Pith Number

pith:OKCQ5GKA

pith:2010:OKCQ5GKAZJ2YZYA3VUVSWTKYPQ

not attested not anchored not stored refs pending

The index of a transverse Dirac-type operator: the case of abelian Molino sheaf

Alexander Gorokhovsky, John Lott

arxiv:1005.0161 v4 · 2010-05-02 · 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{OKCQ5GKAZJ2YZYA3VUVSWTKYPQ}

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	2026-05-18T02:24:09.376826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72850e9940ca758ce01bad2b2b4d587c05d863b6fb750c7c0b3e3113a75d6641

Aliases

arxiv: 1005.0161 · arxiv_version: 1005.0161v4 · doi: 10.48550/arxiv.1005.0161 · pith_short_12: OKCQ5GKAZJ2Y · pith_short_16: OKCQ5GKAZJ2YZYA3 · pith_short_8: OKCQ5GKA

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/OKCQ5GKAZJ2YZYA3VUVSWTKYPQ \
  | 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: 72850e9940ca758ce01bad2b2b4d587c05d863b6fb750c7c0b3e3113a75d6641

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73d8912e32328214d4c6be4685acd25aeb682b358a178742ceb226d69672c170",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-05-02T19:52:30Z",
    "title_canon_sha256": "473495a198117f2daaf5f1d296aa7bb9bc7c2fb3347af097dec78bf4bbde691e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.0161",
    "kind": "arxiv",
    "version": 4
  }
}