[MPS] 🌠 Wander/漫步者: Issue #265 Hydrodynamics from Quantum Chains (Self-Proposed Challenge, not for Adjudication)

tracks/mps/solutions/Wander/issue265/.gitignore

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+__pycache__/
+*.py[cod]
+*.h5
+*.npz
+*.npy
+*.out
+*.err
+.pytest_cache/
+data/
+results/
+jobs/
+tracks/

tracks/mps/solutions/Wander/issue265/CURRENT_STATUS.md

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+# Current Status and Evidence Ledger — 2026-07-30
+
+## Status at a glance
+
+```text
+public-trajectory result: finite-window surrogate supported
+confirmatory program:     convergence datasets are the active evidence gate
+confirmation interval:     sealed
+next scientific selection: scalar / independent two-Burgers / coupled two-mode / memory
+```
+
+The public result and confirmatory result have different scopes. The
+single-trajectory pilot has completed its registered analysis and establishes
+the finite-window Burgers benchmark. The confirmatory program measures how a
+shared closure transfers across conditions and observables. Converged
+Production-A data create the registered model-selection record.
+
+## Scientific evidence completed
+
+### Public Heisenberg trajectory
+
+- Route B2 ingests the public high-temperature \(\Delta=1\) domain-wall data.
+- Weak and strong forms recover \(a\simeq0.230\) and
+  \(D_{\rm cl}\simeq1.97\), close to the published values.
+- The closed-loop profile audit reports \(0.167\%\) integrated relative
+  difference.
+- The measured-window width and moment-diffusivity exponents are \(0.6802\)
+  and \(0.3372\), respectively.
+- The moment bridge gives \(A_W=0.741842\) and
+  \(A_B/A_W=0.999154\), quantitatively identifying the finite-window tangent
+  mechanism.
+- Long deterministic continuation exposes the scalar PDE's rarefaction flow:
+  its local width exponent moves from approximately \(0.665\) near
+  \(t=200\) to approximately \(0.851\) at \(t=5000\).
+
+### Analytical interpretation
+
+- Microscopic magnetization continuity is exact.
+- Spin flip fixes the parity of a physical one-field current and supplies the
+  field-identification gate.
+- Nonlinear stochastic averaging retains variance/covariance currents.
+- The equal-coupling two-field flux diagonalizes algebraically into
+  opposite-chirality Burgers modes \(u_\pm=m\pm\phi\).
+- The moment identity connects fitted Burgers parameters to the wall's
+  scale-dependent broadening and predicts rolling coefficient powers
+  \((-1/3,+1/3)\) under the tangent interpretation.
+
+### Synthetic calibration
+
+- Constant-Burgers ground truth \((a,D)=(0.24,1.9)\) is recovered as
+  \((0.239529,1.898051)\).
+- Its instantaneous practical diffusivity variation is \(0.052\%\) in relative
+  range and \(0.015\%\) in relative standard deviation.
+- A \(D(t)\propto t^{1/3}\) control recovers
+  \(\gamma=0.332998\pm1.67\times10^{-5}\), with a \(29.446\%\) relative
+  range.
+
+## Protocol and implementation completed
+
+- Protocol v1.2, the condition matrix, decision thresholds, and all time
+  splits were frozen before Production-A results.
+- The base manifest contains 74 rows: 12 convergence, 31 Production A, and 31
+  sealed Production B.
+- Production-v2 contains 34 logical rows in each stage. Production A uses 32
+  new executions and two fine-row reuse paths; Production B uses 34 new
+  executions.
+- The Production-v2 observable panel includes seven logical FCS rows in A and
+  three in B, plus equilibrium and opposite-sign pulse responses.
+- The scalar, independent two-Burgers, and coupled two-mode fitting and
+  cross-validation paths are implemented.
+- The stochastic
+  [`solver budget`](results_research_program/two_mode/solver_budget.json) is
+  frozen at 1,024 screening trajectories and at least 2,048 final
+  trajectories, selected from solver-convergence targets ahead of quantum
+  model scoring.
+- The one-time confirmation guard and Production-B transaction controller are
+  implemented. The committed snapshot is at the sealed pre-authorization
+  stage.
+
+## Backend validation completed
+
+- Infinite-temperature purification TEBD is implemented with conserved
+  \(S^z\), second-order evolution, and a backward disentangler.
+- Magnetization, local/complete-cut current, connected \(C^{zz}\), and genuine
+  two-measurement transfer FCS are recorded.
+- Small-chain spin-flip agreement is within \(2\times10^{-15}\) of exact, and
+  total magnetization is conserved within approximately \(10^{-14}\).
+- The original lattice-continuity smoke test reaches agreement within
+  \(4.17\times10^{-4}\).
+- Dense \(L=6\) evolution agrees at \(10^{-9}\) or better for the original
+  validation observables.
+- An actual interrupted HDF5 run resumes bit-identically through the compared
+  interval.
+- The grouped two-physical-spin implementation includes all
+  next-nearest-neighbour terms crossing the physical current cut.
+- At \(J_2=0.1\), both wall orientations agree with dense evolution within
+  \(8.3\times10^{-10}\).
+- At \(J_2=0\), grouped and ordinary backends agree within
+  \(1.0\times10^{-8}\), below the frozen \(2\times10^{-7}\) threshold.
+- Cross-version continuation preserves the exact 1,001-point output grid,
+  canonical job identity, and all stored arrays with zero difference.
+- The source gate recognizes the two fully validated runner/backend pairs and
+  carries successful attestations for all 12 registered convergence rows.
+
+## SCNet execution evidence
+
+### Convergence campaign
+
+Twelve jobs were submitted for four representative conditions at coarse,
+medium, and fine resolution:
+
+```text
+23009466  23009467  23009468  23009469
+23009470  23009471  23009472  23009473
+23009474  23009475  23009476  23009477
+```
+
+The archived launch audit records all twelve as started with initial
+checkpoints and clean startup logs. Controller `23009668` was registered with
+dependencies on the twelve jobs. It can continue checkpointed
+scheduler-resource slices and then run the frozen convergence audit. Human
+review handles terminal states outside that resource-continuation path.
+
+This public document treats those scheduler observations as a dated archive.
+The next scheduler refresh creates a new dated record. Final datasets and the
+generated convergence summary are the evidence that advances Production A.
+
+### \(J_2\) compute-node validation
+
+The latest committed record
+`results_research_program/hpc/j2_validation_20260730.json` has status `pass`:
+
+- SCNet job `23015027` completed with exit code `0:0` in 48 seconds;
+- exact \(J_2\) up/down, symmetry, FCS, grouped-equivalence, and checkpoint
+  summaries all passed;
+- source hashes match the registered backend and manifest;
+- the base Production-A \(J_2\) gate rebuilt to 31 ready rows;
+- the submission record remains at its prepared stage while the convergence
+  gate produces its accepted-resolution artifact.
+
+## Evidence gates that remain in sequence
+
+1. **Convergence acceptance**
+   - validate the four three-resolution condition groups;
+   - require profile difference below \(0.002\) and width difference below
+     \(0.003\);
+   - choose the accepted resolution from numerical-consistency observables
+     ahead of model scoring.
+2. **Production A**
+   - run the registered amplitudes, orientations, widths, shapes,
+     backgrounds, controls, equilibrium, responses, currents, correlations,
+     and FCS through \(t=200\);
+   - materialize the two fine-data reuse attestations.
+3. **Frozen selection**
+   - fit on \(50\le t\le150\);
+   - evaluate time, condition, and orientation holdouts on
+     \(150<t\le200\);
+   - use 2,000 paired 10-time-unit bootstrap blocks;
+   - create a hash-bound scalar/two-mode selection record.
+4. **One-time confirmation**
+   - preview the exact action;
+   - require explicit `--confirm-unblind` human authorization;
+   - record evidence hashes, model identity, parameters, seeds, and time.
+5. **Production B**
+   - run the surviving registered forecast once on \(200<t\le400\);
+   - report future-time prediction independently of model development.
+
+The machine-readable contracts store adjacent endpoint pairs, while the
+executable masks assign `t=150` to training and `t=200` to validation.  This
+makes the three scoring sets disjoint.
+
+## Decisive scientific readouts
+
+The confirmatory program answers five concrete questions:
+
+| Question | Decisive evidence |
+|---|---|
+| How stable are the public coefficients across numerical resolution? | medium-to-fine profile and width gates |
+| How broadly do they transfer across trajectories? | leave-one-condition/orientation-out prediction and coefficient spread |
+| How precisely do they follow the finite-window moment tangent? | rolling \(a,D_{\rm cl},A_W,A_B,W_*\) and future-time width flow |
+| Which physical or chiral field carries the Burgers current? | spin-flip, amplitude/orientation law, current and pulse-response prediction |
+| Which scalar or two-mode closure organizes the full hydrodynamics? | joint profile/current/correlation/FCS holdouts and sealed Production B |
+
+## Claim boundary for the current PR
+
+The present package supports the following reviewer-facing statement:
+
+> The machine-learned deterministic Burgers equation is a quantitatively
+> accurate, trajectory-conditioned finite-window closure for the public weak
+> domain-wall profile.  Exact field symmetry, nonlinear stochastic averaging,
+> deterministic rarefaction, and higher-order observables define the tests
+> required to identify a transferable scalar or two-mode hydrodynamic law.
+> Those tests are preregistered, implemented, numerically preflighted, and
+> progressing through the convergence evidence gate.
+
+For the full reasoning and primary literature, see
+[`SCIENTIFIC_CASE.md`](SCIENTIFIC_CASE.md).  For the immutable scientific
+contract, see
+[`docs/RESEARCH_PROTOCOL_BURGERS_UNIVERSALITY.md`](docs/RESEARCH_PROTOCOL_BURGERS_UNIVERSALITY.md).