Pith Number

pith:ETKQWKE4

pith:2016:ETKQWKE4Z7YJHKATKKTU5FFUWI

not attested not anchored not stored refs pending

The $k$-proper index of graphs

Jinfeng Liu, Lin Chen, Xueliang Li

arxiv:1601.03503 v1 · 2016-01-14 · 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{ETKQWKE4Z7YJHKATKKTU5FFUWI}

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	2026-05-18T01:22:53.295447Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24d50b289ccff093a81352a74e94b4b23ab1a2ae19bd8c1d1b433e761bb4c784

Aliases

arxiv: 1601.03503 · arxiv_version: 1601.03503v1 · doi: 10.48550/arxiv.1601.03503 · pith_short_12: ETKQWKE4Z7YJ · pith_short_16: ETKQWKE4Z7YJHKAT · pith_short_8: ETKQWKE4

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/ETKQWKE4Z7YJHKATKKTU5FFUWI \
  | 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: 24d50b289ccff093a81352a74e94b4b23ab1a2ae19bd8c1d1b433e761bb4c784

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eedf4d73b43e4416bee2646b4fea09fcd0eca2849bc69667f6f697e76aa45fca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-14T06:44:04Z",
    "title_canon_sha256": "17a32efdb1be22cb6897841c832980d0304bc625c5617ef94b38731997bcf9a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03503",
    "kind": "arxiv",
    "version": 1
  }
}