# Reproduction Manifest (paper-grade runs only)

One row per number/figure that can appear in the paper: the claim, the exact
command (or the note that records it), the output directory, and the note that
interprets it. `outputs/` is gitignored — these runs are the regenerable
ground truth behind the ledger (note 36). Anything in `outputs/` NOT listed
here is an exploratory/superseded/smoke run and must not be cited.

Environment: python 3.13, torch (CPU, float64), `requirements.txt`. All runs
deterministic given the seeds shown. Long runs use `nohup`.

## Static geometry (T1-T3 + overlap)

| claim | command | outputs | note |
|---|---|---|---|
| Beta law, tails, multilayer product (700k samples, D=64..4096) | `python scripts/capacity_empirical_validation.py --dimensions 64 128 256 512 1024 2048 4096 --samples 100000 --batch-size 2048 --seed 123 --plot` | `capacity_empirical_validation/` | 02 |
| surprisal `S~Exp(1)`, `sum S ~ Gamma(L,1)` (max KS 0.0042) | `python scripts/multilayer_capacity_distribution.py --dimensions 64 256 1024 4096 --layers 1 2 4 8 16 --samples 100000 --batch-size 8192 --seed 456 --plot` | `multilayer_capacity_distribution/` | 02 |
| minimax: isotropic attains 1/D, alternatives below | `python scripts/minimax_initialization.py --dimension 32 --feedback-samples 20000 --target-samples 10000 --seed 11 --subspace-dim 4 --plot` | `minimax_initialization/` | 02 |
| coverage distributions per scheme | `python scripts/initialization_distribution_matching.py --dimension 128 --target-samples 100000 --feedback-samples 100000 --batch-size 8192 --seed 2026 --subspace-dim 8 --anisotropy 64 --plot` | `initialization_distribution_matching/` | 02 |
| hard rank loss + kd/P overlap | `python scripts/functional_capacity_overlap.py --parameters 96 --task-rank 24 --constraint-ranks 0 24 48 72 84 96 --trials 100 --seed 5 --plot` | `functional_capacity_overlap/` | 02 |

## The soft ramp (dense sweep) + closed form (T7)

| claim | command | outputs | note |
|---|---|---|---|
| dense T=30000 ramp: gap 0.1468 -> 0.000162, smooth, log-linear R^2=0.993 | `python scripts/downstream_capacity_sweep.py --task random --widths 20 22 24 26 28 30 32 34 36 38 40 --train-samples 128 --test-samples 1024 --probe-samples 64 --steps 30000 --lr 0.01 --optimizer sgd --init-seeds 1 --feedback-seeds 32 --data-seed 0 --skip-jacobian --plot --outdir outputs/phase_transition_dense_T30000_352traj` (config preserved in its `summary.json`) | `phase_transition_dense_T30000_352traj/` | 22 |
| closed form, matched data+init: corr 0.933 matched / 0.982 5-init geo mean; lam_min ensemble corr 0.987 | `python scripts/closed_form_soft_ramp.py --torch-threads 8` (reads the dense dir) | `closed_form_soft_ramp/` | 34, 37 |
| hard-k null model overpredicts (2x-250x) | `python scripts/soft_erosion_theory_vs_empirical.py` (reads the dense dir; see note 25 for the recorded run) | `soft_erosion_theory_vs_empirical/` | 25 |

## Initial erosion (T5 + T6)

| claim | command | outputs | note |
|---|---|---|---|
| no-fit erosion = hidden share, max abs error <= 0.008 across 6 widths x 6 inits (predicted span 0.15-0.45); "0.4378/0.4403" headline retired (note 37 §4) | `python scripts/actual_fa_initial_operator_moments.py --widths 16 24 32 48 64 96 --init-seeds 6 --feedback-samples 512 --torch-threads 8 --outdir outputs/actual_fa_initial_operator_moments` | `actual_fa_initial_operator_moments/` | 29, 42 |
| e0 exactly Gaussian; KS p 0.13-0.999; sampler = real FA backward, linear identity <= 8.9e-16 | `python scripts/actual_fa_initial_erosion_distribution.py --widths 16 32 64 128 --init-seeds 3 --feedback-samples 4096 --torch-threads 8 --outdir outputs/actual_fa_initial_erosion_distribution` | `actual_fa_initial_erosion_distribution/` (pre-fix snapshot kept in `*_pre_fix_backup/`) | 32, 37 |

## Finite-time chain (lazy validity -> drift -> estimator)

| claim | command | outputs | note |
|---|---|---|---|
| T=5 frozen-K(0) local exactness: corr 0.99947, MAE 0.00083; horizon table T=1..50 | recorded invocation in note 10 (fixed width 64, N in {64..320}, SGD lr 1e-3, 4 init x 8 feedback) | `downstream_capacity_fixed_width64_sgd_T5_N*/`, `fa_tangent_kernel_fixed_width64_sgd_T5_*` | 10 |
| oracle time-varying K(t) removes T=50 error: gap MAE 0.0277 -> 0.000273 | `python scripts/finite_time_kernel_diagnostic.py --width 64 --train-samples 128 --steps 50 --lr 1e-3 --init-seeds 2 --feedback-seeds 4` | `finite_time_kernel_probe_T50_N128_8runs/` | 13 |
| scalar early predictors fail across N (corr 0.124) | `python scripts/early_kernel_predictors.py ...` (recorded in note 14) | `early_directional_predictors_T50_width64_N*/` | 14 |
| estimator, 256 traj: velocity MAE 0.00189, corr 0.99885; fixed K(0) 10x worse; retangent upper bracket | `python scripts/compressed_operator_predictor.py --width 64 --hidden-layers 2 --train-samples <N> --target-steps 50 --early-steps 20 --lr 1e-3 --init-seeds 4 --feedback-seeds 8` for N in {64,96,128,160,192,224,256,320}, then `python scripts/plot_compressed_operator_results.py` | `compressed_operator_s20_256traj_T50_width64_N*/`, `*_plots/` | 15 |
| stress grid: corr 0.994-0.99989 across depth {1,2,3} x width {32,64,96} x horizon {25,50,100} | per-setting runs recorded in note 16, then `python scripts/summarize_operator_stress_grid.py` + `python scripts/plot_operator_overlap_grid.py` | `stress_depth*_*/`, `operator_stress_grid_summary/` | 16, 17 |
| first-order derivative extrapolation diverges (MAE 270) | `python scripts/fa_tangent_hierarchy_derivative_probe.py` (eps 0.05; recorded in note 31) | `fa_tangent_hierarchy_derivative_probe_eps005/` | 31 |

## Real data + generalization

| claim | command | outputs | note |
|---|---|---|---|
| MNIST e0: 16 configs, share 0.39-0.82, abs diff <= 0.0089 | `python scripts/real_data_validation.py --part a --torch-threads 16` | `real_data_validation_mnist/e0_mnist_*` | 38 |
| MNIST estimator: 96 traj, velocity MAE 0.00196 (3.9% rel), bias -0.0006, corr 0.911; fixed MAE 0.0061 | `python scripts/real_data_validation.py --part b --est-widths 128 256 --lr-safety 0.05 --torch-threads 16` | `real_data_validation_mnist/estimator_mnist_*` | 38 |
| kernel code self-test vs autograd (<= 5.3e-15) | `python scripts/real_data_validation.py --self-test` | stdout | 38 |
| teacher task: train gap 0.249->0.0069 soft; test gap sign flip (-0.120+/-0.013 at w=32) | `python scripts/downstream_capacity_sweep.py --task mlp --teacher-width 64 --teacher-hidden-layers 2 --normalize-targets --widths 8 12 16 24 32 48 64 96 --train-samples 256 --test-samples 2048 --probe-samples 32 --steps 8000 --lr 0.01 --optimizer sgd --init-seeds 3 --feedback-seeds 8 --data-seed 7 --skip-jacobian --plot --outdir outputs/teacher_test_gap_sgd_T8000` then `python scripts/plot_teacher_test_gap.py` | `teacher_test_gap_sgd_T8000/` | 39 |

## Focused-paper controls added 2026-07-21

| claim | command | outputs | note |
|---|---|---|---|
| FA and DFA exact initialization calibration through depth 6: 60 rows, max abs error 0.009164 | `python scripts/aaai_depth_experiments.py --part init --depths 1 2 3 4 6 --width 64 --train-samples 64 --init-seeds 6 --feedback-draws 256 --torch-threads 16 --outdir outputs/aaai_depth_experiments` | `aaai_depth_experiments/initialization_rows.csv` | 43 |
| FA finite-time depth x width grid: matrix-alignment proxy drops 18.06 orders while width-64 gap grows 0.0421 -> 0.3461; frozen MAE 0.06693; two-snapshot MAE 0.01043 / 0.01394 | `python scripts/aaai_depth_experiments.py --part finite --depths 1 2 3 4 6 --finite-widths 32 64 96 --train-samples 64 --finite-init-seeds 4 --finite-feedback-seeds 8 --lr 0.001 --horizon 50 --early-step 20 --torch-threads 16 --outdir outputs/aaai_depth_experiments`, then `--part summarize` | `aaai_depth_experiments/finite_time_*`, `mismatch_vs_cost_by_depth.*` | 43 |
| parameter-matched depth control around P=5376: widths 269/64/47/39/31; gap is nonmonotone and peaks at depth 4 | `python scripts/parameter_matched_depth_control.py --depths 1 2 3 4 6 --reference-depth 2 --reference-width 64 --train-samples 64 --init-seeds 4 --feedback-seeds 8 --lr 0.001 --horizon 50 --early-step 20 --torch-threads 16 --outdir outputs/parameter_matched_depth_control` | `parameter_matched_depth_control/` | 43 |
| initialization-rate compensation reduces but does not remove the gap (29-51% reduction); separate stability-confirmed tuning preserves a gap | `python scripts/learning_rate_compensation.py --depths 1 2 3 4 6 --width 64 --train-samples 128 --steps 200 --base-lr 0.001 --tune-init-seeds 4 --tune-feedback-seeds 4 --eval-init-seeds 6 --eval-feedback-seeds 8 --torch-threads 16 --outdir outputs/learning_rate_compensation` | `learning_rate_compensation/` | 43 |
| cross-entropy CNN initialization identity for FA and DFA: max abs error 0.008309, max standardized error 1.308 | `python scripts/cnn_initialization_validation.py --train-samples 128 --image-size 8 --channels 8 12 --init-seeds 4 --feedback-draws 2048 --torch-threads 8 --outdir outputs/cnn_initialization_validation` | `cnn_initialization_validation/` | 43 |
| two focused three-panel figures | `python scripts/plot_aaai_main_figures.py --outdir outputs/aaai_main_figures` | `aaai_main_figures/` | 43 |

## Figure -> file map (current best versions)

| paper figure (plan in note 41) | file |
|---|---|
| focused Figure 1: mismatch vs exact initial cost | `aaai_main_figures/figure1_mismatch_vs_initial_cost.{png,pdf}` |
| focused Figure 2: later cost and operator evolution | `aaai_main_figures/figure2_training_dynamics.{png,pdf}` |
| soft ramp + closed form + ramp law | `closed_form_soft_ramp/closed_form_vs_measured_ramp.png` |
| e0 moment calibration (synthetic) | `actual_fa_initial_operator_moments/predicted_vs_empirical_initial_erosion_mean.png` |
| e0 Gaussian panels | `actual_fa_initial_erosion_distribution/e0_distribution_theory_vs_empirical.png` |
| estimator scatter (synthetic 256 traj) | `compressed_operator_s20_256traj_T50_width64_plots/T50_s20_prediction_scatter.png` |
| estimator trajectories + band | `compressed_operator_s20_256traj_T50_width64_plots/T50_s20_velocity_theory_band_empirical_trajectories.png` |
| MNIST e0 calibration | `real_data_validation_mnist/e0_mnist_calibration.png` |
| MNIST estimator scatter | `real_data_validation_mnist/estimator_mnist_scatter.png` |
| teacher train vs test gap | `teacher_test_gap_sgd_T8000/teacher_train_vs_test_gap.png` |
| static beta (appendix) | `capacity_empirical_validation/` plots |
| stress grid (appendix) | `operator_stress_grid_summary/stress_grid_*` |

All paper figures will be re-rendered to AAAI column dimensions during the
writing pass (note 41, week 2); the files above are the data-correct sources.

## Not paper-grade (do not cite)

Everything else under `outputs/`, in particular: all `*smoke*`, all
`downstream_capacity_random_*` / `downstream_capacity_sweep*` Adam-era sweeps
(superseded by SGD runs; notes 05-07), `phase_transition_sgd_*` short-T probes
(superseded by the dense run), `compressed_operator_T50_*` and
`*_retangent_*` intermediate variants (subsumed by the s20 256-traj set +
stress grid), `trajectory_*` bridge-era runs (notes 02/08; historical), and
`fa_tangent_hierarchy_first_order_try/` (negative result recorded in note 31).