07-EFT.WP.Core.Threads v1.0 | Preface

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Preface

I. Scope and Objectives

1. Define a unified abstraction, notation, and minimal implementable interface for the concurrency domain, spanning thr (thread/actor), the execution graph G=(V,E), message channels chan, temporal consistency hb (happens-before), backpressure bp, rate and waiting metrics (lambda, mu, rho, W, W_q), and service objectives (SLI/SLO).
2. Core objectives:
   • Establish a verifiable semantics-and-metrics framework for concurrency so that key quantities—T_make(G), rho, P99, etc.—are estimable and constrainable at design time.
   • Provide cross-volume anchors and bindings so data, equations, metrology, and concurrent behavior close the loop under a single system of symbols and identifiers.
   • Offer a minimal yet complete implementation binding set (I70 family) to ensure traceability and testability from specification to code.

II. Audience and Prerequisites

1. Intended readers:
   • Practitioners in systems architecture, distributed computing, real-time control, and data platforms.
   • Technically versed readers familiar with G=(V,E), lambda/mu, backpressure and rate limiting, and SLI/SLO practices.
2. Prerequisites:
   • Working knowledge of the conventions and numbering across this series: Core.DataSpec, Core.Equations, Core.Metrology, Core.Parameters, Core.Errors.
   • Ability to distinguish a monotonic clock tau_mono from UTC wall clock ts and use them appropriately.

III. Core Abstractions at a Glance (Unified Terms)

• Threads and state: thr (thread/actor), pid_thr (thread id), state ∈ {"new","ready","running","blocked","done","canceled"}.
• Execution graph: G=(V,E), dependency dep(u,v), critical path crit(G), node cost w(v), edge cost c(e), makespan T_make(G).
• Channels and messages: chan, q_len, cap, bp, msg, ack, idemp_key, delivery semantics sem ∈ {"at_most_once","at_least_once","exactly_once*"} (best-effort via dedup).
• Queues and stability: lambda, mu, rho = lambda / mu, L, L_q, W, W_q, with Little’s Law L = lambda * W.
• Temporal & fault tolerance: hb (happens-before), deadline, timeout, cancel_token, jitter J, p_drop, p_retry.
• Resources & observability: R_cpu/R_mem/R_io, quota, cgroup, SLI/SLO, QPS, P99, ErrRate, SLA_window.
• Cross-volume anchors: c_ref, gamma(ell), d ell, L_gamma = ( ∫ 1 d ell ), n_eff(x,t), T_arr.

IV. Design Principles and Postulates (Concurrency Domain)

• P71-1 Causality Preservation: any observable effect e2 that depends on e1 must preserve hb(e1, e2); otherwise supply compensation and idempotence to mask reordering.
• P71-2 Stability First: under steady-state assumptions, each service station satisfies rho < 1; if not, a backoff or backpressure policy must be provided.
• P71-3 Observability Closure: each thr/chan exposes a minimal SLI set (latency, throughput, error rate) aggregable to SLO over SLA_window.
• P71-4 Budgetable Resources: prior to admission into the execution graph, each job declares upper bounds or elastic ranges for R_cpu/R_mem/R_io; scheduling must not exceed the assigned quota.
• P71-5 Idempotence and Deduplication: cross-process/network interactions default to at_least_once; use idemp_key and a dedup window Delta_t_dedup to attain practical exactly_once*.

V. Metrics and Approximations (Engineering Predictability)

• Makespan upper bound (critical-path approximation):
  T_make(G) approx ∑_{v∈crit(G)} w(v) + ∑_{e∈crit(G)} c(e)；document contention correction terms when shared-resource competition is non-negligible.
• Retry-timeout upper bound:
  W_retry <= timeout * (retries + 1) + J_total；J_total accumulates across the path.
• Backpressure signal (suggested):
  bp = f(q_len, cap, W_q), where f is monotone increasing and triggers rate limiting or dropping as q_len -> cap.
• Stability criterion: if using an M/M/1 approximation, report estimation sources and confidence for lambda, mu; when rho < 1 is violated, define anneal, shed, or scale-out strategy.

VI. Cross-Volume Binding and the Two Arrival-Time Forms

1. This volume references the two T_arr formulations for time calibration or propagation-delay modeling:
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
2. Two-form discrepancy:
   delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |。If delta_form exceeds threshold, Chapter 9 use cases must include calibration steps and an error budget.
3. Fixed cross-volume citations and numbering: see Core.DataSpec, Core.Equations, Core.Metrology, Core.Parameters, Core.Errors for the relevant S/P/M/I references.

VII. Implementation Bindings and Compliance (I70 Family)

1. Minimal interface set (see Appendix A for details):
   • Threads & tasks: spawn, join, cancel, set_affinity, set_priority.
   • Exec graph & scheduling: build_graph, run_graph, topo_sort, critical_path.
   • Channels & backpressure: chan_open, chan_put, chan_get, set_backpressure.
   • Timeout/retry/idempotence: with_timeout, retry, ensure_idempotent.
   • Resources & isolation: set_quota, reserve, release.
   • Rate limiting & telemetry: rate_limiter, limit_acquire, metric_emit, trace_span, trace_link.
   • Contracts & SLOs: assert_thread_contract, sli_slo_compute.
2. Compliance requirements:
   • All implementations must pass the Chapter 8 SLO validations and the baseline tests from Appendix B’s strategy templates.
   • Exported metric names and label keys are standardized to avoid ambiguity and collisions.

VIII. Relation to the Companion White Papers

• With Core.DataSpec: runtime artifacts (logs, metrics, traces) produced by the execution graph are materialized under data contracts; the Trace chain spans spawn -> run_graph -> chan_* -> metric_emit/trace_span.
• With Core.Equations: minimal equations (e.g., diffusion/propagation) can be mapped to node operators; node costs w(v) and their dimensions are validated by Core.Metrology.
• With Core.Metrology: any metric (W, P99, R_cpu) must carry unit(x) and dim(x); only metrics passing check_dim(expr) may be published.
• With Core.Parameters: scheduling and resource controls are parameterized under a common schema_version and binding interface, enabling gradual and rolling adjustments.
• With Core.Errors: failure semantics, retry, and compensation policies use the unified error taxonomy and budget model.

IX. Reading Path and Deliverables

1. Suggested sequence:
   • Chapters 1–2: establish the shared language for thr, G=(V,E), and T_make(G).
   • Chapters 3 & 7: close the loop with channels, backpressure, and rate limiting.
   • Chapters 4 & 5: ensure reliable semantics via causality, consistency, retry/timeout/idempotence.
   • Chapters 6 & 8: make the system operable through resource budgeting and SLOs.
   • Chapters 9 & 10: validate cross-volume bindings and end-to-end use cases.
2. Deliverables:
   The full set of P71-* / S72-* / Mx-* / I70-*; three reference use-case scripts; observation and alerting dashboard templates; compliance templates and a self-check list.

X. Naming and Symbol Conflict Constraints

• Do not mix: T_fil (tension) with T_trans (transmission coefficient); strictly distinguish n (number density) from n_eff (effective refractive index).
• All inline symbols are enclosed in backticks; any expression that includes division, integration, or composite operators uses parentheses, with the path declared as gamma(ell) and the measure as d ell.
• Formulas, symbols, and definitions are in English plain text; numbering and cross-volume citations follow the fixed format and prior conventions.