Pith Number

pith:5WHDEXKO

pith:2022:5WHDEXKOK4V4FPCY4V2R3U6YGJ

not attested not anchored not stored refs pending

Poincar\'e constant on manifolds with ends

Alexander Grigor'yan, Laurent Saloff-Coste, Satoshi Ishiwata

arxiv:2205.06100 v3 · 2022-05-12 · math.DG · math.FA · 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{5WHDEXKOK4V4FPCY4V2R3U6YGJ}

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	2026-07-05T05:46:15.565166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed8e325d4e572bc2bc58e5751dd3d8326a5db06ee79acadacb03931169edc584

Aliases

arxiv: 2205.06100 · arxiv_version: 2205.06100v3 · doi: 10.48550/arxiv.2205.06100 · pith_short_12: 5WHDEXKOK4V4 · pith_short_16: 5WHDEXKOK4V4FPCY · pith_short_8: 5WHDEXKO

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/5WHDEXKOK4V4FPCY4V2R3U6YGJ \
  | 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: ed8e325d4e572bc2bc58e5751dd3d8326a5db06ee79acadacb03931169edc584

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "318f9cab84509ac6fb815348924fa78d04ef7b16fd50e8c0fbad6acd1a5d2baf",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2022-05-12T14:08:45Z",
    "title_canon_sha256": "19b5b7e7edfd437b3a62584f429d447be393f008ff60b5612f0c34fa3010deef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.06100",
    "kind": "arxiv",
    "version": 3
  }
}