Pith Number

pith:PBTENHLR

pith:2015:PBTENHLRWGZDWYQ25MZ4GWEVVM

not attested not anchored not stored refs pending

A fixed point theorem on noncompact manifolds

Hang Wang, Peter Hochs

arxiv:1512.07812 v4 · 2015-12-24 · math.KT · math.DG · math.OA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PBTENHLRWGZDWYQ25MZ4GWEVVM}

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	2026-05-18T00:19:31.253533Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7866469d71b1b23b621aeb33c35895ab14c7b326fddd3196036766a9ca7636be

Aliases

arxiv: 1512.07812 · arxiv_version: 1512.07812v4 · doi: 10.48550/arxiv.1512.07812 · pith_short_12: PBTENHLRWGZD · pith_short_16: PBTENHLRWGZDWYQ2 · pith_short_8: PBTENHLR

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/PBTENHLRWGZDWYQ25MZ4GWEVVM \
  | 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: 7866469d71b1b23b621aeb33c35895ab14c7b326fddd3196036766a9ca7636be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2238e611c71a42de82bbd8c91a5495fbfda4b7ac38aa725f8e9dfe09729aacbb",
    "cross_cats_sorted": [
      "math.DG",
      "math.OA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-12-24T13:45:39Z",
    "title_canon_sha256": "d9b380429c4925ee95046f72533943f3b8b08bb7b46260cb52add5c7012118a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07812",
    "kind": "arxiv",
    "version": 4
  }
}