27-EFT.WP.Packets.Light v1.0 | Chapter 3 — Framing & Timebase (epoch / frame / slot / sym)

Home ／ Docs-Technical WhitePaper ／ 27-EFT.WP.Packets.Light v1.0

Chapter 3 — Framing & Timebase (epoch / frame / slot / sym)

One-sentence goal: Define the timebase and framing hierarchy for optical packets—epoch → frame → slot → sym—and provide computable conventions and interfaces for alignment, timing, and timestamping so arrival time, queuing, and scheduling are auditable and persistable on a unified clock.

I. Scope & Objects

1. Inputs
   • TX/RX timebases: timebase_tx, timebase_rx; a unified settlement timebase tau_mono and publication instant ts (see the TimeBase/Sync volume).
   • Framing spec: epoch, frame, slot, sym with { T_epoch, T_f, T_slot, T_sym, T_guard }.
   • Pilots / sync: pilot, preamble, training, and timestamp label ts_tag.
   • Physical parameters: sampling rate Fs, symbol rate Rs = 1 / T_sym, coding / overhead { R_c, OH }.
2. Outputs
   • Frame alignment / timing estimates: { offset, skew, J } and arrival-time mapping t_rx ↔ t_tx.
   • Structured boundaries: { epoch_id, frame_id, slot_id, sym_id }, the framed packet structure, and conservation checks.
   • Two-form discrepancy: timing difference between counting and continuous conventions, delta_form_frame.
3. Boundary
   Physical propagation and dispersion are not repeated here; their residuals are external corrections (see Chapters 2 and 8). This chapter focuses on timebase / framing and synchronization.

II. Terms & Variables

• Hierarchy & durations:
  T_epoch = N_f * T_f; T_f = N_slot * T_slot;
  T_slot = N_sym * T_sym + N_gap * T_guard.
• Bits / symbols & rates: modulation order M, code rate R_c; net throughput
  R_net = (R_c * log2(M)) / T_sym * (1 - OH).
• Timebase mapping:
  t_rx = (1 + skew) * t_tx + offset + J(t), where skew is frequency offset and J is jitter.
• Sync indicators: arrival-time estimate \hat T_arr, frame alignment error e_align, clock drift drift = d(skid) / dt.
• Dimensions: unit(T_*) = "[T]", unit(offset) = "[T]", unit(skew) = "1", unit(J) = "[T]".
• Two forms: a counting convention (derive time from { epoch, frame, slot, sym }) and a continuous convention (integrate / interpolate on tau_mono directly).

III. Postulates P603-*

• P603-1 (Hierarchical conservation):
  T_epoch = ∑_k T_f(k), T_f = ∑_m T_slot(m), T_slot ≥ N_sym * T_sym, and T_guard ≥ 0.
• P603-2 (Two forms in parallel):
  For any packet, compute both the counting estimate t̂_cnt and the continuous estimate t̂_cont of arrival time and record delta_form_frame = | t̂_cnt - t̂_cont |.
• P603-3 (Explicit measures):
  Any integral or average declares its window ( ∫_{t∈W} • dt ); any counting declares its domain { sym_id }.
• P603-4 (Dimensional compliance):
  All times / rates entering equations must pass check_dim( y - f(x) ).
• P603-5 (Traceable timestamps):
  Frame boundaries and timing corrections are persisted via ts_tag, including hash(frame_spec) and RefCond.

IV. Minimal Equations S603-*

1. Hierarchy-to-time mapping
   • Counting form:
     t̂_cnt = t_epoch₀ + epoch_id*T_epoch + frame_id*T_f + slot_id*T_slot + sym_id*T_sym + k_guard*T_guard.
   • Continuous form:
     t̂_cont = ( ∫_{tau_mono,win} w(τ) τ dτ ) / ( ∫_{tau_mono,win} w(τ) dτ ) (weighted centroid of correlation peaks / pilot matching).
2. Clock model & correction
   • TX→RX mapping: t_rx = (1+skew) * t_tx + offset + J(t).
   • Linear LS estimate:
     min_{offset,skew} ∑_i | t_rx(i) - (1+skew) t_tx(i) - offset |^2, solve for skew, offset.
   • Jitter RMS: σ_J = sqrt( E[ ( J(t) - E[J] )^2 ] ), evaluated in a sliding window.
3. Frame sync / pilot correlation
   • Autocorrelation peak: r_xy(τ) = ( ∫ x(t) y(t-τ) dt ), boundary locator τ* = argmax_τ r_{pilot,rx}(τ).
   • Symbol timing offset: e_sym = τ* mod T_sym, frame alignment error e_align = τ* mod T_f.
4. Guard conservation & collision avoidance
   T_slot = N_sym*T_sym + N_gap*T_guard, with conservation assertion:
   T_guard ≥ T_guard_min ≥ 2*σ_J + ΔCD + ΔPMD (includes ISI margin from residual dispersion / PMD).
5. Rates & throughput
   R_sym = 1 / T_sym; net throughput (with overhead):
   R_net = ( log2(M) * R_c ) * ( N_sym / ( N_sym + N_gap*T_guard/T_sym ) ) / T_sym * (1 - OH ).
6. Two-form discrepancy
   delta_form_frame = | t̂_cnt - t̂_cont |; publication condition: delta_form_frame ≤ tol_frame (see contracts).

V. Metrology Pipeline M60-3 (Ready → Modeling → Estimation → Checks → Persistence)

1. Ready: freeze frame_spec = { T_epoch, T_f, T_slot, T_sym, T_guard, N_* }, RefCond, and pilot; align tau_mono / ts.
2. Modeling: set up the clock model and initial values; configure pilot / training and correlation windows; define tol_frame and conservation thresholds.
3. Estimation:
   • Counting form via direct index mapping to t̂_cnt;
   • Continuous form via correlation / PLL / zero-crossing to obtain t̂_cont, offset, skew, J;
   • Compute e_align, σ_J, and throughput R_net.
4. Checks: run check_dim; verify two-form gap and guard conservation; ensure offset / skew / J are within limits; confirm residual ΔCD / ΔPMD margins satisfy (S603-4).
5. Persistence:
   manifest.packet.frame.* = { frame.hash, RefCond, t̂_cnt, t̂_cont, delta_form_frame, offset/skew/J, e_align, R_net, contracts.*, signature }.

VI. Contracts & Assertions C60-3x (Suggested Thresholds)

• C60-301 (Two-form gap): delta_form_frame_p95 ≤ tol_frame (recommend tol_frame = 0.02*T_sym or 1e−3*T_f).
• C60-302 (Guard conservation): T_guard ≥ 2*σ_J + ΔCD + ΔPMD.
• C60-303 (Clock stability): |skew| ≤ skew_max (e.g., 10 ppm), σ_J ≤ J_max.
• C60-304 (Alignment error): e_align_p95 ≤ e_align_max (e.g., 0.05*T_f).
• C60-305 (Dimensional compliance): all T_* fields pass check_dim = "[T]".
• C60-306 (Panel freshness): published offset / skew / J are updated within Δt_panel_max.

VII. Implementation Bindings I60-3* (interfaces, I/O, invariants)

• I60-31 design_frame(schema, timebase) -> frame_spec
• I60-32 timestamp_from_indices(ids, frame_spec) -> t̂_cnt
• I60-33 estimate_timing(rx_stream, pilot, window) -> { t̂_cont, offset, skew, J }
• I60-34 align_frames(rx_stream, frame_spec, pilot) -> { e_align, locks, diag }
• I60-35 guard_budget(residuals, jitter) -> T_guard_min
• I60-36 throughput(frame_spec, mod, fec, overhead) -> R_net
• I60-37 emit_frame_manifest(results, policy) -> manifest.packet.frame
  Invariants: unit(T_*) = "[T]"; two_forms_present = true; delta_form_frame ≤ tol_frame; RefCond and frame.hash are traceable.

VIII. Cross-References

• Physical baselines & residual ΔCD / ΔPMD: Chapter 2.
• Arrival-time harmonization & path corrections: Chapter 8 and the PathCorrection volume.
• Switching / queuing & guard budgeting: Chapter 10.
• Online metrology & paneling: Chapter 11.
• Timebase & synchronization fields: TimeBase/Sync volume (tau_mono / ts / offset / skew / J).

IX. Quality & Risk Control

• SLI / SLO: delta_form_frame_p99, e_align_p95, σ_J_p95, skew_ppm_p95, latency_p95, R_net_stability.
• Fallback strategies: PLL instability → stronger pilot / longer training; increased σ_J → raise T_guard and lower throughput; out-of-limit skew → trigger re-timing or bypass to previous frame_spec.
• Audit: persist frame.hash / pilot.hash, two-form gap history, threshold changes, manifest signatures, and panel replays.

Summary

• This chapter establishes the engineering conventions for the four-layer timebase and framing—epoch / frame / slot / sym—and enforces release consistency via the dual-track counting vs. continuous verification.
• It provides an end-to-end chain from design and estimation to contracts and manifest persistence (P603 / S603 / M60-3 / C60-3x / I60-3*), supplying a unified timescale and conservation boundaries for downstream modulation/detection, routing/queuing, and arrival-time harmonization.