Pith Number

pith:ZQVE47AX

pith:2024:ZQVE47AXFFOM664Y2JXVDSCNLJ

not attested not anchored not stored refs pending

Extension on spectral extrema of gem-free graph with given size

Ligong Wang, Yuxiang Liu

arxiv:2411.19110 v1 · 2024-11-28 · 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{ZQVE47AXFFOM664Y2JXVDSCNLJ}

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	2026-07-05T09:41:57.291827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc2a4e7c17295ccf7b98d26f51c84d5a717a4e258a6896ff5d15cb57841f20d3

Aliases

arxiv: 2411.19110 · arxiv_version: 2411.19110v1 · doi: 10.48550/arxiv.2411.19110 · pith_short_12: ZQVE47AXFFOM · pith_short_16: ZQVE47AXFFOM664Y · pith_short_8: ZQVE47AX

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/ZQVE47AXFFOM664Y2JXVDSCNLJ \
  | 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: cc2a4e7c17295ccf7b98d26f51c84d5a717a4e258a6896ff5d15cb57841f20d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d93ef48766611985d2e16484128aa130ca83a23c25bc83ba7d1904785884957",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-11-28T12:57:37Z",
    "title_canon_sha256": "3f7691f1e05d4d5e65a4e4263765af57fb56d5eaea43d5dd9a91b3d2e22116d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.19110",
    "kind": "arxiv",
    "version": 1
  }
}