Pith Number

pith:GCLROKDR

pith:2012:GCLROKDRHJWGBC7B735G4NHEHT

not attested not anchored not stored refs pending

A relative higher index theorem, diffeomorphisms and positive scalar curvature

Guoliang Yu, Zhizhang Xie

arxiv:1204.3664 v4 · 2012-04-16 · math.KT · math.DG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GCLROKDRHJWGBC7B735G4NHEHT}

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	2026-05-18T03:47:52.669832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30971728713a6c608be1fefa6e34e43cd48d48cb0ce309f3792d61ad8e22d942

Aliases

arxiv: 1204.3664 · arxiv_version: 1204.3664v4 · doi: 10.48550/arxiv.1204.3664 · pith_short_12: GCLROKDRHJWG · pith_short_16: GCLROKDRHJWGBC7B · pith_short_8: GCLROKDR

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/GCLROKDRHJWGBC7B735G4NHEHT \
  | 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: 30971728713a6c608be1fefa6e34e43cd48d48cb0ce309f3792d61ad8e22d942

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d63d794295b9fccd8a65f54b04f415f392fc7341e758b58042ffa31e6efdee3f",
    "cross_cats_sorted": [
      "math.DG",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-04-16T22:02:15Z",
    "title_canon_sha256": "b19976f4745bdad439f2eb526206e76b9905cdc0bc4c6913f0b82595a34cbf8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3664",
    "kind": "arxiv",
    "version": 4
  }
}