25-EFT.WP.STG.Dynamics v1.0 | Foreword

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Foreword

One-Sentence Positioning
This volume presents a unified framework and deployment workflow for Spacetime Graph (STG) dynamics from modeling → inference → control → operations, covering graph signals, network flows, and coupled systems with engineering implementations and metrological compliance.

I. Goals and Applicability

• Provide a unified description on G = (V, E) for node states x_v(t), edge flows f_e(t), exogenous inputs u(t), and observations y(t), compatible with continuous/discrete time and static/dynamic graphs.
• Establish a computable chain from spectral graph operators to system dynamics
  dx/dt = F(x, u, t; θ), x_{k+1} = Φ_{Δt}(x_k, u_k; θ).
• Deliver axioms/equations/workflows/interfaces (P7xx / S7xx / M7-* / I70-*), the contract library (C70-*), runtime panel fields, and the minimal key set for manifest.stg.*.
• Typical scenarios: power/water/transport/logistics networks; microservice dependency graphs; social/knowledge diffusion; epidemic spread.

II. Objects, I/O, and Boundaries

• Inputs: the graph and its time-varying forms G(t), trajectories/events traj, operators & hyperparameters { L, U, Λ, Δt, T_s }, constraints and reference states RefCond.
• Outputs: states/predictions x(t) / x_k, invariants & metrics (e.g., spectral_gap, energy dissipation), control laws K_ctrl, runtime diagnostics and uncertainties { u(x), U, nu_eff }, and persisted manifest.stg.*.
• Boundaries: require explicit units and dimensions—unit(field), dim(field)—and pass check_dim; when topology changes frequently or strong nonlinearity impairs differentiability, switch to MC/Bootstrap routes (see Ch. 13 and Appendix E).

III. Unified Conventions and Numbering

1. Numbering system: axioms P7xx-*; minimal equations S7xx-*; metrology workflows M7-*; implementation bindings I70-*; contracts C70-*.
2. Dual-form consistency (mirroring cross-volume practice):
   • Continuous-time: x(t+Δt) ≈ x(t) + ( ∫_{t}^{t+Δt} F dt ).
   • Discrete-time: x_{k+1} = Φ_{Δt}(x_k, u_k; θ).
   • Compute in parallel and define delta_form = | x(t+Δt) − x_{k+1} |; assert delta_form ≤ tol_Tarr (see C70-*).
3. Conflict-name enforcement: do not mix T_fil (tension) and T_trans (transmittance); strictly distinguish n from n_eff; formulas/symbols/definitions must not use Chinese.
4. Corrections: any environmental/operational correction is written as corr_env(x; RefCond) with RefCond persisted.

IV. Methodology and Implementation Path (Master Workflow M7-1)

• Ready: build/clean graphs and operators (Chs. 2–4); finalize RefCond and unit systems.
• Model/Identify: select physical priors and operator learning (Chs. 5–7); assess controllability/observability (Ch. 8).
• Numerics & Stability: choose integrators and step-size policies (Ch. 9); pass stability and energy contracts.
• Causality/Intervention: identify invariant structures and design interventions (Ch. 10).
• Multiscale/Assimilation: coarsen and enforce cross-level consistency (Ch. 11); filter/assimilate (Ch. 12).
• Uncertainty & Release: compose Delta/GUM with MC (Ch. 13); publish manifest.stg.uncertainty.
• Runtime: windows/caches/fallbacks and dashboards (Ch. 14).
• Delivery: reference implementations and use cases (Ch. 15).

V. Reader Paths and Role Mapping

• Fast path (productization): Chs. 2 → 4 → 7 → 8 → 12 → 14 → 15.
• Algorithms/Research: Chs. 2 → 4 → 5 → 7 → 10 → 11 → 13.
• Ops/SRE: Chs. 12 → 13 → 14 and Appendices A/B/C.
• Compliance/Audit: manifest.stg.*, contracts.*, dual-form and uncertainty fields (Chs. 13–14, App. B/C).

VI. Data, Metrology, and Compliance

• Data protocol: graphs/trajectories/events are persisted with traceable hashes and provenance; RefCond is mandatory.
• Metrology: all metrics carry unit() and dim(); check_dim( y − f(x) ) must pass.
• Compliance modules: dual-form gap delta_form, runtime freshness & coverage, stability & energy-conservation contracts (see C70-*).
• Uncertainty publication: compute both u_c = sqrt( J V_x J^T ) and MC quantiles; publish coverage and nu_eff explicitly (Ch. 13, App. E).

VII. Cross-References

• Time semantics/sync: companion Energy Filaments white paper Chs. 2/3 (S/P/M/I).
• Path physics / medium corrections: EFT.WP.Metrology.PathCorrection v1.0.
• Topological objects & stability: EFT.WP.Particle.TopologyAtlas v1.0.
• Data cleaning & dual-form practices: EFT Technical Whitepapers & Memos — Comprehensive Checklist v0.1.

VIII. Deliverables and Acceptance

• Artifacts: I70-* interface implementations, C70-* contract playbooks, panels panel.stg.*, manifest.stg examples, and benchmark reports.
• SLO/SLI: stability pass-rate, delta_form_p95, forecast quantiles, assimilation innovation statistics, streaming latency and drop rates.
• Audit: traceable versions/dependencies/seeds and data provenance, with replayed results and panel snapshots archived.

IX. Risks and Fallbacks

• Nonstationarity & topological changes: trigger adaptive recalibration or coarsening fallback.
• Stiffness & numerical blow-up: switch to BDF/splitting; shorten Δt and add guardbands.
• Streaming pressure: backpressure / down-sampling / circuit-breaker strategies, with panel- and contract-driven alerts.

X. Structural Guide (at-a-glance map)

• Chs. 1–4: domain definition and mathematical/spectral baselines.
• Chs. 5–8: coupling, identification, controllability/observability.
• Chs. 9–12: numerical stability, causality, assimilation.
• Chs. 13–15: uncertainty & runtime, use-case delivery.
• Appendices: interfaces / contracts / manifests / metrics / error propagation / change logs.

This foreword is the operational guide and compliance template for the entire volume. Subsequent chapters must inherit this numbering, notation, and dual-form publication requirements without deviation.