Pith Number

pith:L5V6VVOV

pith:2015:L5V6VVOVEUJ6PND2GJFZ44NTBE

not attested not anchored not stored refs pending

Log-Sobolev, isoperimetry and transport inequalities on graphs

Liming Wu, Ran Wang, Yutao ma

arxiv:1505.04552 v1 · 2015-05-18 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5V6VVOVEUJ6PND2GJFZ44NTBE}

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	2026-05-18T02:07:25.161169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f6bead5d52513e7b47a324b9e71b30906a85356446a51e50555e3b8000b05b2

Aliases

arxiv: 1505.04552 · arxiv_version: 1505.04552v1 · doi: 10.48550/arxiv.1505.04552 · pith_short_12: L5V6VVOVEUJ6 · pith_short_16: L5V6VVOVEUJ6PND2 · pith_short_8: L5V6VVOV

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/L5V6VVOVEUJ6PND2GJFZ44NTBE \
  | 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: 5f6bead5d52513e7b47a324b9e71b30906a85356446a51e50555e3b8000b05b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11970025a2fce7e74c4d18472d1b29ee74d1a1229f255ce26e58461f529435da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-05-18T08:42:35Z",
    "title_canon_sha256": "ad626acdb055ef591c437a6bb6409ffcce01086b54e17bddff9a9a14b447ca45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04552",
    "kind": "arxiv",
    "version": 1
  }
}