Pith Number

pith:BGYTZYAF

pith:2007:BGYTZYAFQ2BSGK7YY44P6D7CPL

not attested not anchored not stored refs pending

Hamilton's gradient estimate for the heat kernel on complete manifolds

Brett Kotschwar

arxiv:math/0701335 v1 · 2007-01-12 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BGYTZYAFQ2BSGK7YY44P6D7CPL}

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.

Cited by

1 paper in Pith

Heat kernel geometry and Gromov's volume growth conjecture

Receipt and verification

First computed	2026-07-04T14:58:42.130249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09b13ce0058683232bf8c738ff0fe27acfd6922c5acf69f3886afb6f4819efe4

Aliases

arxiv: math/0701335 · arxiv_version: math/0701335v1 · doi: 10.48550/arxiv.math/0701335 · pith_short_12: BGYTZYAFQ2BS · pith_short_16: BGYTZYAFQ2BSGK7Y · pith_short_8: BGYTZYAF

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/BGYTZYAFQ2BSGK7YY44P6D7CPL \
  | 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: 09b13ce0058683232bf8c738ff0fe27acfd6922c5acf69f3886afb6f4819efe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "552810b4d6645bab61f028a89384dc415b5efb46854a6882b63c84c7aef1659f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-01-12T00:03:14Z",
    "title_canon_sha256": "fc4dec6cfb513231debb92af4aa2f4054128215fffc4e51d69b9be7794e22e22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701335",
    "kind": "arxiv",
    "version": 1
  }
}