Pith Number

pith:7QJCLJUC

pith:2013:7QJCLJUCAGERSMVDRVIMCVDZMZ

not attested not anchored not stored refs pending

Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions

Eric Vigoda, Juan C. Vera, Linji Yang

arxiv:1306.0431 v2 · 2013-06-03 · cs.DM · 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{7QJCLJUCAGERSMVDRVIMCVDZMZ}

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	2026-05-18T02:48:02.392475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc1225a68201891932a38d50c154796670de31fefed3dc623ac99b9cd96e7327

Aliases

arxiv: 1306.0431 · arxiv_version: 1306.0431v2 · doi: 10.48550/arxiv.1306.0431 · pith_short_12: 7QJCLJUCAGER · pith_short_16: 7QJCLJUCAGERSMVD · pith_short_8: 7QJCLJUC

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/7QJCLJUCAGERSMVDRVIMCVDZMZ \
  | 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: fc1225a68201891932a38d50c154796670de31fefed3dc623ac99b9cd96e7327

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fe14c9ff6d83ad39649f99108e833be7c70fe4b213208d1dc352e871c1dceb9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2013-06-03T14:26:50Z",
    "title_canon_sha256": "900a382f595d9d0b78ee5e4d05c539af98c3c0bb34c19d50c74bf018cb20a4ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0431",
    "kind": "arxiv",
    "version": 2
  }
}