Pith Number

pith:BPBC3L3W

pith:2021:BPBC3L3WYX7HYXLKOUTKABAWBG

not attested not anchored not stored refs pending

Bipartite-ness under smooth conditions

Jie Ma, Sean Longbrake, Tao Jiang

arxiv:2109.01311 v4 · 2021-09-03 · 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{BPBC3L3WYX7HYXLKOUTKABAWBG}

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	2026-07-05T05:31:44.102242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bc22daf76c5fe7c5d6a7526a0041609b848160a6c3d2a242273a7c49ae1eb31

Aliases

arxiv: 2109.01311 · arxiv_version: 2109.01311v4 · doi: 10.48550/arxiv.2109.01311 · pith_short_12: BPBC3L3WYX7H · pith_short_16: BPBC3L3WYX7HYXLK · pith_short_8: BPBC3L3W

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/BPBC3L3WYX7HYXLKOUTKABAWBG \
  | 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: 0bc22daf76c5fe7c5d6a7526a0041609b848160a6c3d2a242273a7c49ae1eb31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2fcd4f0c7a9fa6a99ab108c0b97747ed6d63057743be98545922bf475973249",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-09-03T04:58:13Z",
    "title_canon_sha256": "842553ed0e656ada96ca6cdd9734b8b1349fa3bcb78a40165ae3d9fa56ff09c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.01311",
    "kind": "arxiv",
    "version": 4
  }
}