Pith Number

pith:ZNVYJ3AE

pith:2016:ZNVYJ3AE7EDEORTTTZ2EQLVYPT

not attested not anchored not stored refs pending

Special Ulrich bundles on non-special surfaces with $p_g=q=0$

Gianfranco Casnati

arxiv:1609.07915 v5 · 2016-09-26 · 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{ZNVYJ3AE7EDEORTTTZ2EQLVYPT}

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	2026-05-18T00:39:56.899939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb6b84ec04f9064746739e74482eb87cfb5d47c0d160af3efd722973ce168dea

Aliases

arxiv: 1609.07915 · arxiv_version: 1609.07915v5 · doi: 10.48550/arxiv.1609.07915 · pith_short_12: ZNVYJ3AE7EDE · pith_short_16: ZNVYJ3AE7EDEORTT · pith_short_8: ZNVYJ3AE

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/ZNVYJ3AE7EDEORTTTZ2EQLVYPT \
  | 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: cb6b84ec04f9064746739e74482eb87cfb5d47c0d160af3efd722973ce168dea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8ec31e14f5e7d7aa331abd482c71a81fcadff1f96ae6a29f3c0c67a8fcf5e35",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-09-26T10:32:59Z",
    "title_canon_sha256": "2d6cad4fb23a668edd9d14f53f7c45ecd93eb8fbeb5fe4f302e7e28075d7a00a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07915",
    "kind": "arxiv",
    "version": 5
  }
}