Scope
Reproduces the 97x batched-Jacobi gain, the four-model TwoNN intrinsic-dimension survey, the curvature-warp 0/12 cross-model null, and the HJB pre-training feasibility result.
Hardware target
- Local: 8 GB CUDA GPU is sufficient for the Jacobi micro-benchmark and the 8B TwoNN survey.
- Mistral-Nemo-12B with full axiom-samples 512: g6e.xlarge L40S (24 GB resident), about 60 minutes.
Prerequisites
- Same toolchain as Paper A.
- For the cross-model TwoNN: model files for SmolLM2-135M, Gemma-4-E2B and Phi-3.5-mini in addition to Llama-3.1-8B.
1. Batched-Jacobi micro-benchmark
.\build_host\geodessical.exe $model `
--axex-jacobi --axex-jacobi-batch 32 -p "warm" -n 8 --temp 0
Expected: a 97x speedup over the per-element Jacobi reference.
2. TwoNN intrinsic-dimension survey
python scripts\axiom_survey.py `
--models smollm2-135m,gemma-4-e2b,phi-3.5-mini,llama-3.1-8b `
--axiom-samples 256 --axiom-probe 1024
Expected k_int at 95 percent variance: 17 (SmolLM2), 25 (Gemma-4), 11 (Phi-3.5), about 1682 for Llama-3.1-8B (note the 8B value is attention-only; FFN sits much higher).
3. Curvature warp cross-model null
python scripts\curvature_warp_eval.py
Expected: 0 of 12 cross-model arms exceed the equivariance gate. This is the negative result reported in Paper D and it is the correct outcome.
4. HJB pre-training feasibility
python scripts\hjb_residual_pretrain.py --steps 200
Expected: HJB residual decreases monotonically and converges within
the 200-step budget. Outputs land in
docs/figures/paper-d/hjb_feasibility/.
Outputs
docs/figures/paper-d/jacobi_speedup.csvdocs/figures/paper-d/twonn_survey.jsondocs/figures/paper-d/curvature_warp_results.csvdocs/figures/paper-d/hjb_feasibility/
Tolerances
- Jacobi gain: plus or minus 5x. The 97x figure is the median over 8 reps.
- TwoNN k_int: integer-valued, deterministic for a given seed.
- Curvature warp: 0 of 12 should be reproduced exactly. Any positive arm indicates a regression.