Pith Number

pith:G76OY4X5

pith:2002:G76OY4X5ETHGZ4QYPEKUJH5XBN

not attested not anchored not stored refs pending

The entropy formula for the Ricci flow and its geometric applications

Grisha Perelman

arxiv:math/0211159 v1 · 2002-11-11 · math.DG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G76OY4X5ETHGZ4QYPEKUJH5XBN}

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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.

Cited by

54 papers in Pith

Uncountably many non-rotationally symmetric type II ancient Yamabe flows on the sphere

A Levi-type decomposition on two-step solvable Lie algebras with a complex structure

Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three

Ricci solitons as critical points of quadratic curvature functionals

The Ollivier Ricci flow with prescribed curvature on infinite graphs

Receipt and verification

First computed	2026-07-04T14:36:43.218425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37fcec72fd24ce6cf2187915449fb70b57679b5af420f0c45479bac62f9279e8

Aliases

arxiv: math/0211159 · arxiv_version: math/0211159v1 · doi: 10.48550/arxiv.math/0211159 · pith_short_12: G76OY4X5ETHG · pith_short_16: G76OY4X5ETHGZ4QY · pith_short_8: G76OY4X5

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/G76OY4X5ETHGZ4QYPEKUJH5XBN \
  | 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: 37fcec72fd24ce6cf2187915449fb70b57679b5af420f0c45479bac62f9279e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91a07d077dfb8acd36050936eda9ea990baa027d152b796ddfdc5e32851c398d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2002-11-11T16:11:49Z",
    "title_canon_sha256": "cc8c7de9ebe9263de812604687ea3bd4629cf244335b6d5f81576a16553fdc76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0211159",
    "kind": "arxiv",
    "version": 1
  }
}