Pith Number

pith:BKP5LLWI

pith:2013:BKP5LLWIMPH5R5YMDDGXE4O6DO

not attested not anchored not stored refs pending

Sharp Hamilton's Laplacian estimate for the heat kernel on complete manifolds

Jia-Yong Wu

arxiv:1305.0618 v1 · 2013-05-03 · 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{BKP5LLWIMPH5R5YMDDGXE4O6DO}

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	2026-05-18T03:26:33.191220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a9fd5aec863cfd8f70c18cd7271de1bb48af7d2812ffcafeae95d8153a9e225

Aliases

arxiv: 1305.0618 · arxiv_version: 1305.0618v1 · doi: 10.48550/arxiv.1305.0618 · pith_short_12: BKP5LLWIMPH5 · pith_short_16: BKP5LLWIMPH5R5YM · pith_short_8: BKP5LLWI

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/BKP5LLWIMPH5R5YMDDGXE4O6DO \
  | 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: 0a9fd5aec863cfd8f70c18cd7271de1bb48af7d2812ffcafeae95d8153a9e225

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57979eda63c377b8d418499acdc3f98efe6ba944ade6d13fa0f730d5fdc2eda5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-05-03T03:48:39Z",
    "title_canon_sha256": "8292e40e1177ff72af0724cbe84314d401a767c774de7798ef18d4e4c36166a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0618",
    "kind": "arxiv",
    "version": 1
  }
}