51-Pipeline Card Template v1.0 | Chapter 2 — Terms & Symbols (Pipeline Minimal Set)

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Chapter 2 — Terms & Symbols (Pipeline Minimal Set)

I. Core Objects & Topology

• Pipeline: a processing flow composed of stages and directed edges.
• DAG(V,E): a directed acyclic graph of stage set V and dependency edge set E.
• Stage: the minimal executable unit; has input contracts and output contracts.
• Operator: an operator inside a stage (parallel/concurrent capable).
• Artifact: stage outputs (tables/files/reports/figures).
• Context (ctx): execution context (parameters, environment, idempotency key, trace IDs).
• Contract (Schema): data contract (fields/types/units/dimensions/constraints).
• Idempotency Key: the key that ensures Exactly-Once semantics.
• State Machine: state ∈ {pending, running, succeeded, failed, rolled_back}.

II. Data & Path (when path quantities are involved)

• gamma(ell): path parametrization; unit m.
• d ell: path measure element; unit m.
• n_eff(ell): effective refractive index along the path; dimensionless 1.
• T_arr: arrival time; unit s.
• Phi: accumulated phase; unit rad.
• Unified (two equivalent forms):
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell );
  T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Phase: Phi = ( 2π / λ_ref ) * ( ∫ n_eff d ell ).

For path quantities the text must explicitly show gamma(ell) and d ell, and the data side must record delta_form ∈ {general, factored}.

III. References & Units

• c_ref: reference propagation limit; m/s.
• λ_ref: reference wavelength; m.
• k_ref = 2π / λ_ref: reference wavenumber; 1/m.
• SI/international symbols: m, s, rad, 1, Pa, N, J, Hz.
• Dimensional-closure requirement: p_dim = 1.0, attach check_dim_report.json.

IV. KPIs & Quality

• Latency_P50/P95: latency quantiles (s).
• Throughput: throughput/bandwidth (context-specific).
• ρ: resource utilization (1).
• Q_res: robust residual metric (1, lower is better).
• p_dim: dimensional-closure pass rate (1, must be 1).
• ε_flux: paraxial conservation error (1).
• σ_y(τ): Allan deviation (1).
• SLA/SLO: service-level targets (latency/availability/error bounds).

V. Control & UQ Propagation

• J: Jacobian ∂f/∂x |_{x̂}.
• Σ: covariance matrix Cov(x).
• Delta (stage-level first-order): u^2(y) ≈ J · Σ · Jᵀ.
• Composition: u_c (combined standard uncertainty), U = k · u_c (expanded uncertainty).
• Coverage forms: k-coverage / alpha significance / quantile[p_lo, p_hi].

VI. Idempotency & Faults

• idempotency_key: dedup/idempotent execution key.
• retry_policy: retry strategy {max_retries, backoff, deadline}.
• checkpoint: checkpoint/replay marker.
• Error classes: E_INPUT / E_DIM / E_GATE / E_SYNC / E_UQ / E_INTERNAL.

VII. Quality Gates (pipeline-level)

• G1 Schema completeness; G2 Citation compliance (anchor coverage ≥ 90%); G3 Path conventions; G4 Dimensional closure;
• G5 Freshness; G6 Coverage conventions;
• G7 Covariance consistency; G8 Uniqueness.
• Stops: S1–S5 (dimensional failure / freshness failure / path missing / covariance mismatch / citation non-compliance).

VIII. Style & Conflict Names

• Wrap inline symbols with backticks (e.g., T_arr, Phi, n_eff, c_ref).
• Parentheses required for any division/integral/composite operator.
• Conflicts: T_fil (tension) ≠ T_trans (transmittance); n (number density) ≠ n_eff (effective refractive index).
• Forbidden bare symbols: c, T, n.

IX. Machine-Readable Snippets (minimal)
A. Stage spec stage.yaml

version: "1.0.0"

stage:

id: "stage-30-arrival"

inputs: ["path.gamma_ell","path.d_ell","medium.n_eff_profile","ref.c_ref"]

outputs: ["obs.T_arr"]

control:

form: "T_arr = ∫ ( n_eff / c_ref ) d ell"

delta_form: "general"

quality_gates: ["G1","G3","G4"]

see:

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

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

B. Pipeline graph pipeline_graph.json (excerpt)

{

"nodes":[{"id":"ingest"},{"id":"calibrate"},{"id":"arrival"}],

"edges":[{"from":"ingest","to":"calibrate"},{"from":"calibrate","to":"arrival"}],

"idempotency_key":"run_id+partition"

}

C. Validation report validate_report.json (excerpt)

{
  "gates": {
    "G1": true,
    "G2": 0.93,
    "G3": true,
    "G4": true,
    "G5": true,
    "G6": true,
    "G7": true,
    "G8": true
  }
}

X. Normative Examples

• Path consistency: len(gamma_ell)=len(d_ell)=len(n_eff)≥2; Δell ≤ ( c_ref / f_s ) / max(n_eff).
• Phase convention: align the reference window before computing r_phi; report intervals via Fisher-z and back-transform.
• Results-page fields: Latency_P95, Throughput, Q_res, p_dim, ε_flux, σ_y(τ).

XI. Results & References

• Dual figure exports: PDF/SVG and PNG; explicit axis units; captions include see[]/version.
• Citation format: See "<Volume> vX.Y" <Chapter> <Anchor>, prioritize P/S/M/I; external links/aliases are forbidden.