Pith Number

pith:N73ZQ2XW

pith:2013:N73ZQ2XWOTUUHZFQMLKQVL3YWK

not attested not anchored not stored refs pending

The free energy in a multi-species Sherrington-Kirkpatrick model

Dmitry Panchenko

arxiv:1310.6679 v2 · 2013-10-24 · math.PR · math-ph · 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{N73ZQ2XWOTUUHZFQMLKQVL3YWK}

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	2026-05-18T01:23:59.022074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ff7986af674e943e4b062d50aaf78b2998bea34b22817f926e6546731b7aad4

Aliases

arxiv: 1310.6679 · arxiv_version: 1310.6679v2 · doi: 10.48550/arxiv.1310.6679 · pith_short_12: N73ZQ2XWOTUU · pith_short_16: N73ZQ2XWOTUUHZFQ · pith_short_8: N73ZQ2XW

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/N73ZQ2XWOTUUHZFQMLKQVL3YWK \
  | 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: 6ff7986af674e943e4b062d50aaf78b2998bea34b22817f926e6546731b7aad4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2faa12d378d93587e4afbdca423c7f572aa957a0cbf03791d749312ac309f29",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-24T17:26:01Z",
    "title_canon_sha256": "d3409f8a5238bd9c098110eb1a445bc0d3ce3a94e2c25a1749789746492f2bcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6679",
    "kind": "arxiv",
    "version": 2
  }
}