Pith Number

pith:YXARJWFD

pith:2012:YXARJWFDPGR3AUBZUGX455Q7QZ

not attested not anchored not stored refs pending

Mantel's Theorem for random graphs

Bobby DeMarco, Jeff Kahn

arxiv:1206.1016 v1 · 2012-06-05 · math.PR · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YXARJWFDPGR3AUBZUGX455Q7QZ}

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	2026-05-18T03:54:15.527430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5c114d8a379a3b05039a1afcef61f8652672639c4fc268a8975dbfa24cafd11

Aliases

arxiv: 1206.1016 · arxiv_version: 1206.1016v1 · doi: 10.48550/arxiv.1206.1016 · pith_short_12: YXARJWFDPGR3 · pith_short_16: YXARJWFDPGR3AUBZ · pith_short_8: YXARJWFD

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/YXARJWFDPGR3AUBZUGX455Q7QZ \
  | 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: c5c114d8a379a3b05039a1afcef61f8652672639c4fc268a8975dbfa24cafd11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cff5ebf47b12aa0805249fee3efb2c5aadc665123cfe49c3be1c9b9a63a49f38",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-05T18:27:31Z",
    "title_canon_sha256": "ba03345988a9433290053d57fd484a35adba55df5d6ab6697f2ebd2d774296e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1016",
    "kind": "arxiv",
    "version": 1
  }
}