Pith Number

pith:RDSQ667K

pith:2026:RDSQ667K7RQT5CLVHNLBKE7ADB

not attested not anchored not stored refs pending

Proofs of Two Conjectures of Alon on Subgraph Counts

Jiasheng Zeng, Peiru Kuang, Shuang Sun, Yan Wang

arxiv:2606.18321 v1 · 2026-06-16 · 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{RDSQ667K7RQT5CLVHNLBKE7ADB}

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	2026-06-19T16:10:57.888890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88e50f7beafc613e89753b561513e018598c0e94e3b0429cb1f32782c1f6d190

Aliases

arxiv: 2606.18321 · arxiv_version: 2606.18321v1 · doi: 10.48550/arxiv.2606.18321 · pith_short_12: RDSQ667K7RQT · pith_short_16: RDSQ667K7RQT5CLV · pith_short_8: RDSQ667K

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/RDSQ667K7RQT5CLVHNLBKE7ADB \
  | 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: 88e50f7beafc613e89753b561513e018598c0e94e3b0429cb1f32782c1f6d190

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8e98d6a48e1e9d64dc5dc5da6666fda75db63d300e087380ba9f98437b68c26",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-16T14:10:12Z",
    "title_canon_sha256": "5d030891f44a141a591eb9cc92a9983b713d8e18fb338cd6dc8033727194029c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18321",
    "kind": "arxiv",
    "version": 1
  }
}