Pith Number

pith:I5AURNMI

pith:2012:I5AURNMIBBTTPF2Z7BWUWF7ND7

not attested not anchored not stored refs pending

Critical two-point functions for long-range statistical-mechanical models in high dimensions

Akira Sakai, Lung-Chi Chen

arxiv:1204.1180 v4 · 2012-04-05 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I5AURNMIBBTTPF2Z7BWUWF7ND7}

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	2026-05-18T02:22:30.312859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

474148b5880867379759f86d4b17ed1ffd169580e87faf9bdd1ba1c99aea8942

Aliases

arxiv: 1204.1180 · arxiv_version: 1204.1180v4 · doi: 10.48550/arxiv.1204.1180 · pith_short_12: I5AURNMIBBTT · pith_short_16: I5AURNMIBBTTPF2Z · pith_short_8: I5AURNMI

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/I5AURNMIBBTTPF2Z7BWUWF7ND7 \
  | 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: 474148b5880867379759f86d4b17ed1ffd169580e87faf9bdd1ba1c99aea8942

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e4734e74890eeee7b58805bf917b38130ea3cd9c1c08ac98c30d47226bf5fca",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-04-05T11:08:24Z",
    "title_canon_sha256": "5f15681409c90d6d41ff8b2eb22f59c28f603402bf759fc59b04629dc4fd4de5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1180",
    "kind": "arxiv",
    "version": 4
  }
}