Pith Number

pith:PVXEJ2IX

pith:2015:PVXEJ2IXYW4IDPZE5LL47U323F

not attested not anchored not stored refs pending

Lower bounds for regular genus and gem-complexity of PL 4-manifolds

Biplab Basak, Maria Rita Casali

arxiv:1504.00771 v2 · 2015-04-03 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PVXEJ2IXYW4IDPZE5LL47U323F}

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	2026-05-18T00:40:52.034337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d6e44e917c5b881bf24ead7cfd37ad96138f098bfeb5025549f0f099a130290

Aliases

arxiv: 1504.00771 · arxiv_version: 1504.00771v2 · doi: 10.48550/arxiv.1504.00771 · pith_short_12: PVXEJ2IXYW4I · pith_short_16: PVXEJ2IXYW4IDPZE · pith_short_8: PVXEJ2IX

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/PVXEJ2IXYW4IDPZE5LL47U323F \
  | 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: 7d6e44e917c5b881bf24ead7cfd37ad96138f098bfeb5025549f0f099a130290

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb81d91ed48572916a0e886fcd7df1af66c16e09850fd2be43791cee1a91949a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-04-03T08:07:16Z",
    "title_canon_sha256": "d6ed00cb116b96b5957df5226d9f8c9b1a917b3dc60bebd10b3c06d9e7209726"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00771",
    "kind": "arxiv",
    "version": 2
  }
}