Pith Number

pith:RENA2D3M

pith:2004:RENA2D3MN653YJTM2W7VXV22BI

not attested not anchored not stored refs pending

The range of the heat operator

Brian C. Hall

arxiv:math/0409308 v2 · 2004-09-17 · math.DG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RENA2D3MN653YJTM2W7VXV22BI}

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	2026-05-18T04:42:34.676038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

891a0d0f6c6fbbbc266cd5bf5bd75a0a07266d0c1da02b938e65b0256e489047

Aliases

arxiv: math/0409308 · arxiv_version: math/0409308v2 · doi: 10.48550/arxiv.math/0409308 · pith_short_12: RENA2D3MN653 · pith_short_16: RENA2D3MN653YJTM · pith_short_8: RENA2D3M

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/RENA2D3MN653YJTM2W7VXV22BI \
  | 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: 891a0d0f6c6fbbbc266cd5bf5bd75a0a07266d0c1da02b938e65b0256e489047

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6022113f464e51cea353c482124bd97198a906a4f726774e98057f70af7decd2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2004-09-17T17:44:39Z",
    "title_canon_sha256": "4db901985f8c8b417c2c2b18465ba04907101faebb5c9f03751a7fa0fc76cf35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409308",
    "kind": "arxiv",
    "version": 2
  }
}