Pith Number

pith:RF6ID5ZL

pith:2009:RF6ID5ZLYPU74OMEIPVOJFE5EQ

not attested not anchored not stored refs pending

Derived invariance of the number of holomorphic 1-forms and vector fields

Christian Schnell, Mihnea Popa

arxiv:0912.4040 v5 · 2009-12-20 · 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{RF6ID5ZLYPU74OMEIPVOJFE5EQ}

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	2026-05-18T04:38:50.740389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

897c81f72bc3e9fe398443eae4949d2415f0baa28fed116501ccbed4ed9b3fb2

Aliases

arxiv: 0912.4040 · arxiv_version: 0912.4040v5 · doi: 10.48550/arxiv.0912.4040 · pith_short_12: RF6ID5ZLYPU7 · pith_short_16: RF6ID5ZLYPU74OME · pith_short_8: RF6ID5ZL

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/RF6ID5ZLYPU74OMEIPVOJFE5EQ \
  | 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: 897c81f72bc3e9fe398443eae4949d2415f0baa28fed116501ccbed4ed9b3fb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ecff26b78f924df4b4708d4ed556d477d8e8768f2ee9a95e38bcd67d631fb2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-12-20T18:27:11Z",
    "title_canon_sha256": "9a2d2bf5b06f2957c0fbcf06c6dd4a4a749e0c999ab267041ea29ce12292dc05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4040",
    "kind": "arxiv",
    "version": 5
  }
}