Pith Number

pith:RQQEJVNA

pith:2023:RQQEJVNAHNMMNVUWIJ3VCEOVOZ

not attested not anchored not stored refs pending

On the maximum number of edges in k-critical graphs

Cong Luo, Jie Ma, Tianchi Yang

arxiv:2301.01656 v1 · 2023-01-04 · 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{RQQEJVNAHNMMNVUWIJ3VCEOVOZ}

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	2026-07-05T05:30:39.322327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c2044d5a03b58c6d69642775111d576548226168b1eba771581a5637638b9af

Aliases

arxiv: 2301.01656 · arxiv_version: 2301.01656v1 · doi: 10.48550/arxiv.2301.01656 · pith_short_12: RQQEJVNAHNMM · pith_short_16: RQQEJVNAHNMMNVUW · pith_short_8: RQQEJVNA

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/RQQEJVNAHNMMNVUWIJ3VCEOVOZ \
  | 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: 8c2044d5a03b58c6d69642775111d576548226168b1eba771581a5637638b9af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2105ea6a3e0b4ae3618914ab401d766dc959cb391354668079c6cad22e81d27e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-01-04T15:01:40Z",
    "title_canon_sha256": "9dfae4328ba2a2df73b6fd9e923d03d894a7987f8a522f19da22444666c72205"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.01656",
    "kind": "arxiv",
    "version": 1
  }
}