Pith Number

pith:ATP2T65K

pith:2026:ATP2T65KUUOZOQFAEAEWRTC6MA

not attested not anchored not stored refs pending

Average degrees of edge-$\Delta$-critical multigraphs

Guantao Chen, Shengze Wang, Yimo Su, Yuying Ma

arxiv:2606.12271 v1 · 2026-06-10 · 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{ATP2T65KUUOZOQFAEAEWRTC6MA}

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	2026-06-11T01:10:58.946685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04dfa9fbaaa51d9740a0200968cc5e60131c654a71f9cbaf567069c4b496d622

Aliases

arxiv: 2606.12271 · arxiv_version: 2606.12271v1 · doi: 10.48550/arxiv.2606.12271 · pith_short_12: ATP2T65KUUOZ · pith_short_16: ATP2T65KUUOZOQFA · pith_short_8: ATP2T65K

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/ATP2T65KUUOZOQFAEAEWRTC6MA \
  | 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: 04dfa9fbaaa51d9740a0200968cc5e60131c654a71f9cbaf567069c4b496d622

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "182f5b57fa18b56505bbba74df7d978486b3f6442458e819a21a542652b648a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-10T16:11:41Z",
    "title_canon_sha256": "7afea346844e703808933775d2c688258ca5ccf7aa904545131df52012358782"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12271",
    "kind": "arxiv",
    "version": 1
  }
}