Pith Number

pith:VPUSKUBD

pith:2025:VPUSKUBDEEZ7MQIFUBHAVHNNZH

not attested not anchored not stored refs pending

A topological approach to the Cahn-Hilliard equation and hyperuniform fields

Abel H. G. Milor, Axel Voigt, Heather A. Harrington, Marco Salvalaglio, Otto Sumray

arxiv:2509.05339 v1 · 2025-09-01 · cond-mat.soft · cond-mat.dis-nn · cond-mat.stat-mech · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPUSKUBDEEZ7MQIFUBHAVHNNZH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T12:05:45.364085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abe92550232133f64105a04e0a9dadc9f351211a5211e0890e70228d15e3067c

Aliases

arxiv: 2509.05339 · arxiv_version: 2509.05339v1 · doi: 10.48550/arxiv.2509.05339 · pith_short_12: VPUSKUBDEEZ7 · pith_short_16: VPUSKUBDEEZ7MQIF · pith_short_8: VPUSKUBD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VPUSKUBDEEZ7MQIFUBHAVHNNZH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: abe92550232133f64105a04e0a9dadc9f351211a5211e0890e70228d15e3067c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc915bb4a58b76a25926a02012b2f2e80e0085929519b48384e0fdd550c5a33d",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cond-mat.stat-mech",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.soft",
    "submitted_at": "2025-09-01T14:42:29Z",
    "title_canon_sha256": "e905579d3357537d2672894dd7beb2a07bff71e646f216cb70b73000d1e8628c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05339",
    "kind": "arxiv",
    "version": 1
  }
}