Pith Number

pith:QIBWQGXY

pith:2019:QIBWQGXYXYARVARTF2UOIFUNI5

not attested not anchored not stored refs pending

Nontrivial example of the composition of the brane product and coproduct on Gorenstein spaces

Shun Wakatsuki

arxiv:1902.10936 v1 · 2019-02-28 · 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{QIBWQGXYXYARVARTF2UOIFUNI5}

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	2026-05-17T23:52:26.325168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8203681af8be011a82332ea8e4168d4748db249ca9141fdebac870321cc92bff

Aliases

arxiv: 1902.10936 · arxiv_version: 1902.10936v1 · doi: 10.48550/arxiv.1902.10936 · pith_short_12: QIBWQGXYXYAR · pith_short_16: QIBWQGXYXYARVART · pith_short_8: QIBWQGXY

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/QIBWQGXYXYARVARTF2UOIFUNI5 \
  | 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: 8203681af8be011a82332ea8e4168d4748db249ca9141fdebac870321cc92bff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3df9b95a2282960a9ed85f794e454a0233c69d7e77179703f1836399f9fbf681",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2019-02-28T07:44:59Z",
    "title_canon_sha256": "0917057882cb6fb16f6966bcc6012dda8f52d7c132ad28fdda009afcd0b8672c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.10936",
    "kind": "arxiv",
    "version": 1
  }
}