Pith Number

pith:JKO5VR77

pith:2019:JKO5VR77QDVESWOJTSG62KQTQF

not attested not anchored not stored refs pending

Positive scalar curvature on manifolds with odd order abelian fundamental groups

Bernhard Hanke

arxiv:1908.00944 v4 · 2019-08-02 · math.DG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JKO5VR77QDVESWOJTSG62KQTQF}

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	2026-07-05T02:29:08.141097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a9ddac7ff80ea4959c99c8ded2a13817f739c06031a3a5a844e48eaa237f2ec

Aliases

arxiv: 1908.00944 · arxiv_version: 1908.00944v4 · doi: 10.48550/arxiv.1908.00944 · pith_short_12: JKO5VR77QDVE · pith_short_16: JKO5VR77QDVESWOJ · pith_short_8: JKO5VR77

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/JKO5VR77QDVESWOJTSG62KQTQF \
  | 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: 4a9ddac7ff80ea4959c99c8ded2a13817f739c06031a3a5a844e48eaa237f2ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5d47e1c71ea5594544f98246a8b5603434bd54e0788b0695c680b790e7ff070",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-08-02T16:29:17Z",
    "title_canon_sha256": "d402491900c0e0668878012b8751a31cb30dcc94547daeeb625f70d6c291b612"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.00944",
    "kind": "arxiv",
    "version": 4
  }
}