Pith Number

pith:ZO5EOYNJ

pith:2013:ZO5EOYNJNQG452S5QT6WHD7DNU

not attested not anchored not stored refs pending

Caustics of plane curves, their birationality and matrix projections

Fabrizio Catanese (Universitaet Bayreuth)

arxiv:1304.3861 v2 · 2013-04-13 · math.AG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZO5EOYNJNQG452S5QT6WHD7DNU}

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	2026-05-18T03:20:09.057609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbba4761a96c0dceea5d84fd638fe36d0f39e001b4c8ae95944e6e7dd8ee9376

Aliases

arxiv: 1304.3861 · arxiv_version: 1304.3861v2 · doi: 10.48550/arxiv.1304.3861 · pith_short_12: ZO5EOYNJNQG4 · pith_short_16: ZO5EOYNJNQG452S5 · pith_short_8: ZO5EOYNJ

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/ZO5EOYNJNQG452S5QT6WHD7DNU \
  | 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: cbba4761a96c0dceea5d84fd638fe36d0f39e001b4c8ae95944e6e7dd8ee9376

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae419e1697b02bef3b1ca147daed7f696c990904c5ecec4f0100fc36bf4dc012",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-04-13T22:17:57Z",
    "title_canon_sha256": "aeef92af9b95951af93eead14514c3e4c759649b4060281498a56e3fca7c29c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3861",
    "kind": "arxiv",
    "version": 2
  }
}