Pith Number

pith:CI76NX65

pith:2004:CI76NX65QLO3KEDXF2M5M64MDR

not attested not anchored not stored refs pending

A note on the free energy of the coupled system in the Sherrington-Kirkpatrick model

Dmitry Panchenko

arxiv:math/0405359 v1 · 2004-05-18 · math.PR · cond-mat.dis-nn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CI76NX65QLO3KEDXF2M5M64MDR}

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	2026-05-18T04:08:42.913560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

123fe6dfdd82ddb510772e99d67b8c1c443ed3e0fa12366abcf69db2e92bdfc8

Aliases

arxiv: math/0405359 · arxiv_version: math/0405359v1 · doi: 10.48550/arxiv.math/0405359 · pith_short_12: CI76NX65QLO3 · pith_short_16: CI76NX65QLO3KEDX · pith_short_8: CI76NX65

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/CI76NX65QLO3KEDXF2M5M64MDR \
  | 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: 123fe6dfdd82ddb510772e99d67b8c1c443ed3e0fa12366abcf69db2e92bdfc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e77b65ac893c9bb3b3f8083e6e98b25fef63c732c9d5eaa270e99109432014da",
    "cross_cats_sorted": [
      "cond-mat.dis-nn"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-05-18T22:12:54Z",
    "title_canon_sha256": "6683d97043e8d3b34c1aa91a11998d2a687cd6109630549d610b36f43132a3e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0405359",
    "kind": "arxiv",
    "version": 1
  }
}