12-EFT.WP.Methods.Repro v1.0 | Chapter 1 Positioning, Scope, and Reproducibility Levels

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Chapter 1 Positioning, Scope, and Reproducibility Levels

I. Scope and Objectives

1. This chapter defines the methodological boundary of the volume: treating data and algorithmic artifacts as first-class objects, it sets the levels, metrics, and pass gates for reproducible, replicable, and portable results, thereby establishing the minimal compliance required across environments and sites.
2. Objectives
   • Establish a tiered reproducibility system and a metric family, with core measures delta_rep and R_coef.
   • Provide a unified gauge and calibration flow for the time-base mapping ts = alpha + beta * tau_mono.
   • Specify the minimal manifest and audit-trail fields so that traceability and compliance verification are actionable.
   • Bind implementation prototypes I30-* and metrology flows Mx-3* to enable automated acceptance.
3. Pass criteria (summary)
   • Numerical domain: delta_rep <= tau_rep and R_coef >= 1 - tau_rep.
   • Spectral domain: | var(x) - ( ∫ S_xx(f) df ) | <= tau_psd.
   • Gauge consistency: when arrival time is involved, publish both gauges in parallel, T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) and T_arr = ( ∫ ( n_eff / c_ref ) d ell ), report the difference delta_form, and submit the path gamma(ell) with measure d ell.

II. Terminology and Symbols

1. Reproducibility tiers
   • Reproducible: same site, same EnvLock, same seed; outputs satisfy the delta_rep gate.
   • Replicable: different sites or minor environmental deltas; outputs satisfy statistical- and spectral-consistency gates.
   • Portable: across hardware/OS/accelerator stacks, interface and metric gates are unchanged and still pass.
2. Metrics and gates
   • delta_rep = ( norm( y_new - y_ref ) / max( norm( y_ref ), eps_floor ) )
   • R_coef = 1 - delta_rep
   • gate.rep: the reproducibility gate set, including numerical gate tau_rep, spectral gate tau_psd, and time-base gate tau_tb.
   • eps_floor: a positive floor to avoid degeneracy in denominators; default eps_floor = 1e-12 (configurable).
3. Time base and randomness
   • tau_mono internal monotonic time; ts external publication time; mapping ts = alpha + beta * tau_mono.
   • seed random seed; rng_family RNG family; rng_device device-side RNG identifier.
4. Environment and signatures
   EnvLock environment lock; hash(•) artifact hash; fingerprint aggregated version & dependency hash.
5. Collision rules and cross-volume gauges
   • T_fil denotes tension; T_trans denotes transmission coefficient. Do not mix n and n_eff.
   • Path and measure must be written uniformly as gamma(ell) with d ell.

III. Postulates and Minimal Equations

• P31-1 Deterministic replay postulate
  With fixed EnvLock and seed, the same pipeline on the same inputs yields identically distributed outputs; if no stochastic branch exists, byte-identical artifacts are produced (hash(outputs) equal).
• P31-2 Time-base alignment postulate
  For any observation sequence there exists an affine mapping ts = alpha + beta * tau_mono that renders cross-device timelines comparable; alpha, beta are obtained by calibration and drift slowly over stable windows.
• P31-3 Artifact immutability postulate
  Any ingested object is content-addressed: oid = hash(bytes(obj)). Any modification yields a new oid and fingerprint.
• S32-1 Result-difference minimal equation
  delta_rep = ( norm( y_new - y_ref ) / max( norm( y_ref ), eps_floor ) ), R_coef = 1 - delta_rep.
• S32-2 Spectral consistency and energy conservation
  | var( x ) - ( ∫ S_xx(f) df ) | <= tau_psd, with integration domain, window, and ENBW declared explicitly.
• S32-3 Parallel dual-gauge discrepancy
  When T_arr is involved, publish delta_form = | T_arr(form1) - T_arr(form2) | / max( |T_arr(form2)|, eps_floor ), together with c_ref and the medium manifest.

IV. Data and Manifest Gauges

1. Minimal ingestion fields (example; Core.DataSpec naming)
   • Basics: project_id, dataset_id, schema.version, submit_ts
   • Source: source.uri, source.oid = hash(•), fingerprint
   • Environment: EnvLock.os, EnvLock.kernel, EnvLock.driver, EnvLock.accel, EnvLock.libs[]
   • Randomness: seed, rng_family, rng_device
   • Time base: alpha, beta, tau_mono_origin, ts_origin
   • Window & measure: window = [t0, t1], fs, window_fn, U_w, ENBW
   • Path gauge: if path integrals are used, provide gamma(ell) parameterization & support, measure d ell
   • Arrival time: when using dual gauges, include c_ref, the n_eff gauge, and delta_form
   • Metrics: delta_rep, R_coef, tau_rep, tau_psd, pass (bool)
2. Units and dimensions
   Execute check_dim(expr) for all quantities. Dimensionless: delta_rep, R_coef, alpha, beta (if ts and tau_mono share units, then beta is dimensionless).
3. Traceability and compliance
   The manifest must support single-point restoration: {EnvLock, PipelineCard, ParamCard, inputs} → outputs. Any missing item must be explicitly marked via missing.* fields.

V. Algorithms and Implementation Bindings

1. Prototypes (aligned with Appendix B)
   • I30-1 freeze_environment(config:dict) -> EnvLock
   • I30-2 emit_pipeline_card(state:any) -> dict
   • I30-3 run_benchmark_suite(card:dict) -> BenchReport
   • I30-4 verify_reproduction(golden:any, candidate:any, metrics:dict) -> RepReport
   • I30-6 align_timebase(trace:any, reference:any) -> {alpha:float, beta:float, fit:dict}
2. Idempotency and exceptions
   • All I30-* calls are idempotent: repeated calls return the same artifact identifier or are explicit no-ops.
   • Exceptions: E_ENV_DRIFT, E_DATA_MISMATCH, E_TIMEBASE_SKEW, E_NONDETERMINISM, E_SEED_INVALID, E_SCHEMA_MISMATCH.

VI. Metrology Workflow and Run Graph

1. Mx-31 Repro bootstrap
   • Run I30-1 to freeze the environment and produce EnvLock.
   • Emit PipelineCard and ParamCard (I30-2).
2. Mx-32 Time-base alignment
   • Collect alignment segments; compute alpha, beta = I30-6(...).
   • Write the results to the manifest and set the gate tau_tb.
3. Mx-33 Benchmark runs
   • Replay the benchmark suite under EnvLock (I30-3).
   • Produce candidate artifacts and intermediate TS.* metrics.
4. Mx-34 Reproduction verification and release
   • Compute delta_rep, R_coef, and spectral consistency.
   • Evaluate gate.rep, generate RepReport = I30-4(...).
   • If qualified, ingest and publish; otherwise execute the rollback playbook.
5. Key observations and alerts
   • Time-base drift alert: |beta - 1| > tau_tb or |alpha| > tau_tb_shift.
   • Nondeterminism alert: with the same seed, variance of repeated delta_rep exceeds the threshold.

VII. Verification and Test Matrix

1. Minimum cases
   • Deterministic case with fixed seed: expect delta_rep = 0.
   • Statistical case with random noise: expect E[delta_rep] <= tau_rep with confidence >= 1 - p_alpha.
   • Spectral-consistency case: expect tau_psd to pass.
2. Edge and extreme scenarios
   • GPU/atomic-order/parallel reduction order changes.
   • Sampling-rate drift and missing packets.
   • Data-type switches (float32 ↔ float64).
3. SLOs and gates (starting points; project-level overrides allowed)
   • tau_rep <= 2e-2, tau_psd <= 1e-3, tau_tb <= 5e-4.
   • Statistical power: sample size sufficient to detect delta_rep >= tau_rep with power >= 0.8.

VIII. Cross-References and Dependencies

• Core.Threads: concurrency semantics, TS.*, hb, bp.
• Core.Sea: tau_mono, ts, and time-base alignment.
• Core.Metrology: S_xx(f), U_w, ENBW gauges.
• Core.DataSpec: manifests and schema evolution.
• Core.Errors: gates, statistical power, and alert levels.
• Core.Equations, Core.DrawingKinetics: alignment requirements when T_arr dual gauges and path measures are involved.

IX. Risks, Limits, and Open Questions

• Sources of nondeterminism (thread scheduling, hardware instructions, library code paths) cannot be fully eliminated; statistical gates are the safety net.
• Cross-site EnvLock cannot be strictly equivalent; publish difference lists and impact assessments.
• Long-term drift (drivers, microcode, compilers) can break binary compatibility; maintain LTS artifacts and rebuild playbooks.
• Open problems: cross-accelerator numerical equivalence, and budget allocation for mixed-precision impacts on delta_rep.

X. Deliverables and Versioning

1. Output checklist
   • EnvLock, PipelineCard, ParamCard
   • BenchReport, RepReport, AuditTrail (with hash(•) and fingerprint)
   • Release bundle and long-term snapshot (including alpha, beta, tau_*)
2. Version policy
   • Semantic versioning; channels canary / stable / LTS.
   • Change classes: ADD/MOD/FIX/PERF/SEC/DOC.
   • Dual-run strategy: run old and new versions in parallel, compute delta_rep and R_coef; auto-rollback if not passed.
3. Publication requirements
   All artifacts must be single-point restorable. When arrival time is involved, publish both gauges in parallel with delta_form.