Pith Number

pith:N2RGZ3NC

pith:2009:N2RGZ3NCCQTQQQDNGYWWRZFDTL

not attested not anchored not stored refs pending

Focal values of plane cubic centers

Hans-Christian Graf v. Bothmer, Jakob Kr\"oker

arxiv:0902.3415 v1 · 2009-02-19 · math.AG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N2RGZ3NCCQTQQQDNGYWWRZFDTL}

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	2026-05-18T04:36:49.411981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ea26ceda2142708406d362d68e4a39acba68d9be47781a2a1e79cffce073542

Aliases

arxiv: 0902.3415 · arxiv_version: 0902.3415v1 · doi: 10.48550/arxiv.0902.3415 · pith_short_12: N2RGZ3NCCQTQ · pith_short_16: N2RGZ3NCCQTQQQDN · pith_short_8: N2RGZ3NC

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/N2RGZ3NCCQTQQQDNGYWWRZFDTL \
  | 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: 6ea26ceda2142708406d362d68e4a39acba68d9be47781a2a1e79cffce073542

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f3b948567cade3aad4575c5225b4198e1660ab950d59805d771586538aa31c1",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-02-19T17:20:53Z",
    "title_canon_sha256": "d1d321b0088714c931e606c05da94a9f4435de350e012d1309ee307e69bc4448"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.3415",
    "kind": "arxiv",
    "version": 1
  }
}