Pith Number

pith:CRKDXZ2X

pith:2025:CRKDXZ2XSA6U3IWXI5JB2GRS3Q

not attested not anchored not stored refs pending

Level area of spin random fields: a chaos decomposition

Francesca Pistolato, Michele Stecconi

arxiv:2507.08550 v1 · 2025-07-11 · math.PR · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CRKDXZ2XSA6U3IWXI5JB2GRS3Q}

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	2026-07-05T11:35:41.875543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14543be757903d4da2d747521d1a32dc2ea8d1d69f22e8bd3b211eec05be20b1

Aliases

arxiv: 2507.08550 · arxiv_version: 2507.08550v1 · doi: 10.48550/arxiv.2507.08550 · pith_short_12: CRKDXZ2XSA6U · pith_short_16: CRKDXZ2XSA6U3IWX · pith_short_8: CRKDXZ2X

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/CRKDXZ2XSA6U3IWXI5JB2GRS3Q \
  | 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: 14543be757903d4da2d747521d1a32dc2ea8d1d69f22e8bd3b211eec05be20b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "961db83e61e060aa9110bcf71b145582336662da2bf3825e7940fbc455d0d454",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-11T12:55:36Z",
    "title_canon_sha256": "ac8227cf4ea28401f755f1cb01154456db20b10b13bc14c9fc76544f4912b6ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.08550",
    "kind": "arxiv",
    "version": 1
  }
}