Pith Number

pith:4YO6FQAW

pith:2017:4YO6FQAW52TGN7YQMXRTFDXF5T

not attested not anchored not stored refs pending

Koszul duality between Betti and Cohomology numbers in Calabi-Yau case

Alexander Pavlov

arxiv:1711.06931 v1 · 2017-11-18 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4YO6FQAW52TGN7YQMXRTFDXF5T}

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	2026-05-18T00:30:15.145338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e61de2c016eea666ff1065e3328ee5ecf0c654108bb9c73bff0a1f76f80ff81a

Aliases

arxiv: 1711.06931 · arxiv_version: 1711.06931v1 · doi: 10.48550/arxiv.1711.06931 · pith_short_12: 4YO6FQAW52TG · pith_short_16: 4YO6FQAW52TGN7YQ · pith_short_8: 4YO6FQAW

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/4YO6FQAW52TGN7YQMXRTFDXF5T \
  | 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: e61de2c016eea666ff1065e3328ee5ecf0c654108bb9c73bff0a1f76f80ff81a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ad8110adc1f9aef849452a4e2b1057f72f78c4b80b35a86893f040138f4fb98",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-11-18T22:14:42Z",
    "title_canon_sha256": "61b2c69decd6ba0adec6676880ebad9f330e4946c1f7cf81728163b314f9d378"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.06931",
    "kind": "arxiv",
    "version": 1
  }
}