Pith Number

pith:YWQCQTRG

pith:2011:YWQCQTRGIM2KCAQKQFJ2NKDU6O

not attested not anchored not stored refs pending

The logarithmic entropy formula for the linear heat equation on Riemannian manifolds

Jia-Yong Wu

arxiv:1109.0136 v4 · 2011-09-01 · 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{YWQCQTRGIM2KCAQKQFJ2NKDU6O}

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	2026-05-18T03:56:22.522579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5a0284e264334a1020a8153a6a874f397aaf54a95f472f605f53b6f7f2ea345

Aliases

arxiv: 1109.0136 · arxiv_version: 1109.0136v4 · doi: 10.48550/arxiv.1109.0136 · pith_short_12: YWQCQTRGIM2K · pith_short_16: YWQCQTRGIM2KCAQK · pith_short_8: YWQCQTRG

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/YWQCQTRGIM2KCAQKQFJ2NKDU6O \
  | 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: c5a0284e264334a1020a8153a6a874f397aaf54a95f472f605f53b6f7f2ea345

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35b07b98cd34b5a3291f1a2fd71bb83b6a2bc431ed70124c635196ea132a5ee6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-09-01T09:22:20Z",
    "title_canon_sha256": "3f1824741de6630aa42f1c39e1adfd49d5d9e565146942031fa5b940c5dbaf01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0136",
    "kind": "arxiv",
    "version": 4
  }
}