Pith Number

pith:4MB4Q6KB

pith:2007:4MB4Q6KBCMBBLLFJVUTMLUYV3U

not attested not anchored not stored refs pending

Traces of heat operators on Riemannian foliations

Ken Richardson

arxiv:0710.1324 v2 · 2007-10-05 · 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{4MB4Q6KBCMBBLLFJVUTMLUYV3U}

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	2026-05-18T04:25:02.188929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e303c87941130215aca9ad26c5d315dd3db1753fc8a6d9102bab1f8736baa011

Aliases

arxiv: 0710.1324 · arxiv_version: 0710.1324v2 · doi: 10.48550/arxiv.0710.1324 · pith_short_12: 4MB4Q6KBCMBB · pith_short_16: 4MB4Q6KBCMBBLLFJ · pith_short_8: 4MB4Q6KB

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/4MB4Q6KBCMBBLLFJVUTMLUYV3U \
  | 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: e303c87941130215aca9ad26c5d315dd3db1753fc8a6d9102bab1f8736baa011

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e3c5416e35e428a9314f144277cbd9926f8cd24162b4024c2517b5fe2323356",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2007-10-05T22:25:02Z",
    "title_canon_sha256": "8ff20ec252b63bc104e736fa7d67ba3f77392d8221b298cb2142b737e6c4816e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.1324",
    "kind": "arxiv",
    "version": 2
  }
}