Pith Number

pith:6NYIJR45

pith:2016:6NYIJR45FIWOT2Z6TF2QEGFJO3

not attested not anchored not stored refs pending

Phase Coexistence for the Hard-Core Model on ${\mathbb Z}^2$

Antonio Blanca, Dana Randall, David Galvin, Prasad Tetali, Yuxuan Chen

arxiv:1611.01115 v2 · 2016-11-03 · math.PR · cs.DM · math-ph · math.CO · 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{6NYIJR45FIWOT2Z6TF2QEGFJO3}

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	2026-05-18T00:19:42.584482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f37084c79d2a2ce9eb3e99750218a976c283374b0c4d44bd3e9f8a059a3a42eb

Aliases

arxiv: 1611.01115 · arxiv_version: 1611.01115v2 · doi: 10.48550/arxiv.1611.01115 · pith_short_12: 6NYIJR45FIWO · pith_short_16: 6NYIJR45FIWOT2Z6 · pith_short_8: 6NYIJR45

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/6NYIJR45FIWOT2Z6TF2QEGFJO3 \
  | 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: f37084c79d2a2ce9eb3e99750218a976c283374b0c4d44bd3e9f8a059a3a42eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1db834c538237408fa119572bb0857f242bb032bc5f8f720018e5a8abbb969f5",
    "cross_cats_sorted": [
      "cs.DM",
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-03T18:07:34Z",
    "title_canon_sha256": "0fcdd80b7a7363b346dd6a98509d595f0aacaa5c0cd8caa5dcd76e138c8c13fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01115",
    "kind": "arxiv",
    "version": 2
  }
}