Pith Number

pith:BQDPFBFT

pith:2020:BQDPFBFTKAVDCZXAC3FLHSSRKQ

not attested not anchored not stored refs pending

Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound

Ryunosuke Ozawa, Taiki Yamada, Yohei Sakurai

arxiv:2011.11418 v2 · 2020-11-20 · math.DG · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BQDPFBFTKAVDCZXAC3FLHSSRKQ}

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	2026-07-05T04:01:40.522126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c06f284b3502a3166e016cab3ca51540e2ef7e92690d66bca57182c837e3781

Aliases

arxiv: 2011.11418 · arxiv_version: 2011.11418v2 · doi: 10.48550/arxiv.2011.11418 · pith_short_12: BQDPFBFTKAVD · pith_short_16: BQDPFBFTKAVDCZXA · pith_short_8: BQDPFBFT

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/BQDPFBFTKAVDCZXAC3FLHSSRKQ \
  | 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: 0c06f284b3502a3166e016cab3ca51540e2ef7e92690d66bca57182c837e3781

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "321d4efd08f1e881503756a75cbd33b2a5ecd6407e65d3c4f80a25b971010dc9",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-11-20T01:09:49Z",
    "title_canon_sha256": "866493b6e8eee1b060aedef8f739f3c9c83c08859913d8e014ad18a732d26c1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.11418",
    "kind": "arxiv",
    "version": 2
  }
}