11-EFT.WP.Core.DrawingKinetics v1.0 | Chapter 1 Objectives, Scope, and Object Model

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Chapter 1 Objectives, Scope, and Object Model

I. Scope and Objectives

1. Establish a unified object model and layered gauges for filament drawing/tension processes, covering geometry and kinematics, conservation, constitutive behavior, observation, and metrology.
2. Clarify applicable scenarios: industrial continuous drawing lines, laboratory bench validation, numerical simulation, and digital-twin coupling.
3. Pass criteria
   • The key quantities lambda(x,t), s(x,t), v(x,t), A(x,t), rho_L(x,t), J(x,t), T_fil(x,t) are quantifiable and consistently ingested into the data lake.
   • Quality gates meet thresholds: mass gate gate.mass, unit gate check_dim(expr), synchronization gate |delta_form|.
   • Data and reports are published with schema.core.drawing/v1, and the Mx-1* workflow is reproducible.

II. Terminology and Symbols

1. Path and measure: centerline gamma(ell), arc-length coordinate ell, measure d ell. When expressed in Euclidean coordinates x, adopt x = gamma(ell).
2. Geometry and kinematics: lambda(x,t) (stretch ratio), s(x,t) = ( d/dt ) ( ln( lambda ) ) (strain rate), v(x,t) (drawing speed), A(x,t) (cross-sectional area).
3. Conservation and flux: rho(x,t) (volumetric density), rho_L(x,t) = rho(x,t) * A(x,t) (line density), J(x,t) = rho_L(x,t) * v(x,t) (mass flux), Q (cumulative volumetric/mass throughput, declared by context).
4. Tension and constitutive parameters: T_fil(x,t) (tension), K_el, K_vis (constitutive parameters).
5. Time and arrival time: monotonic internal base tau_mono, published base ts, mapping ts = alpha + beta * tau_mono; two arrival-time conventions
   • T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell )
   • T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell )
6. Collision constraints: T_fil denotes tension only; T_trans denotes transmission coefficient only; strictly distinguish n and n_eff.

III. Postulates and Minimal Equations

• P11-1 (slenderness approximation): cross-section varies slowly and radial gradients are higher-order, enabling a 1D axial description; A(x,t) and lambda(x,t) are related by geometric constraints.
• P11-2 (measurability): after calibration, observation mappings for lambda, v, and T_fil satisfy a linear clock model with unit consistency.
• S12-0 (kinematic identity): s(x,t) = ( d/dt ) ( ln( lambda(x,t) ) ).
• S12-1 (continuity, line-density form): ( d/dt ) rho_L + ( d/dell ) J = 0.
• S12-2 (1D axial momentum, preview): gradients of tension balance inertia and viscous/frictional terms; domain-specific gauges and term ordering are detailed in Chapter 3.

IV. Data Gauges and Manifest

1. Minimal object family (schema.core.drawing/v1)
   • meta.run_id : str, meta.schema_version : str
   • time.ts : float, time.tau_mono : float, time.alpha : float, time.beta : float
   • path.gamma_param : str (e.g., ell), path.domain : [float,float], path.note : str
   • geom.A : float, geom.lambda : float, kin.v : float, kin.s : float
   • cons.rho : float, cons.rho_L : float, cons.J : float
   • tension.T_fil : float, tension.params : dict
   • env.T : float, env.humidity : float (optional)
   • quality.flag : int, quality.notes : str
2. Windowing: all spectral quantities report window energy U_w and equivalent noise bandwidth ENBW; each dataset carries its window definition.
3. Path gauge: for any integral, explicitly declare path and measure, e.g., ( ∫_{gamma(ell)} f(ell) d ell ). Compute both arrival-time conventions in parallel and publish delta_form.
4. Units and dimensions: run check_dim(expr) before data-lake ingestion; publish unit.* lists (SI base units or declared conversions).

V. Algorithms and Implementation Bindings

1. Prototype interfaces (see Appendix B for details)
   • I10-1 update_draw_state(state, bc:dict, dt:float) -> StepReport
   • I10-2 estimate_tension(lambda:float, s:float, params:dict) -> float
   • I10-3 compute_instability_metrics(state) -> dict
   • I10-4 calibrate_kinematics(trace:any, sensors:list, timebase:dict) -> CalReport
   • I10-5 emit_metrics_drawing(state) -> dict
2. Idempotency and compensation: I10-1 must produce identical output for repeated state, bc, dt; on failure, return E_UNSTABLE_STEP and a suggested step ( dt_new < dt ).
3. Error enumeration: E_BC_INVALID, E_DIMENSION_MISMATCH, E_CONSERVATION_FAIL, E_UNSTABLE_STEP.

VI. Metrology Workflow and Run Graph

1. Workflow skeleton: Mx-10 bootstrap -> Mx-11 timebase-geo-cal -> Mx-12 constitutive-fit -> Mx-13 conservation-check -> Mx-14 benchmark-report.
2. Key observation points
   • Time-base alignment: fit alpha, beta and verify residuals of ts = alpha + beta * tau_mono within gate.
   • Geometric calibration: A and scale mapping, consistency and drift checks.
   • Conservation audit: on sliding windows, verify residual spectra of ( d/dt ) rho_L + ( d/dell ) J ≈ 0.
3. Alerts and rollback: when |delta_form| exceeds threshold or gate.mass fails, reduce step size or replay with compensating transactions.

VII. Verification and Test Matrix

1. Minimum required tests
   • Dimensions & units: all expressions pass check_dim(expr).
   • Kinematic consistency: random-segment verification of s = ( d/dt ) ( ln( lambda ) ) with numerical approximation error bounds.
   • Conservation gate: eps_mass and eps_norm within thresholds.
   • Arrival-time gate: discrepancy delta_form computed and within thresholds (when T_arr is involved).
2. Boundaries and edge scenarios: high stretch ratios, rapid steps, thermal perturbations, and grip slip.
3. SLOs and observability: publish end-to-end latency, loss, and sampling jitter via TS.* metrics.

VIII. Cross-References and Dependencies

• Core.Equations: conservation framework and symbol gauges (Chapter 3 cites S12-*).
• Core.Density, Core.Sea: measures, time bases, and the two T_arr conventions.
• Core.Metrology: metrological uncertainty, windowing, and spectral gauges.
• Core.Threads: concurrency semantics, hb, bp, SLOs, and TS.*.
• Core.DataSpec: schema.* and publication compliance.
• Core.Errors, Core.Parameters: error budgets and parameter calibration gauges.

IX. Risks, Limits, and Open Questions

• Slenderness applicability: when transverse gradients of A are non-negligible, annotate the distortion of the 1D model.
• Sensor slip and latency: bias in lambda and v must be disclosed via quality.flag and uncertainty fields.
• Constitutive nonlinearity and thermal coupling: nonlinear terms in T_fil and thermo-rate couplings are addressed by domain in Chapter 4.
• Time-base drift: drift of beta requires periodic recalibration, otherwise ts mismatch accumulates.

X. Deliverables and Version Management

1. Artifacts
   • Definition and sample datasets for schema.core.drawing/v1
   • Templates for parameter and operating-condition cards (params.card, bc.card)
   • Mx-1* workflow scripts and replay logs
   • Quality-gate and compliance reports (including gate.mass, gate.norm, delta_form, TS.*)
2. Versioning strategy
   • Semantic versioning MAJOR.MINOR.PATCH; breaking changes occur only on MAJOR with a migration guide.
   • Change logs labeled ADD/MOD/FIX/PERF/SEC/DOC, with compatibility flags and deprecation timelines.

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