Empirical Hessian Receipt Pass

Purpose

This implementation turns the Hessian-basis recompute from a heuristic routing table into measured curvature receipts.

It uses hessian-eigenthings as the matrix-free curvature backend. The project rule is:

do not materialize the full Hessian;
query directional pressure via HVP/matvec;
emit receipts for stiffness, flatness, saddle risk, and residual quality.

Added files

Path	Purpose
`5-Applications/tools-scripts/famm/hessian_receipt_runner.py`	CLI receipt runner around `hessian-eigenthings`.
`shared-data/schemas/famm_hessian_curvature_receipt.schema.json`	Receipt schema.
`shared-data/examples/famm_hessian_receipt_config.example.json`	Smoke-test config using a diagonal operator.

Route rule

The receipt runner maps measured curvature into route actions:

Curvature signal	Route action
negative eigenvalues	`probe_saddle_scar`
dominant eigenvalue above threshold	`protect_or_seal_stiff_invariant`
enough near-zero eigenvalues	`press_flat_gauge`
high trace	`seal_high_total_curvature`
otherwise	`continue_measured_probe`

Command

pip install hessian-eigenthings

python3 5-Applications/tools-scripts/famm/hessian_receipt_runner.py \
  --config shared-data/examples/famm_hessian_receipt_config.example.json \
  --out shared-data/hessian-receipts/example_receipt.json

Receipt role

The output is not a proof. It is a computational witness that can update:

proof priority
compression priority
scar-probe priority
closure priority

No-drift boundary

A Hessian receipt can route work, rank scars, and justify pressure gates. It cannot replace exact Lean/Fraction/OISC proof receipts.

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