12-EFT.WP.Methods.Repro v1.0 | Chapter 6 Time Base and Randomness Control

Home ／ Docs-Technical WhitePaper ／ 12-EFT.WP.Methods.Repro v1.0

Chapter 6 Time Base and Randomness Control

I. Scope and Objectives

1. This chapter establishes unified gauges for time-base alignment and randomness control, covering calibration between tau_mono ↔ ts, observability of jitter/drift, random-number generation and seeding, shielding of nondeterministic operators, and integration with TS.* observability fields.
2. Objectives
   • Provide estimation and confidence gauges for alpha, beta so that, across devices/threads/backends, event times satisfy ts = alpha + beta * tau_mono.
   • Form an auditable randomness policy (rng_family, seed, stream_id) and define stable seeding for multi-threaded/distributed execution.
   • Define the jitter spectrum S_tt(f) and its reciprocity with time-domain indicators; set thresholds and alerts.
   • Enumerate and shield nondeterministic operators, ensuring replay variance and spectral-consistency gates are met.

II. Terms and Symbols

1. Time base and fitting
   • tau_mono: monotonic time base (monotonic counter).
   • ts: published time base.
   • alpha, beta: linear mapping parameters, ts = alpha + beta * tau_mono.
   • r_tb: statistic of time-base fit residuals, e.g., r_tb = rms( ts - ( alpha + beta * tau_mono ) ).
   • w_k: sample weights.
2. Randomness and seeding
   • rng_family ∈ { mt19937 , pcg32 , xoshiro , philox , threefry , system }.
   • seed: global seed value.
   • stream_id: stream identifier for thread/process/device.
   • H( • ): collision-resistant hash/derivation function for local seed derivation.
   • seed_thread = H( seed_global , rank , device_id , thread_id , op_scope ).
3. Jitter and spectrum
   • S_tt(f): PSD of timestamp sequences.
   • U_w: window energy.
   • ENBW: equivalent noise bandwidth.
   • jitter_rms: root-mean-square jitter.
   • drift_ppm: long-term frequency offset (parts per million).
4. Consistency and gates
   • delta_rep = ( norm( y_new - y_ref ) / max( norm( y_ref ), eps_floor ) ).
   • R_coef = 1 - delta_rep.
   • delta_psd: spectral discrepancy metric (e.g., L2 distance or weighted KL).
   • Gate placeholders: tau_tb (time-base fit), tau_jitter, tau_psd, tau_seed.

III. Postulates and Minimal Equations

• P31-9 Linear time-base alignability postulate
  Under stable temperature/humidity, supply, and a constant sampling chain, there exist alpha, beta such that ts ≈ alpha + beta * tau_mono and r_tb <= tau_tb. Cross-device comparisons must apply this mapping first.
• P31-10 Jitter decomposition postulate
  Short-term jitter and long-term drift decompose by band: S_tt(f) = S_short(f) + S_long(f), where S_long(f) dominates low frequency (drift) and S_short(f) mid/high frequency (jitter).
• P31-11 Deterministic random stream postulate
  With a fixed rng_family and seed_thread derivation, samples for the same stream_id are identically distributed under the same EnvLock and identical operator sequence.
• P31-12 Nondeterministic-operator shielding postulate
  When reduction order is fixed, nondeterministic kernels are disabled, and parallel scheduling is locked, replay variance satisfies var_run <= tau_var, and ( delta_psd | strict_det ) <= ( delta_psd | relaxed ).
• S32-12 Least-squares time-base fit
  min_{alpha,beta} ( ∑_k w_k * ( ts_k - ( alpha + beta * tau_mono_k ) )^2 ), yielding ( alpha , beta ) and covariance cov( alpha , beta ).
• S32-13 Jitter energy–variance reciprocity
  jitter_rms^2 ≈ ( ∫ S_tt(f) df ); with window correction jitter_rms^2 ≈ ( 1 / U_w ) * ( ∫ S_tt(f) df ), with ENBW stated.
• S32-14 Seed-derivation function
  seed_thread = H( seed , rank , device_id , thread_id , op_scope ); H must be collision-resistant, stable, and cross-language consistent.
• S32-15 Nondeterminism probe test
  With fixed seed and EnvLock, rerun N times; var_run = var( y^{(k)} ) must pass var_run <= tau_var; else flag E_NONDETERMINISM.
• S32-16 Drift estimation
  drift_ppm ≈ ( 10^6 ) * ( d/dt ) ( beta - 1 ), obtained by linearly fitting beta(t) over a sliding window.

IV. Data and Manifest Gauges

1. Acquisition window and synchronization
   • Declare sampling window t ∈ [t0 , t1], sync source (GPS/PTP/local), and alignment reference (device of record / reference thread).
   • Ingestion fields: alpha, beta, cov_alpha_beta, r_tb, U_w, ENBW, jitter_rms, drift_ppm, rng_family, seed, seed_policy, H.name, H.version, stream_id_schema.
2. Gauge declarations
   State windows, filters, window type and parameters; band partitioning and thresholds for the jitter spectrum; and whether dual arrival-time calculation was executed — T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) and T_arr = ( ∫ ( n_eff / c_ref ) d ell ) — plus delta_form (if applicable).
3. Traceability requirements
   The randomness manifest must record, per op_scope, each stream_id and derived seed_thread; replay restores per-operation RNG state from these.

V. Algorithms and Implementation Bindings

1. I30-6 align_timebase(trace:any, reference:any) -> {alpha:float, beta:float, fit:dict}
   • Extract ( tau_mono_k , ts_k ) pairs from trace and reference; reject outliers.
   • Estimate ( alpha , beta ) and covariance via S32-12; compute r_tb and confidence intervals.
   • Output fit = {r_tb:float, cov:[[..]], n:int, window:[t0,t1]}.
2. I30-8 set_rng_policy(rng_family:str, seed:int, stream_schema:dict) -> dict
   • Fix rng_family and global seed; define H and the stream_id composition.
   • For each ( rank , device_id , thread_id , op_scope ), derive seed_thread per S32-14.
   • Return the policy and persist it to logs and manifests.
3. I30-9 shield_nondet_ops(plan:list) -> dict
   • Scan the operator graph; flag nondeterministic reductions, atomics, unstable sorts, and kernels with unfixed parallelism.
   • Apply shielding: fix reduction orders, substitute deterministic kernels, disable nondeterministic optimizations, fix threads/affinity.
   • Produce plan.report with rewritten operators and performance tradeoffs.
4. I30-10 estimate_time_jitter(trace:any, window:dict) -> {S_tt:any, jitter_rms:float, drift_ppm:float}
   • Compute S_tt(f) over the window (explicit U_w and ENBW).
   • Obtain jitter_rms from S32-13 and drift_ppm from S32-16.
   • Return spectrum, indicators, and gate verdicts.
5. I30-7 compare_psd(x:any, y:any, window:dict) -> {delta_psd:float, pass:bool}
   Reused for spectral-consistency gates and regression comparisons (see Chapter 8).

VI. Metrology Workflow and Run Graph

1. Mx-35 timebase-fit
   • Collect ( tau_mono , ts ) samples and denoise.
   • Call align_timebase to obtain alpha, beta, r_tb; if r_tb > tau_tb, raise TS.alert.timebase_fit_fail and roll back.
2. Mx-36 rng-lock
   • Call set_rng_policy to fix rng_family, seed, and seed_thread.
   • Replay a small RNG-consistency case 3×; proceed only if var_run <= tau_var.
3. Mx-37 jitter-psd-cal
   • Call estimate_time_jitter to produce S_tt(f), jitter_rms, drift_ppm.
   • If jitter_rms > tau_jitter or |drift_ppm| exceeds the gate, flag E_TIMEBASE_SKEW.
4. Mx-38 nondet-shield-verify
   • Execute shield_nondet_ops and record cost.
   • Run N trials against the golden output; verify var_run and delta_psd gates; on failure, roll back or demote release.channel to canary.

VII. Verification and Test Matrix

1. Time-base alignment
   • Repeat Mx-35 under varying load and temperature; validate stability of alpha, beta; max |Δbeta| <= tau_tb_drift.
   • Cross-device validation: apply device-A ( alpha , beta ) to device-B tau_mono; alignment residual should be no worse than 1.5× each device’s local fit.
2. Randomness control
   • Multi-process/thread/device replay: seed_thread collision-free at the tested scale (collision_rate ≈ 0).
   • Statistical test: for the same stream_id, cross-run distributions pass KS_pvalue >= p_min.
3. Jitter and spectrum
   • Changing window/type should not alter jitter_rms beyond tau_window_bias.
   • PSD comparison to baseline: delta_psd <= tau_psd.
4. Nondeterminism shielding
   After substituting reduction/sort/atomic paths, delta_rep and var_run fall within gates; record that performance regression ≤ tau_perf_penalty.

VIII. Cross-References and Dependencies

• Core.Sea: time-base definitions, dual arrival-time gauges, cross-device mapping and alignment procedures.
• Core.Metrology: PSD estimation gauges S_xx(f), U_w, ENBW, and uncertainty assessment.
• Core.Threads: TS.* observability fields, hb, bp, scheduling and throttling strategies; cross-thread causality.
• Chapter 3: delta_rep, R_coef, spectrum–variance reciprocity. Chapter 5: EnvLock, nondeterminism probes and rollback. Chapter 8: scoring synthesis and gates.

IX. Risks, Limits, and Open Questions

1. Risks
   • Mixed timing sources (TSC/HPET/OS clock) induce implicit nonlinearity, elevating fit residuals.
   • Network clock rollbacks/jumps in distributed systems create low-frequency spikes in S_tt(f).
   • Latent randomness inside libraries (e.g., data augmentation, dropout not wired to the unified seeding) violates seed_policy.
2. Limits
   • Deterministic modes for GPU atomics and unstable sorts can be costly; throughput channels may need trade-offs.
   • Some platforms’ FP exception handling (denorm) and ftz/daz policies are not fully controllable.
3. Open questions
   • Adaptive gates: tune tau_tb, tau_jitter from live S_tt(f) shape and thermal/power conditions.
   • Modeling and compensating nonlinear beta(t) drift for long-running jobs.
   • Cross-language standardization and conformance suites for H.

X. Deliverables and Version Management

1. Artifacts
   • timebase.fit.json: alpha, beta, cov, r_tb, window, and fit quality.
   • rng.policy.json: rng_family, seed, H, stream_id_schema and collision evaluation.
   • jitter.report.json: S_tt(f)@window , jitter_rms , drift_ppm , U_w , ENBW , delta_psd.
   • shield.plan.json: nondeterministic operator list, substitutes, and performance impact.
2. Version management
   • rng.policy and timebase.fit schema.version track EnvLock; MAJOR changes must ship dual-run comparison and rollback playbook.
   • Release bundles must include signatures and fingerprint for this chapter’s artifacts, and must execute the full Mx-35 → Mx-38 validation in the release-channel flow.