Pith Number

pith:QAAC5D54

pith:2016:QAAC5D54A7OBRLI375VSFWHFOQ

not attested not anchored not stored refs pending

On-diagonal lower estimate of heat kernel on graphs

Yiting Wu, Yong Lin

arxiv:1612.08773 v1 · 2016-12-27 · 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{QAAC5D54A7OBRLI375VSFWHFOQ}

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	2026-05-18T00:53:47.191780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80002e8fbc07dc18ad1bff6b22d8e5740eb677b11cb38d7abd0f0ff60d98f992

Aliases

arxiv: 1612.08773 · arxiv_version: 1612.08773v1 · doi: 10.48550/arxiv.1612.08773 · pith_short_12: QAAC5D54A7OB · pith_short_16: QAAC5D54A7OBRLI3 · pith_short_8: QAAC5D54

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/QAAC5D54A7OBRLI375VSFWHFOQ \
  | 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: 80002e8fbc07dc18ad1bff6b22d8e5740eb677b11cb38d7abd0f0ff60d98f992

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f4dc71061461c763582d63bcc77680a92539d2cc969042767d1a8bbc96d731c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-27T23:56:31Z",
    "title_canon_sha256": "7bcc7a154e84fdefc1f8f0fd7d18f648a932e844d594fb52877345a85a185d5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08773",
    "kind": "arxiv",
    "version": 1
  }
}