Pith Number

pith:7Y2WZP2Q

pith:2015:7Y2WZP2QCKP6A3IIIBEUMA2QK5

not attested not anchored not stored refs pending

A Note on Bipartite Subgraphs and Triangle-independent Sets

Honghai Xu

arxiv:1512.06202 v2 · 2015-12-19 · 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{7Y2WZP2QCKP6A3IIIBEUMA2QK5}

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	2026-05-18T01:04:31.040351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe356cbf50129fe06d084049460350577ec40b70069205b493de7e8335b455f1

Aliases

arxiv: 1512.06202 · arxiv_version: 1512.06202v2 · doi: 10.48550/arxiv.1512.06202 · pith_short_12: 7Y2WZP2QCKP6 · pith_short_16: 7Y2WZP2QCKP6A3II · pith_short_8: 7Y2WZP2Q

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/7Y2WZP2QCKP6A3IIIBEUMA2QK5 \
  | 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: fe356cbf50129fe06d084049460350577ec40b70069205b493de7e8335b455f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b257218b0318e08b8c791fb1eeaf952e61291dec0fc16442ea1a9c4b9737ce07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-19T07:45:53Z",
    "title_canon_sha256": "0deb2bc6d2df7fb2b2f5400f08718129412483978adf7f8bad72221bc2b96deb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06202",
    "kind": "arxiv",
    "version": 2
  }
}