Pith Number

pith:FJMFV2JL

pith:2015:FJMFV2JLWE33UYRIVGOQYYS6QL

not attested not anchored not stored refs pending

Strange duality between hypersurface and complete intersection singularities

Atsushi Takahashi, Wolfgang Ebeling

arxiv:1508.02226 v1 · 2015-08-10 · 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{FJMFV2JLWE33UYRIVGOQYYS6QL}

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	2026-05-18T01:35:33.829041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a585ae92bb137ba6228a99d0c625e82d581214676fb24cb07cd3ecae0c6cbcb

Aliases

arxiv: 1508.02226 · arxiv_version: 1508.02226v1 · doi: 10.48550/arxiv.1508.02226 · pith_short_12: FJMFV2JLWE33 · pith_short_16: FJMFV2JLWE33UYRI · pith_short_8: FJMFV2JL

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/FJMFV2JLWE33UYRIVGOQYYS6QL \
  | 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: 2a585ae92bb137ba6228a99d0c625e82d581214676fb24cb07cd3ecae0c6cbcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e0ad7c7179e378e33f8dc33ed0b283644dc30b480293ddb9245668eef571e2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-08-10T12:50:08Z",
    "title_canon_sha256": "d8100a36e4e9ec1110f4e7dac06cd0c2576cfcb5c98fbf46918ac016ca79a35b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02226",
    "kind": "arxiv",
    "version": 1
  }
}