27-EFT.WP.Packets.Light v1.0 | Chapter 1 — Packets.Light Domain: Definition & Scope

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Chapter 1 — Packets.Light Domain: Definition & Scope

One-sentence goal: Delimit the objects, I/O, and engineering boundaries of optical packets / optical pulses (Packets.Light) across fiber / free-space / hybrid networks, and establish a unified publication convention for two-form arrival time and dimension compliance.

I. Scope & Objects

1. Objects (Propagation & Devices)
   • Segmented path gamma(ell) = gamma_fiber ⊕ gamma_fso ⊕ gamma_dev, with path length L_gamma = ( ∫_gamma 1 d ell ).
   • Medium / device parameters: n_eff(f, x), alpha_fiber(f), beta(omega), beta2, PMD, and amplifiers / switching devices (EDFA / WSS / ROADM).
2. Objects (Timebase & Framing)
   Framing stack: epoch → frame → slot → sym; packet duration T_pkt, guard interval T_guard.
3. Inputs
   Transmit signal x(t) (or symbol stream); link and device inventories (with hash/id and validity intervals); RefCond (temperature / weather / time-zone / sampling rate); timebase & sync offset/skew/J; policies and thresholds.
4. Outputs
   Receive signal y(t) (soft / hard decisions); arrival time T_arr and correction terms; link metrology OSNR / Q / EVM / BER; runtime panel SLI / SLO; manifest.packet.*.
5. Boundaries / Exclusions
   General metrology methodology is not restated (see EFT Technical White Paper & Memo Templates — Complete Index v0.1). Radio and copper serve only as comparators and are outside this volume’s implementation scope.

II. Terms & Variables

• Path & Geometry: gamma(ell), L_gamma, t_hat, r_i, los / nlos.
• Medium & Dispersion: n_eff(f, x), n_phi(f), n_g(f), beta(omega), beta2, D, PMD, alpha_fiber.
• Timebase & Framing: epoch, frame, slot, sym, T_sym, T_guard, T_pkt.
• Energy & Noise: P_tx, P_rx, ASE, OSNR, N0, SNR(f).
• Modulation & Detection: mod ∈ { OOK, PAM, QAM, PSK, OFDM, PPM }, EVM, LLR, R_c.
• Multiplexing & Labels: lambda (wavelength), k_sub (subcarrier), label, wss.
• Arrival Time & Two Forms: T_arr, c_ref, delta_form, tol_Tarr.
• Metrology & Uncertainty: RefCond, corr_env(x; RefCond), u(x), U = k * u_c, nu_eff.
• Dimensional examples: unit(T_arr) = "[T]", unit(n_eff) = "-" / dim = "1", unit(OSNR) = "dB" (record linear conversion).

III. Postulates P601-*

• P601-1 (Explicit & Monotone Path): The propagation path is explicitly segmented; non_decreasing(ell); segments connect with geometric and boundary continuity.
• P601-2 (Two Forms in Parallel): Arrival time is computed with both the constant-factored and the general form; persist their difference delta_form.
• P601-3 (Dimensional Compliance): Any quantity entering an equation declares unit / dim and must pass check_dim( y - f(x) ).
• P601-4 (Framing Conservation): The budgets for T_guard and T_pkt are conserved after switching / queuing / compensation unless a policy explicitly relaxes them and the relaxation is persisted.
• P601-5 (Traceable Environmental Correction): Any compensation / database write-back is recorded as corr_env(x; RefCond) with source and version.
• P601-6 (Name Disambiguation, Mandatory): T_fil (tension) ≠ T_trans (transmittance); n (number density) ≠ n_eff (effective index).

IV. Minimal Equations S601-*

1. S601-1 (Two-Form Arrival Time)
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff(f,x) d ell ).
   • General: T_arr = ( ∫_{gamma(ell)} ( n_eff(f,x) / c_ref ) d ell ).
   • Two-form discrepancy: delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |.
2. S601-2 (Group Delay & Dispersion)
   • Group-delay density: dT_g = ( 1 / v_g ) d ell = ( n_g / c_ref ) d ell, with n_g = n_phi - f * ( d n_phi / d f ).
   • Second-order dispersion: beta2 = d^2 beta / d omega^2, dispersion parameter D = - ( 2*pi*c_ref / lambda^2 ) * beta2.
3. S601-3 (Segment-Level Accumulation)
   Segmental sum: T_arr = ∑_{seg} ( ∫_{gamma_seg} ( n_eff / c_ref ) d ell ), seg ∈ { fiber, fso, device }.
4. S601-4 (Power & OSNR Baseline)
   OSNR_lin = P_signal / P_ASE, with P_ASE = n_sp * h * f_0 * (G - 1) * RBW (link approximation; persist device parameters).
5. S601-5 (Framing Conservation)
   T_pkt = N_sym * T_sym + N_gap * T_guard; queuing must keep T_guard ≥ T_guard_min.

V. Metrology Pipeline M60-1 (Domain Ready → Modeling → Verification → Persistence)

• Domain ready: freeze RefCond, timebase / framing; construct the segmented path and device inventory (with hash / id, validity intervals).
• Model / estimate: medium parameters n_eff / n_g / alpha_fiber / beta2 / PMD and FSO turbulence; build segment-level transfer functions and compensation kernels.
• Two-form computation: compute both T_arr forms and delta_form in parallel; estimate OSNR / Q / EVM.
• Checks: check_dim, delta_form ≤ tol_Tarr, framing conservation, residual dispersion / PMD bounds; record uncertainty u / U.
• Persist: emit manifest.packet with keys { TraceID, gamma.hash, RefCond, T_parts, delta_form, tol_Tarr, metrics.*, u/U, contracts.*, signature }.

VI. Contracts & Assertions C60-1x (Suggested Thresholds)

• C60-101: delta_form_p95 ≤ tol_Tarr (default tol_Tarr = 1e−3 * T_arr).
• C60-102: check_dim( T_arr ) = "[T]"; check_dim( OSNR ) validated with unit conversion.
• C60-103: T_guard ≥ T_guard_min; if violated after queuing / switching, record compensation or degradation strategy.
• C60-104: Residual dispersion | D_res | ≤ D_max; residual PMD ≤ PMD_max (modulation-dependent).
• C60-105: RefCond completeness (temperature / weather / sampling rate / time-zone / link version).

VII. Implementation Bindings I60-1* (interfaces, I/O, invariants)

• I60-11 build_path(segments, geom) -> gamma, meta (segmented fiber / FSO / device; non_decreasing(ell)).
• I60-12 eval_tex_arr(n_eff, c_ref, gamma) -> { T_arr_form1, T_arr_form2, delta_form }.
• I60-13 estimate_dispersion(params) -> { beta2, D, PMD }.
• I60-14 estimate_osnr(trace, rbw, edfa_list) -> OSNR (includes noise-equivalent bandwidth).
• I60-15 check_framing_guard(frame_spec, scheduler) -> report.
• I60-16 emit_packet_manifest(results, policy) -> manifest.packet.
  Invariants: check_dim(*) passes; delta_form ≤ tol_Tarr; units(trace) consistent; segment hashes & versions traceable.

VIII. Cross-References

• Path / medium correction & two-form publication: EFT.WP.Metrology.PathCorrection v1.0, Chapters 2 / 10 / 11.
• Timebase / sync: EFT.WP.Metrology.TimeBase v1.0; EFT.WP.Metrology.Sync v1.0.
• Link metrology & instrumentation: EFT.WP.Metrology.Instrument v1.0.
• Runtime & panels: EFT.WP.STG.Dynamics v1.0, Chapter 14.

IX. Quality & Risk Control

• SLI / SLO: delta_form_p99, osnr_drift, cd_residual, pmd_drift, latency_p99, drop / erasure_rate.
• Fallback strategies: dispersion / PMD drift → write back online compensation gain; FSO fading → redundant routing / rate adaptation; queuing congestion → increase T_guard and bypass; metrology drift → re-sign manifest.
• Audit: path & device hashes, RefCond, two-form gap and threshold history, panel snapshots and replay consistency (dual-environment bias ≤ ε_dual).

Summary

• This chapter establishes the domain-level baseline for Packets.Light—objects, I/O, and the two-form arrival-time and dimensional-compliance conventions.
• It provides an executable skeleton across P601 / S601 / M60-1 / C60-1x / I60-1*, with releases audited and published as manifest.packet.*.