Pith Number

pith:WZETJ5JV

pith:2025:WZETJ5JVWQQ3VCVEBJYZLPLC32

not attested not anchored not stored refs pending

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces

Xiang-Dong Li

arxiv:2505.03202 v1 · 2025-05-06 · math.DG · math.MG · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WZETJ5JVWQQ3VCVEBJYZLPLC32}

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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

1 paper in Pith

On weak formulations of (super) Ricci flows

Receipt and verification

First computed	2026-07-05T10:59:12.097085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b64934f535b421ba8aa40a7195bd62debf2e3de162f4e5fb126bf1d0a5c281b8

Aliases

arxiv: 2505.03202 · arxiv_version: 2505.03202v1 · doi: 10.48550/arxiv.2505.03202 · pith_short_12: WZETJ5JVWQQ3 · pith_short_16: WZETJ5JVWQQ3VCVE · pith_short_8: WZETJ5JV

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/WZETJ5JVWQQ3VCVEBJYZLPLC32 \
  | 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: b64934f535b421ba8aa40a7195bd62debf2e3de162f4e5fb126bf1d0a5c281b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83c7845300b12bf534e2e394bf23587cf14e995495f6032060bcd1348dded446",
    "cross_cats_sorted": [
      "math.MG",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-05-06T05:37:47Z",
    "title_canon_sha256": "0088cf26af3c068525f79129a329150a57ca963e4cbf0565ee6b0b5b7914228f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.03202",
    "kind": "arxiv",
    "version": 1
  }
}