Pith Number

pith:XNBK5XGA

pith:2009:XNBK5XGAA76NQJQ64AC66HUZ4O

not attested not anchored not stored refs pending

Exceptional singular Q-homology planes

Karol Palka

arxiv:0909.0772 v2 · 2009-09-04 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XNBK5XGAA76NQJQ64AC66HUZ4O}

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	2026-05-18T02:58:33.140021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb42aedcc007fcd8261ee005ef1e99e3b336a4e5fe3cdfb727fa1f897dff64fc

Aliases

arxiv: 0909.0772 · arxiv_version: 0909.0772v2 · doi: 10.48550/arxiv.0909.0772 · pith_short_12: XNBK5XGAA76N · pith_short_16: XNBK5XGAA76NQJQ6 · pith_short_8: XNBK5XGA

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/XNBK5XGAA76NQJQ64AC66HUZ4O \
  | 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: bb42aedcc007fcd8261ee005ef1e99e3b336a4e5fe3cdfb727fa1f897dff64fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36e6a17af9c6b0c34f9f567028128018a2870cf0e19670b037117f247060456e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-09-04T16:54:04Z",
    "title_canon_sha256": "ca611ac692a5130545b1dccf9cd4f68dd2f5f882120126b17310d40b8898b0a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0772",
    "kind": "arxiv",
    "version": 2
  }
}