json/contract.yaml; all numeric fields explicitly show units & dimensions.
• For path quantities, explicit gamma(ell)/d ell recorded with delta_form; len(path) ≥ 2, Δell compliant.
• Unified forms used for arrival/phase with parentheses.
• Coverage mode consistent between data & publication (k/alpha/quantile); p_dim = 1.0 and check_dim_report.json attached.
• see[]/references[]/version compliant with anchor coverage ≥ 90%; no external links/aliases.