Pith Number

pith:M6X5WQRT

pith:2003:M6X5WQRTAYTUV5N6KB25FULBNN

not attested not anchored not stored refs pending

Heat kernels and the index theorems on even and odd dimensional manifolds

Weiping Zhang

arxiv:math/0304269 v1 · 2003-04-18 · math.DG · 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{M6X5WQRTAYTUV5N6KB25FULBNN}

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	2026-05-18T01:05:28.960550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67afdb423306274af5be5075d2d1616b5e0b490078f22a45eb62b7c03029f2f5

Aliases

arxiv: math/0304269 · arxiv_version: math/0304269v1 · doi: 10.48550/arxiv.math/0304269 · pith_short_12: M6X5WQRTAYTU · pith_short_16: M6X5WQRTAYTUV5N6 · pith_short_8: M6X5WQRT

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/M6X5WQRTAYTUV5N6KB25FULBNN \
  | 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: 67afdb423306274af5be5075d2d1616b5e0b490078f22a45eb62b7c03029f2f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "540d6fcdefef12ab3a881e4dbe2107e0b99950713813fab6c9deeb0900daadc9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2003-04-18T19:17:46Z",
    "title_canon_sha256": "48ffe48dbb2d001a79ba1353a3f25fd6b4aa1e03be0a8c2880333e1da203a581"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0304269",
    "kind": "arxiv",
    "version": 1
  }
}