Pith Number

pith:J3TOXOG7

pith:2010:J3TOXOG7L5D4GLFM4YP2XJSG6Q

not attested not anchored not stored refs pending

Value distribution of the Gauss map of improper affine spheres

Daisuke Nakajo, Yu Kawakami

arxiv:1004.1484 v4 · 2010-04-09 · math.DG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3TOXOG7L5D4GLFM4YP2XJSG6Q}

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	2026-05-18T03:55:22.098780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ee6ebb8df5f47c32cace61faba646f41041033a7d43e31e32d888e01689dc0a

Aliases

arxiv: 1004.1484 · arxiv_version: 1004.1484v4 · doi: 10.48550/arxiv.1004.1484 · pith_short_12: J3TOXOG7L5D4 · pith_short_16: J3TOXOG7L5D4GLFM · pith_short_8: J3TOXOG7

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/J3TOXOG7L5D4GLFM4YP2XJSG6Q \
  | 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: 4ee6ebb8df5f47c32cace61faba646f41041033a7d43e31e32d888e01689dc0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba31c16c7e3452aa8e9500bda6455a12ef3fdc57579e39d32092ab941014f7cf",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-04-09T07:46:04Z",
    "title_canon_sha256": "cab4b5bd56118cf4d91895324e51979151c1fa37cd2e9554eac0a4c5de47865d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1484",
    "kind": "arxiv",
    "version": 4
  }
}