Pith Number

pith:D6EU5F7A

pith:2003:D6EU5F7AP776ACWJTQAC4UZHPZ

not attested not anchored not stored refs pending

The entropy formula for linear heat equation

Lei Ni

arxiv:math/0306147 v2 · 2003-06-09 · 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{D6EU5F7AP776ACWJTQAC4UZHPZ}

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	2026-07-04T14:37:23.476637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f894e97e07fffe00ac99c002e53277e418262e553c780dcec8db04bc57843a0

Aliases

arxiv: math/0306147 · arxiv_version: math/0306147v2 · doi: 10.48550/arxiv.math/0306147 · pith_short_12: D6EU5F7AP776 · pith_short_16: D6EU5F7AP776ACWJ · pith_short_8: D6EU5F7A

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/D6EU5F7AP776ACWJTQAC4UZHPZ \
  | 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: 1f894e97e07fffe00ac99c002e53277e418262e553c780dcec8db04bc57843a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9b480dd4b0b999b5a9cccf42c7d3f710c628613ff7730cd6da13e94f997d25e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2003-06-09T17:38:24Z",
    "title_canon_sha256": "cbab4b40b871b733fe75ea84aad23458a0e4b8da50fed236af4bd22eca5d7766"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306147",
    "kind": "arxiv",
    "version": 2
  }
}