Uncertainty propagation and validation

Owner closeout, 4 Nov 2026 (OQ-52): scoped M4 certification, frozen-closure acceptance and reduced-scope M5 physicist sign-off are recorded. Full current-baseline UQ remains incomplete. Earlier pending-gate wording below belongs to the dated research history; unresolved numerical properties retain their original status.

Uncertainty propagation and validation

Current continuous baseline: numerical convergence passed

all 33 original cases reach five seconds at all three maximum-step settings: 99 of 99 valid trajectories and 264 of 264 passing endpoint comparisonsC-305. the largest changes are 0.219% for coarse-to-middle and 0.0423% for middle-to-fine, both below the 1% acceptance limitC-306. The successful research integration combines a changed continuous guarded closure, strict Newton acceptance and rejected-step rollback (the new research baseline uses a continuous guarded closure, Newton trials accepted only after residual decrease, and adaptive rollback of the complete state and auxiliary dataC-304), with independently reconstructed physical residuals (maximum accepted physical-channel L1 is 1.76 × 10⁻⁹ against a 10⁻⁸ gate, and native mean L1 is 1.01 × 10⁻¹⁴ against 10⁻¹⁰; no crash occursC-307).

The complete technical protocol explains the original case coverage, adaptive maximum-step comparisons and raw checks. The sections below retain the earlier uncertainty study and hard-switch ladder failures. Their arrays and conclusions are not rewritten. The new result supports the numerical baseline; a later uncertainty/sensitivity design must explicitly adopt it. Physical discrepancy and physicist sign-off remain open.

Constrained flux representation through full processing

The first shadow preserves the admitted served finite-volume rate after native masking, clipping/floors and patches, before radial smoothing. At admitted unpatched faces it seeds diffusion with the baseline smoothed value and solves bounded velocity for the same rate. The bracketed facewise root uses implicit derivatives. Rejected/protected faces retain their coefficients, and the alternative receives the unchanged native particle preprocessing, smoothing, power-law face stencil and additional total-coefficient terms.

The construction is feasible on the tested states, but the full operator comparison does not support expansion (the selected particle-face difference falls from 5.76626% to 4.92144%, but complete-grid total rate L1 difference rises from 15.86765% to 16.23066% and divergence difference from 47.64620% to 49.04301%C-316). Across the six particle side states, complete-grid rate and divergence differences worsen despite the selected-face gain. The cap context has global gains but a worse selected-face difference, and its paired rate differences plateau across the three tested boundary offsets (the shadow paired total-rate difference stays near 5.10177% across a hundredfold reduction in cap offset, while the baseline difference shrinks by approximately the same hundredfold factorC-317).

The remap’s binary eligibility switch explains that new issue. Near the cap, the original continuous served pair tends to fallback. The trial switches to a different diffusion representation on the admitted side and compensates velocity to preserve only its local pre-smoothing rate. Radial mixing exposes the representation difference at neighboring faces. This is a limitation of the shadow; the original continuous closure remains the numerical baseline.

The unchanged strict AD/FD checks corroborate all new shadow components, while retaining inherited unresolved controls (174 observations pass bounds, algebra and baseline parity; all 48 new shadow derivative components pass strict corroboration; 368 of 372 combined components pass, with four inherited cap controls unresolvedC-318). Branch-local derivatives and pre-smoothing algebra do not establish cross-branch continuity or a useful postprocessed operator. No physical accuracy tolerance is inferred.

A successor needs continuous remapping under the same admission and coefficient limits and an objective defined after the full native processing. Its feasibility must be tested before matched trajectory windows. The current negative result is specific to this construction and does not rule out other formulations.

Narrative companion: entry 100, local draft pending publication approval.

Identical-state radial-smoothing controls

Native radial coefficient smoothing and continuous guard/split transitions are separate operations. This control changes only the radial Gaussian HWHM while holding the continuous transition widths and each complete local context fixed. The mask excludes the inner patch and pedestal region; normalized weights below the native cutoff are removed and rows are normalized again. Zero width gives the identity on the retained grid, not a demonstrated continuum limit.

The native producer evaluates six side states in each of the particle-split and coefficient-cap contexts at HWHM 0, 0.025, 0.05 and 0.1. It retains raw, served, native turbulent and total particle transport, face rates, matrix divergence, branch masks and directional AD. Geometry, clipping, floors, patches, admission, fallback and auxiliary history remain fixed. These are historical local contexts, not checkpoints on a newly integrated baseline trajectory.

The selected particle response is nonmonotone across the nonzero widths (the selected particle rate is 0%, 6.76754%, 9.05578% and 5.76626% less inward than the raw target at radial HWHM 0, 0.025, 0.05 and 0.1 respectivelyC-312). Its left density-cell derivative reverses sign at two widths, while the narrow nonzero control remains insufficiently corroborated (the target derivative is +39.9009; native values are +39.9009, +0.4076, −43.8378 and −38.8539 across the same widths; the +0.4076 value lacks strict finite-difference corroborationC-313). The cap comparison separates radial mixing from the served closure’s existing departure from the raw target (the selected cap rate is already 96.87350% less inward than the raw target without radial smoothing, compared with 81.44208%, 63.19414% and 65.09036% at the three nonzero widthsC-314).

A separate NumPy reconstruction checks the native kernel, masked regions, clipping/patch order, full face/matrix algebra and invariance of non-radial terms. The baseline-width observations and AD arrays reproduce the original evidence, including identical nonfinite masks outside the selected target face. Those inherited entries do not supply a full-face derivative certificate.

The unchanged derivative rule requires two adjacent branch-preserving centered stencils to agree with AD within 1e-8 * max(abs(target_rate), 1) + 1e-4 * abs(JVP). Coverage and unresolved components are retained explicitly (696 observations pass algebra/invariant reconstruction and 174 baseline observations reproduce the parent evidence; 996 of 1008 derivative components and 45 of 48 complete direction sets meet the strict ruleC-315). The original cap attempt crashed while an inherited periodic stack dump was printing during staging. A separate request cancels that diagnostic timer with identical numerical function ASTs and unchanged hard limits. Causality remains suspected rather than proven. A separate checker correction handles inherited nonfinite masks without changing the target-face derivative rule.

No physical radius or density/flux bias tolerance is selected. The next bounded diagnostic should compare a constrained particle-flux shadow through the full native postprocessing operator, preserving admissibility and deliberate regularization. Any trajectory comparison must start from valid baseline state/post checkpoints and separate temporal, radial and transition-width effects. The existing endpoint QoI criterion is not a density/flux bias tolerance.

Narrative companion: entry 99, local draft pending publication approval.

Numerical methods

An ordered typed input specification states independent marginal distributions and their units. A seeded scrambled Sobol sequence maps through inverse CDFs on the host. One transport member stays fixed throughout each trajectory. Sample order is shuffled before assigning members, avoiding aliasing between member indices and Sobol leading bits. Chunked vmap keeps memory bounded. Samples with nonfinite outputs or failed/coarse solver steps are retained in the raw record and explicitly excluded from valid statistics.

Forward Jacobians at the nominal point form the first-order covariance J S Jᵀ. With ensemble members the input term is averaged across members and the covariance of their nominal outputs is added by total variance. The reported standard-deviation cross-check flags disagreement above the fixed criterion, as well as nonfinite derivatives; it never silently accepts a failed derivative.

First-order Saltelli and total Jansen indices use independent factor columns from a doubled-dimensional scrambled Sobol design. Each column substitution changes one factor, including the categorical member. Centering the output in the first-order estimator removes large-offset sensitivity. Total indices include interactions and need not sum to one. Row bootstrap intervals are retained as heuristic diagnostics; their coverage is not established for the quasi-random design.

ITER study

The minimal OQ-47 study evolves the shipped ITER hybrid scenario with transport, upper-launcher EC heating and EPEDNN. Each sample rebuilds consistent initial profiles, composition, source profiles and post-processing before the fixed-step scan. Density changes the line-average target, edge boundary and prescribed pedestal density; power scales generic and EC heating; pedestal height multiplies only accepted EPEDNN temperatures. Existing guards reject out-of-domain or physically inadmissible evaluations without clipping inputs. Diagnostics are re-evaluated on accepted states, not internal solver evaluations.

The declared ranges are independent sensitivity priors, not measured experimental distributions. The transport term combines a sampled member with a coherent signed-log shift from the hybrid marginal conformal half-widths. This is a specified discrepancy law, not a joint conformal guarantee. All Monte Carlo and sensitivity calculations finish (all 256 retained Monte Carlo outputs are finite with zero native linear-step error codes, and 2048 sensitivity evaluations drop no rows; those codes do not establish nonlinear-residual or temporal convergenceC-292); every linearisation cross-check flags nonlinear response (all four outputs fail the fixed 10% standard-deviation cross-check; disagreements are 46.2%, 43.4%, 43.1% and 59.7% for fusion power, thermal energy, central electron temperature and central ion temperatureC-287).

The report attributes available validation evidence to solver, transport, EC, pedestal and equilibrium. They are measured in different native quantities and cannot be added into a final-power error bar. Pedestal model-form discrepancy and equilibrium uncertainty remain unquantified (K-035). Conditional calibration against Tier A reference labels does not supply experimental validation. The full numerical record, prior definitions and scientific figures are retained in the private M5 report for physicist review.

Reusable execution and independent replay

The fitted Tier A EC fallback ships with its original artifact digest. An isolated source checkout without ignored datasets exercises the actual three-module driver. Each distinct future study supplies a new request path, and its preflight binds the two-direction interval selection, source, models, fallback and proof resources. The historical completed request remains consumed.

Future sensitivity records retain the sampled unit design, physical inputs, categorical members, model outputs and common finite-row mask. The first-order and total estimators can be reconstructed from these arrays without another trajectory run. This retention does not retroactively add raw sensitivity outputs to the earlier study; its original source-bound result and stated audit limits remain intact.

Historical native solver diagnostics

The selected linear predictor-corrector advances a fixed number of corrections. Its native error code is assigned zero unconditionally, and its reported iteration count records that fixed work. Finite retained outputs and zero native error codes therefore do not establish a fine nonlinear residual (all 256 retained Monte Carlo outputs are finite with zero native linear-step error codes, and 2048 sensitivity evaluations drop no rows; those codes do not establish nonlinear-residual or temporal convergenceC-292). Earlier draft wording was stronger than the recorded diagnostic. The native arrays remain unchanged; a source-bound audit identifies the actual scenario and installed solver implementation.

Time-step refinement supplies a separate numerical check on the final quantities. It cannot retrospectively establish nonlinear-residual convergence, experimental validation, or an exact-solution error bound. Accepted-state guard decisions also remain distinct from decisions made inside the solver (K-014).

Historical paired temporal refinement

The refined diagnostic retains the nominal ensemble-mean case and every frozen prior-design case, including every discrete member. Raw final quantities, physical times, accepted-state rejection masks and reasons, and native solver fields are retained at each step size. A separate audit reconstructs final quantities from traces, rejection summaries from masks, solver summaries from native fields and both adjacent endpoint comparisons. Historical overlap prevents instrumentation changes from silently altering the earlier control.

Both comparisons fail the fixed temporal criterion (maximum paired changes remain 19.2654% and 1.9773% across the two refinements, exceeding the fixed 1% limit; all 99 retained rows are finite with zero native linear-step error codes and no exclusionsC-295). No tested replacement step is established and the final propagation remains dependent on that gate. The largest first-pair difference coincides with changes in EC input-domain rejection and some transport decisions. The recorded pedestal decisions agree. Correlation at shared physical times does not establish cause, and these post-step observations do not expose internal predictor-corrector branches.

Further refinement uses a distinct frozen request, independently audited parent arrays and only missing finer evaluations. Both adjacent comparisons must pass for every quantity and every case, retaining invalid or fallback-heavy rows. Finer sampling alone cannot resolve a failed temporal diagnostic. No physics, guard threshold, prior or acceptance tolerance changes to force a pass.

The additional finer ladder also fails both comparisons after independent raw and ancestry reconstruction (the additional finer ladder has maximum paired changes of 1.7092% and 1.8560%, above the unchanged 1% criterion; all 99 assessed rows remain valid and no supported replacement step is establishedC-296). No supported step follows. Before committing a final propagation, its complete sampling and sensitivity design must fit the remaining submission and wall-time limits. Any useful throughput measurement must be part of retained final-design work, with immutable raw checkpoints and all invalid rows preserved. A resource limit cannot be repaired by dropping seeds, cases or sensitivity blocks.

The next full independent ladder audit passes source, design, ancestry, raw/trace and historical-overlap checks, but temporal acceptance still fails (the first pair stays below 1%, but the finer pair changes fusion power by up to 4.1372% and fails three quantities; all 99 assessed rows remain valid, so no replacement step is supportedC-298). The first pair passes; only case20/member19 exceeds 1% in the second, failing fusion power, thermal energy and electron temperature. Its EC and pedestal decisions match at shared times while transport decisions differ. No causal attribution, supported step or final refined uncertainty result follows. The conditional parallel UQ prototype remains unexecuted.

The bounded investigation closes scientifically unresolved after independent stopping review. Further refinement and a sixteen-worker scheduling path remain technically credible, but their complete cost is unmeasured. The stop preserves unused authority and every failed case; it does not claim exhausted compute or impossible convergence.

Domain and discrete-balance diagnosis

The follow-up retains the nominal trajectory, the worst endpoint case and a subthreshold control at the same two finest steps. For every old/new accepted pair, an observer reconstructs channel storage, edge transport, sources and pedestal pinning. Its signed residual is the remainder of that discrete balance. Each channel’s global diagnostic normalizes the residual magnitude by the sum of absolute storage, edge, source and pinning contributions; it is not a local nonlinear residual norm. No observer value feeds back into the trajectory.

Independent domain reconstruction identifies the ion-to-electron temperature ratio as the rejecting feature at the selected face. Finer stepping reduces the failing case’s switch count while increasing sustained fallback occupancy and late balance residuals ([the failing case rejects face seven on 24.766% of coarse and 82.539% of fine accepted states over (3,5] seconds; its median normalized global electron balance residual rises from 0.031813% to 0.962581%]{.claim}C-299). Integer-step windows and native fine-step observations exclude an artifact of subsampling shared times. The control case meets the endpoint criterion despite encountering the same boundary. The discrete thermal-term ledger is an algebraic balance, not a causal physical-error budget. The observer does not clip features or expand the stored domain.

Narrative companion: entry 94 (private draft pending publication).

Internal branches and local residual decomposition

A separate frozen observer replays the canonical predictor and corrector calls with their original old state and context. Denote the last coefficient guess by x1 and the accepted vector by x2. Their transport guard decisions often disagree at the selected face ([the failing case has different last-guess and accepted-state branches on 39.453% of coarse and 73.145% of fine steps over (3,5] seconds; during (3.5,4.5] seconds all fine accepted states fall back while 84.961% of last guesses select the surrogate]{.claim}C-300). All specified parent fields match at frozen tolerances, and every replayed evolving cell equals canonical x2 exactly. Raw out-of-domain candidates retain intentional NaNs; selected transport and evaluated local terms remain finite. Native zero flags retain the limitation in K-036.

At a fixed accepted vector, evaluate residual operators using last-guess coefficients L, accepted-state coefficients A, and their face-specific fallback shadows LF and AF. These four evaluations retain stabilization. Let P use accepted physical coefficients with stabilization disabled. The independently checked identity is

R(P) = [(R(A) - R(AF)) - (R(L) - R(LF))]
     + [R(AF) - R(LF)] + [R(P) - R(A)] + R(L).

The terms are the change in the face’s candidate contribution, remaining coefficient lag under a common fallback at that face, accepted-state stabilization delta, and the last frozen linear-equation residual. Remaining lag includes other-face transport, transients, sources/pinning and frozen stabilization effects. The stabilization delta does not include every effect of stabilization. Shadow evaluations never force an invalid candidate and never advance an altered trajectory.

Absolute cell/time integrals relative to the physical residual norm show a substantial local branch term (the fine failing case has branch-term norm ratios of 0.723 for electron temperature and 0.982 for ion temperature; the signed global branch term cancels and the remaining coefficient lag carries the net defectC-301). These ratios need not sum to one: signed terms cancel. The branch contribution cancels in the signed width-weighted global integral, leaving the common-fallback coefficient lag to carry the net defect in this identity. That does not isolate indirect branch effects through the evolving state. Local L1 normalizations and the earlier global balance ratio have different denominators and must not be compared as the same percentage. The passing endpoint control also has substantial branch terms, preventing attribution of the worst case’s power difference from mismatch counts alone.

The next prepared protocol continues the same undamped Picard map at shared checkpoints, anchors the original iterates and retains x2 as canonical carry. One- and two-step iterate differences, branch histories and physical local residuals would distinguish observed decay from sustained alternation. A finite probe cannot prove a fixed point or rule one out. This protocol is not implemented, frozen or submitted; extra correctors are not an established remedy. Full paired convergence, complete affordable uncertainty propagation and human sign-off remain separate prerequisites.

Narrative companion: entry 95 (private draft pending publication).

Changelog

• 2026-10-28: retained native-solver diagnostic limits and unresolved paired refinement (entries 92–93, private drafts).
• 2026-10-28: added domain/balance diagnosis and internal branch decomposition (entries 94–95, private drafts).

Current-baseline implementation and bounded pilot

The new propagation driver binds the adopted continuous closure and OQ-51 state-level transport calibration. It retains the complete sampling and sensitivity designs, invalid rows, accepted-state diagnostic denominators and member-specific derivative controls. The historical propagation remains evidence for its original discretization and calibration.

three selected five-second trajectories pass the raw audit; only one of ten finite-difference controls survives the derivative timeoutC-327. A finite automatic Jacobian is insufficient: central finite differences must complete before agreement can be assessed. Matching observed adaptive histories alone does not establish smoothness of every internal Newton branch. Conditional derivatives remain labelled conditional, and the development comparison failure is preserved.

the 18,432-trajectory design projects roughly 1,710–1,877 node-hours in the measured worker layout, before derivatives and recoveryC-328. These scenarios include complete trajectory-worker costs but cannot price the censored derivative work or unobserved prior tails. They motivate a throughput and scope decision before production, without changing sample counts or tolerances. No current-baseline Monte Carlo percentiles, Sobol rankings or linearised cross-check are claimed from this pilot. OQ-52 records the owner’s frozen-closure acceptance, scoped M4 certification and M5 physicist sign-off for a bounded research deliverable. Full UQ and derivative agreement remain incomplete and are excluded from that accepted completion scope.