Pith Number

pith:ITKIF73B

pith:2012:ITKIF73BUUQGRVK6YA57HG2TR4

not attested not anchored not stored refs pending

A cohomological formula for the Atiyah-Patodi-Singer index on manifolds with boundary

Bertrand Monthubert (IMT), Jean-Marie Lescure, Paulo Carrillo Rouse (IMT)

arxiv:1207.3514 v3 · 2012-07-15 · math.OA · math.DG · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ITKIF73BUUQGRVK6YA57HG2TR4}

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	2026-05-18T03:04:50.040267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44d482ff61a52068d55ec03bf39b538f25ec606925c373011b5105e6df34eb99

Aliases

arxiv: 1207.3514 · arxiv_version: 1207.3514v3 · doi: 10.48550/arxiv.1207.3514 · pith_short_12: ITKIF73BUUQG · pith_short_16: ITKIF73BUUQGRVK6 · pith_short_8: ITKIF73B

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/ITKIF73BUUQGRVK6YA57HG2TR4 \
  | 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: 44d482ff61a52068d55ec03bf39b538f25ec606925c373011b5105e6df34eb99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43aa4efa23a6b6dfcfa94ff0d9b90d345ab2cf8c37dc703a656898c49cc8db07",
    "cross_cats_sorted": [
      "math.DG",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-07-15T14:52:51Z",
    "title_canon_sha256": "e868a6f212352bb39eae21851f5e072dc5f1e54003a4f3aaaa41d98bf53bb657"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3514",
    "kind": "arxiv",
    "version": 3
  }
}