Pith Number

pith:Q7SOYQJB

pith:2015:Q7SOYQJBMWATNU7R5RSTDQTAI4

not attested not anchored not stored refs pending

Complex unit gain bicyclic graphs with rank 2, 3 or 4

Ligong Wang, Peng Xiao, Yong Lu

arxiv:1511.07589 v1 · 2015-11-24 · 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{Q7SOYQJBMWATNU7R5RSTDQTAI4}

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	2026-05-18T01:26:04.321183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87e4ec4121658136d3f1ec6531c2604739ce97e871b1f50723ee545147ba8a02

Aliases

arxiv: 1511.07589 · arxiv_version: 1511.07589v1 · doi: 10.48550/arxiv.1511.07589 · pith_short_12: Q7SOYQJBMWAT · pith_short_16: Q7SOYQJBMWATNU7R · pith_short_8: Q7SOYQJB

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/Q7SOYQJBMWATNU7R5RSTDQTAI4 \
  | 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: 87e4ec4121658136d3f1ec6531c2604739ce97e871b1f50723ee545147ba8a02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fe57e6766b0477fd6c9e0af1c1f65144d65853ff47d6e16a2d5c95355edfd95",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-24T06:46:08Z",
    "title_canon_sha256": "b3785c2ba02542f9d958e3de33e1e74e63d3de640c23a093a431bb630ff68aa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07589",
    "kind": "arxiv",
    "version": 1
  }
}