Pith Number

pith:WNZYPXOK

pith:2013:WNZYPXOKJ7ROYOMIT7KY4QE5XF

not attested not anchored not stored refs pending

Axiumbilic Singular Points on Surfaces Immersed in R4 and their Generic Bifurcations

Flausino Spindola, Jorge Sotomayor, Ronaldo Garcia

arxiv:1304.0197 v1 · 2013-03-31 · math.DG · 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{WNZYPXOKJ7ROYOMIT7KY4QE5XF}

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	2026-05-18T03:29:25.747161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b37387ddca4fe2ec39889fd58e409db944f9323a8e3bc64b557d7f34f3fb5aa0

Aliases

arxiv: 1304.0197 · arxiv_version: 1304.0197v1 · doi: 10.48550/arxiv.1304.0197 · pith_short_12: WNZYPXOKJ7RO · pith_short_16: WNZYPXOKJ7ROYOMI · pith_short_8: WNZYPXOK

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/WNZYPXOKJ7ROYOMIT7KY4QE5XF \
  | 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: b37387ddca4fe2ec39889fd58e409db944f9323a8e3bc64b557d7f34f3fb5aa0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bbd9ffcf22ee798b25e9ecffc52fb94c620b651f566a7b62309b3ee35453f37",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-03-31T12:53:16Z",
    "title_canon_sha256": "f8c73f7268a3972a7b24f9699487797bcf1ab8c4bdd6aca1802c60894b20e3d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0197",
    "kind": "arxiv",
    "version": 1
  }
}