Pith Number

pith:JGQYVJC3

pith:2013:JGQYVJC3Y2GG3IZA76GQEPDSWI

not attested not anchored not stored refs pending

The codegree threshold for 3-graphs with independent neighbourhoods

Edward Marchant, Emil Vaughan, Oleg Pikhurko, Victor Falgas-Ravry

arxiv:1307.0075 v3 · 2013-06-29 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JGQYVJC3Y2GG3IZA76GQEPDSWI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:55:43.418824Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49a18aa45bc68c6da320ff8d023c72b22c2ddb06ef93258ba71b4077019db902

Aliases

arxiv: 1307.0075 · arxiv_version: 1307.0075v3 · doi: 10.48550/arxiv.1307.0075 · pith_short_12: JGQYVJC3Y2GG · pith_short_16: JGQYVJC3Y2GG3IZA · pith_short_8: JGQYVJC3

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/JGQYVJC3Y2GG3IZA76GQEPDSWI \
  | 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: 49a18aa45bc68c6da320ff8d023c72b22c2ddb06ef93258ba71b4077019db902

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df58788263b011d9f5871f4c5ffba2ae6882c6efa483b0408f3d76733d9ce83c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-29T08:30:05Z",
    "title_canon_sha256": "08cebec65bb57324626a87000e9cf33dd376268ddf49c982728dbbb5089548ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0075",
    "kind": "arxiv",
    "version": 3
  }
}