Pith Number

pith:63IOBN7Y

pith:2011:63IOBN7YTMVQOB2CHEVLNDMXON

not attested not anchored not stored refs pending

On the Perelman's reduced entropy and Ricci flat manifolds with maximal volume growth

Anqiang Zhu, Liang Cheng

arxiv:1111.4013 v2 · 2011-11-17 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{63IOBN7YTMVQOB2CHEVLNDMXON}

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	2026-05-18T03:57:14.119061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6d0e0b7f89b2b070742392ab68d9773497ee4e7fa01b8b02a72127a73d34197

Aliases

arxiv: 1111.4013 · arxiv_version: 1111.4013v2 · doi: 10.48550/arxiv.1111.4013 · pith_short_12: 63IOBN7YTMVQ · pith_short_16: 63IOBN7YTMVQOB2C · pith_short_8: 63IOBN7Y

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/63IOBN7YTMVQOB2CHEVLNDMXON \
  | 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: f6d0e0b7f89b2b070742392ab68d9773497ee4e7fa01b8b02a72127a73d34197

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97f5294cf8e9d8d3fd5f35d4b11d9328caf0187b00067ea5cc950e2e97d40c19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-17T02:51:45Z",
    "title_canon_sha256": "613b60a5e5084aa8892ce146bbb11946f319659bce6ac73e91a1db6457e2e13e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4013",
    "kind": "arxiv",
    "version": 2
  }
}