Pith Number

pith:WPHKW4ND

pith:2019:WPHKW4NDSESYWV5BZOUPVOYB54

not attested not anchored not stored refs pending

Tangent developable surfaces and the equations defining algebraic curves

Lawrence Ein, Robert Lazarsfeld

arxiv:1906.05429 v1 · 2019-06-13 · 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{WPHKW4NDSESYWV5BZOUPVOYB54}

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	2026-05-17T23:43:25.346774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3ceab71a391258b57a1cba8fabb01ef1f784976b7f809c03c708822ee3b42d0

Aliases

arxiv: 1906.05429 · arxiv_version: 1906.05429v1 · doi: 10.48550/arxiv.1906.05429 · pith_short_12: WPHKW4NDSESY · pith_short_16: WPHKW4NDSESYWV5B · pith_short_8: WPHKW4ND

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/WPHKW4NDSESYWV5BZOUPVOYB54 \
  | 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: b3ceab71a391258b57a1cba8fabb01ef1f784976b7f809c03c708822ee3b42d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5265f5ab8d9b541055ad2d629e205a35ef2ce05cee23dde0b4e45b667bcb93b3",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-06-13T00:19:03Z",
    "title_canon_sha256": "580155b41c83217a4b742ad53d891e6a8edd996c4f03e7983fc5f59a238e1260"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.05429",
    "kind": "arxiv",
    "version": 1
  }
}