Pith Number

pith:NU4VRYPT

pith:2015:NU4VRYPTUOWT3NALIE6T7Y4N5D

not attested not anchored not stored refs pending

On the Widom-Rowlinson Occupancy Fraction in Regular Graphs

Emma Cohen, Prasad Tetali, Will Perkins

arxiv:1512.06398 v2 · 2015-12-20 · math.CO · 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{NU4VRYPTUOWT3NALIE6T7Y4N5D}

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	2026-05-18T01:10:59.548645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d3958e1f3a3ad3db40b413d3fe38de8c4cd5b71941559e377e9d1314802134d

Aliases

arxiv: 1512.06398 · arxiv_version: 1512.06398v2 · doi: 10.48550/arxiv.1512.06398 · pith_short_12: NU4VRYPTUOWT · pith_short_16: NU4VRYPTUOWT3NAL · pith_short_8: NU4VRYPT

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/NU4VRYPTUOWT3NALIE6T7Y4N5D \
  | 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: 6d3958e1f3a3ad3db40b413d3fe38de8c4cd5b71941559e377e9d1314802134d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b081a782d4d56a987f7f0aa803aa66b1eb6276e54e87a90448c3e218235948c7",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-20T16:50:22Z",
    "title_canon_sha256": "217ec73ed39276acedb9a45ace9e01a69c1baa19b8cc4da9324f681f79698c91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06398",
    "kind": "arxiv",
    "version": 2
  }
}