05-EFT.WP.Core.Errors v1.0 | Preface

Home ／ Docs-Technical WhitePaper ／ 05-EFT.WP.Core.Errors v1.0

Preface

I. Objectives and Scope

• Focus this volume on a unified classification, modeling, and governance of errors and residuals: from sources of observation- and model-induced error, to the residual construction r = y - f(x; theta), robust estimators rho / psi, outlier detection, error propagation and budgeting, numerical error and convergence, and in-operation recovery and degradation strategies.
• This volume introduces no new physical laws or governing equations; see Core.Equations for physics, Core.Parameters for parameters and priors, and Core.Metrology for units and dimensions. Our outputs standardize cross-volume error conventions, postulates, and implementation bindings I50-*, providing a common baseline for calibration, verification, and operational monitoring.
• Intended audience: algorithm and modeling engineers; metrology and test engineers; platform and reliability teams. Typical tasks include: building residuals and loss functions, defining outlier and retry policies, conducting error propagation and budgeting, and publishing quality metrics and regression baselines.

II. Readers and How to Use This Volume

• R&D and algorithms: use compute_residual, loss_rho, and psi_weight to form reusable templates for fitting and robust estimation, and bind into the I30-* inference chain (MLE/MAP/MCMC).
• Metrology and testing: use propagate_error_delta, propagate_error_mc, and error_budget to build traceable error budgets and uncertainty reports, in collaboration with Core.Metrology’s check_dim, RefCond, and U = k * u_c.
• Reliability and operations: monitor data quality and distribution drift with zscore_detect, hampel_filter, and drift_score; on anomalies, apply retry, fallback, and graceful_degradation to preserve service continuity.

III. Cross-Volume Relationships and Anchors

1. With Core.Metrology: all errors and residuals must preserve dimensional closure; validate with check_dim( y - f(x; theta) ). Environmental corrections must be explicit via corr_env(•; RefCond). Reporting adopts standard uncertainty u(•), combined uncertainty u_c(•), and expanded uncertainty U = k * u_c.
2. With Core.Parameters: error models serve parameter inference; weights and robust scales enter the likelihood or objective. When conditional independence is assumed, declare approx independence explicitly and produce Cov[theta] and sensitivities for diagnostics.
3. With Core.Equations: arrival-time errors must honor the two canonical forms and declare path and measure:
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )。
   • General form: T_arr = ( ∫ ( n_eff / c_ref ) d ell )。
     Here gamma(ell) and d ell must be declared; strictly distinguish n and n_eff; mixing T_fil and T_trans is forbidden.
4. Cross-volume anchor catalog: c_ref, gamma(ell), d ell, L_gamma = ∫ 1 d ell, n_eff(x,t), T_arr, check_dim(expr).

IV. Unified Conventions and Symbols

• Errors and residuals: e, e_i, r = y - f(x; theta), r_bar = r / sigma, w, R = diag(w), chi2 = r^T R r。
• Robust estimation: rho(e; hyper), psi(e) = d rho / d e, s (robust scale); heavy-tailed model StudentT(nu)。
• Propagation and budgeting: J = ∂g/∂x, Cov_y approx J * Cov_x * J^T, EB = { (name_i, u_i, k_i, contrib_i) }。
• Data quality and anomalies: z = ( x - mu ) / sigma, MAD, IQR, mask_outlier ∈ {0,1}, m ∈ {0,1} (missingness)。
• Numerical error and convergence: u_round, h, O(h^p), y0 (Richardson limit)。
• Notation policy: first use with def=; approximations with approx; identities are labeled “identity”. All inline symbols are wrapped in backticks, and all formulas appear as English plain text.

V. Quality, Postulates, and Compliance Principles

• Traceability: error budgets and reports must attach a traceability chain and evidence (see attach_traceability) and record versioned diffs and regression metrics in governance.
• Dimensional closure and unit consistency: every term in any objective or likelihood must pass check_dim; unit conversions are limited to affine forms v_to = a * v_from + b (with b != 0 only for offset units).
• Explicit weights and robustness: weighting criteria are written as min_r ( r^T R r ) or min_r ( rho(r; hyper) ); apply interpretable thresholds and refitting strategies for outliers.
• Numerical stability and convergence: report discrete order O(h^p) and extrapolation interval; distinguish rounding from truncation error.
• Conflict-name prohibition: never mix T_fil with T_trans, or n with n_eff; all cross-volume citations follow the fixed form “see companion white paper Energy Threads, Chapter x, S/P/M/I…”.

VI. Deliverables and Reading Path

1. Deliverables: an error-domain taxonomy and coding standard; a residual and robust-loss library; templates for outlier and drift detection; error-propagation and budgeting workflows; numerical-error and convergence cards; a library of recovery and degradation strategies; and a registry of regression and quality metrics.
2. Suggested reading path:
   • Read this preface and conventions to lock down naming and dimensional baselines.
   • See Chapters 1–2 to establish residual and robust-estimation foundations.
   • See Chapter 3 to complete error propagation and budgeting.
   • See Chapters 4–5 to configure data-quality monitoring and numerical-error control.
   • See Chapters 6–7 for logging, traceability, recovery, and graceful degradation in production.
   • See Chapter 8 and the Core.Parameters / Core.Metrology / Core.Equations volumes to assemble end-to-end use cases and regression.