Pith Number

pith:DZZPJFT6

pith:2010:DZZPJFT6IK4SMFPAVJFJ7BHR3Q

not attested not anchored not stored refs pending

Vanishing products of one-forms and critical points of master functions

Alexander Varchenko, Daniel C. Cohen, Graham Denham, Michael Falk

arxiv:1010.3743 v3 · 2010-10-18 · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZZPJFT6IK4SMFPAVJFJ7BHR3Q}

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	2026-05-18T04:01:00.017429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e72f4967e42b92615e0aa4a9f84f1dc03d1f6cbe9944d3c1fb5c125842b58f5

Aliases

arxiv: 1010.3743 · arxiv_version: 1010.3743v3 · doi: 10.48550/arxiv.1010.3743 · pith_short_12: DZZPJFT6IK4S · pith_short_16: DZZPJFT6IK4SMFPA · pith_short_8: DZZPJFT6

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/DZZPJFT6IK4SMFPAVJFJ7BHR3Q \
  | 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: 1e72f4967e42b92615e0aa4a9f84f1dc03d1f6cbe9944d3c1fb5c125842b58f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72d87591ac267c0f6ea27de82d256224cf2f5cd72980ad6debbf185c5f6f9ba9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-10-18T21:35:15Z",
    "title_canon_sha256": "410e0b2f09cf62ac1dbfbc2f6583b4b91afe446d1996d6752a0fd65868a40f3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3743",
    "kind": "arxiv",
    "version": 3
  }
}