Pith Number

pith:OHFQY6SE

pith:2013:OHFQY6SETMLUSFQ5DROI7UM6DV

not attested not anchored not stored refs pending

Li-Yau inequality on graphs

Dan Mangoubi, Frank Bauer, Gabor Lippner, Paul Horn, Shing-Tung Yau, Yong Lin

arxiv:1306.2561 v2 · 2013-06-11 · math.AP · 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{OHFQY6SETMLUSFQ5DROI7UM6DV}

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	2026-05-18T01:25:39.979743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71cb0c7a449b1749161d1c5c8fd19e1d42747d929aa50fcd4ff208827824a5a6

Aliases

arxiv: 1306.2561 · arxiv_version: 1306.2561v2 · doi: 10.48550/arxiv.1306.2561 · pith_short_12: OHFQY6SETMLU · pith_short_16: OHFQY6SETMLUSFQ5 · pith_short_8: OHFQY6SE

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/OHFQY6SETMLUSFQ5DROI7UM6DV \
  | 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: 71cb0c7a449b1749161d1c5c8fd19e1d42747d929aa50fcd4ff208827824a5a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "defb842c538f35b2116f8e8ce8b51553ca9dcd56ae3d4eedc67ff86d87a94668",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-11T15:49:24Z",
    "title_canon_sha256": "a1005cfab4190663c0ee06d698888ee2109d6f6db049f18b98cf2e34aed5606d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2561",
    "kind": "arxiv",
    "version": 2
  }
}