Governed materials prediction

Check whether a crystal is novel against a registry using an isometry-invariant fingerprint, then attach a PAC-Bayes certified risk bound — both emitting hash-chained Khipu receipts.
Headline number: 1 crystal → a deterministic PDD fingerprint + a McAllester bound (e.g. family intermetallics → risk ≤ 0.0772 at δ=0.05).

Materials-by-design needs two governed surfaces: is this structure new? and how much can I trust a stability prediction about it? The a11oy materials organ answers both — novelty via a Kurlin-style Pointwise Distance Distribution (PDD) fingerprint, and trust via a PAC-Bayes bound.

Honest scope. The fingerprint comparison is REAL (deterministic, isometry-invariant). The receipt chain is REAL (SHA3-256, tamper-evident). Signatures are DSSE_PLACEHOLDER (Sigstore not wired — honest). PDD injectivity is Conjecture 2 — ROADMAP, NOT proven (Lutar/Materials/PDDInjective.lean). The McAllester bound formula is proven on paper and the computation is exact, but the Lean proof is an open SORRY/ROADMAP (Lutar/Materials/PACBayesMaterials.lean) — not in the locked-8. Preset inputs are SAMPLE/MODELED. There is no /materials/predict route. Trust ceiling is never 100%.

Prerequisites

bash

python3 -m pip install httpx

Live base: https://a-11-oy.com. Two routes: POST /materials/novelty, POST /materials/certify.

Quickstart (live, verified)

Novelty — submit a crystal

python

import httpx
BASE = "https://a-11-oy.com"

crystal = {
    "a": 3.6, "b": 3.6, "c": 3.6, "alpha": 90, "beta": 90, "gamma": 90,
    "sites": [{"el": "Cu", "x": 0, "y": 0, "z": 0},
              {"el": "Au", "x": 0.5, "y": 0.5, "z": 0.5}],
}
r = httpx.post(f"{BASE}/api/a11oy/v1/materials/novelty", json=crystal, timeout=60).json()
print("novel:", r["novel"], "| registered_id:", r["registered_id"])
print("fingerprint:", r["fingerprint"])              # e.g. "31:0.0909;36:0.0682;..."
print("fingerprint_digest:", r["fingerprint_digest"])
print("invariant:", r["invariant"])                  # Kurlin-style PDD, isometry-invariant via G=LᵀL
print("receipt chain_head:", r["receipt"]["chain_head"], "depth", r["receipt"]["chain_depth"])

Certify — attach a PAC-Bayes risk bound

python

# Use a known family preset, OR supply explicit {empirical_risk, kl, n, delta}
r = httpx.post(f"{BASE}/api/a11oy/v1/materials/certify",
               json={"family": "intermetallics"}, timeout=60).json()
print("bound:", r["bound"])                          # => 0.0772... (normalized risk, [0,1])
print(r["certificate_text"])
print("proof_status:", r["proof_status"])
print("input_label:", r["inputs"]["input_label"])    # SAMPLE/MODELED — illustrative, NOT measured

The bound formula:

[ R(Q) \le \hat{R}(Q) + \sqrt{\frac{\mathrm{KL}(Q,|,P) + \ln!\frac{2\sqrt{n}}{\delta}}{2n}}. ]

Full walkthrough

Step 1 — The PDD fingerprint

Submit the unit cell (a,b,c,alpha,beta,gamma) and fractional sites. The organ computes the metric tensor G = LᵀL, then a sorted pairwise-distance histogram (Pointwise Distance Distribution). Because it is built from the metric tensor, it is isometry-invariant — a rotated/translated copy of the same crystal yields the same fingerprint.

Step 2 — Novelty verdict + registry

novel: true means no registry entry within the matching tolerance; the structure is registered with a mat-… id and a fingerprint_digest. nearest_match_id/distance are populated when a near-match exists.

Do not claim the fingerprint is a proof of distinctness. Injectivity (distinct crystals ⇒ distinct fingerprints) is Conjecture 2 — OPEN. Two distinct structures could in principle collide; the honest claim is "no match found in the registry," not "provably new."

Step 3 — Certify the trust

certify returns the McAllester (1999) PAC-Bayes bound. Supply explicit {empirical_risk, kl, n, delta} for your own evaluation, or a {family} preset (intermetallics, oxides, refractory_hea) for an illustrative SAMPLE/MODELED number. The bound computation is exact; the Lean proof is an open SORRY — the bound is a bound, not a Lean-certified guarantee.

Step 4 — Verify the receipt chain

Both routes return receipt envelopes (SZL.Materials.NoveltyCert.v1 / SZL.Materials.PACBayesCert.v1) with prev, digest, and chain_head. They form a SHA3-256 hash chain — recompute or cross-check against the lake ledger as in recipe 01.

Honest scope table

Claim	Status
PDD fingerprint comparison	REAL — deterministic, isometry-invariant
Receipt chain	REAL — SHA3-256, tamper-evident
Receipt signature	`DSSE_PLACEHOLDER` — Sigstore not wired (honest)
PDD injectivity	Conjecture 2 — ROADMAP, NOT proven
McAllester bound formula	PROVEN on paper (McAllester 1999, COLT)
McAllester bound computation	EXACT
McAllester Lean proof	SORRY/ROADMAP — not in locked-8
Preset inputs	SAMPLE/MODELED — illustrative, not measured

Cite this recipe

bibtex

@misc{szl_cookbook_governed_materials_2026,
  title        = {Governed materials prediction (SZL Cookbook recipe 18)},
  author       = {{SZL Holdings}},
  year         = {2026},
  howpublished = {\url{https://github.com/szl-holdings/szl-cookbook/blob/main/recipes/18-governed-materials-prediction.md}},
  note         = {PDD novelty (Conjecture 2, open) + McAllester PAC-Bayes (formula proven, Lean SORRY). Λ = Conjecture 1.}
}

References: McAllester 1999, COLT; D. Widdowson & V. Kurlin 2022, "Resolving the data ambiguity for periodic crystals," NeurIPS (Pointwise Distance Distribution); Redlich & Kister 1948.

Doctrine v11 LOCKED — 749/14/163 — kernel c7c0ba17 · Λ = Conjecture 1 · SLSA L1 (honest)

Governed materials prediction ​

Prerequisites ​

Quickstart (live, verified) ​

Novelty — submit a crystal ​

Certify — attach a PAC-Bayes risk bound ​

Full walkthrough ​

Step 1 — The PDD fingerprint ​

Step 2 — Novelty verdict + registry ​

Step 3 — Certify the trust ​

Step 4 — Verify the receipt chain ​

Honest scope table ​

See also ​

Cite this recipe ​