Pith Number

pith:JF6WWPGM

pith:2012:JF6WWPGMWKIUSMVUPY3SSYMJOJ

not attested not anchored not stored refs pending

Phase Coexistence and Slow Mixing for the Hard-Core Model on Z^2

Antonio Blanca, Dana Randall, David Galvin, Prasad Tetali

arxiv:1211.6182 v1 · 2012-11-27 · math.CO · cs.DM · 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{JF6WWPGMWKIUSMVUPY3SSYMJOJ}

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	2026-05-18T01:00:20.939514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

497d6b3cccb2914932b47e3729618972643ce339716d4ad885081e9d5dd42cf3

Aliases

arxiv: 1211.6182 · arxiv_version: 1211.6182v1 · doi: 10.48550/arxiv.1211.6182 · pith_short_12: JF6WWPGMWKIU · pith_short_16: JF6WWPGMWKIUSMVU · pith_short_8: JF6WWPGM

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/JF6WWPGMWKIUSMVUPY3SSYMJOJ \
  | 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: 497d6b3cccb2914932b47e3729618972643ce339716d4ad885081e9d5dd42cf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8170302250abf76daf7c77fc1b8bdcd3174d959c155cb629c1c141449a822eac",
    "cross_cats_sorted": [
      "cs.DM",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-27T02:25:53Z",
    "title_canon_sha256": "79d8d21bbb4497f80b4802544b0fbc363a86164df8f55ed02ad34decebbbb05e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6182",
    "kind": "arxiv",
    "version": 1
  }
}