Pith Number

pith:ECMZYI3Z

pith:2023:ECMZYI3ZWFYZHDG63Y7MYFMHTU

not attested not anchored not stored refs pending

Clique Supersaturation

Benjamin Gunby, Bhargav Narayanan, Quentin Dubroff, Sam Spiro

arxiv:2312.08265 v1 · 2023-12-13 · 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{ECMZYI3ZWFYZHDG63Y7MYFMHTU}

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.

Cited by

1 paper in Pith

Induced rational exponents and bipartite subgraphs in $K_{s, s}$-free graphs

Receipt and verification

First computed	2026-07-05T07:23:43.671724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20999c2379b171938cdede3ecc15879d29d7eec94de1cf1a7aea654382a62f12

Aliases

arxiv: 2312.08265 · arxiv_version: 2312.08265v1 · doi: 10.48550/arxiv.2312.08265 · pith_short_12: ECMZYI3ZWFYZ · pith_short_16: ECMZYI3ZWFYZHDG6 · pith_short_8: ECMZYI3Z

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/ECMZYI3ZWFYZHDG63Y7MYFMHTU \
  | 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: 20999c2379b171938cdede3ecc15879d29d7eec94de1cf1a7aea654382a62f12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c166aa7a619df36efdf022db96d9cb65e71083aaa5cd2a380383e4044538159",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-12-13T16:24:56Z",
    "title_canon_sha256": "5df65d1a8b5a7f0297eda4f2fd0c6808a93abedd5c5bb6f566d68b0aa3d4fb74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.08265",
    "kind": "arxiv",
    "version": 1
  }
}