Pith Number

pith:A3HRLQWP

pith:2012:A3HRLQWP3WQ6R6NWWUNPZYRUBU

not attested not anchored not stored refs pending

On the maximal number of exceptional values of Gauss maps for various classes of surfaces

Yu Kawakami

arxiv:1205.4782 v2 · 2012-05-22 · 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{A3HRLQWP3WQ6R6NWWUNPZYRUBU}

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	2026-05-18T03:41:10.618468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06cf15c2cfdda1e8f9b6b51afce2340d07193df375e6901cdde44866842aa021

Aliases

arxiv: 1205.4782 · arxiv_version: 1205.4782v2 · doi: 10.48550/arxiv.1205.4782 · pith_short_12: A3HRLQWP3WQ6 · pith_short_16: A3HRLQWP3WQ6R6NW · pith_short_8: A3HRLQWP

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/A3HRLQWP3WQ6R6NWWUNPZYRUBU \
  | 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: 06cf15c2cfdda1e8f9b6b51afce2340d07193df375e6901cdde44866842aa021

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb0203a461f80e0ea4f5619df06eb7f2bac5aedf5d418d2f2bd2bae4da8f5655",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-05-22T01:31:29Z",
    "title_canon_sha256": "d7c721692a45f2b82d0f4c41d5e064abe846f3f0c75df8a00127275e46c9bf69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4782",
    "kind": "arxiv",
    "version": 2
  }
}