Pith Number

pith:LK4YK5Y7

pith:2010:LK4YK5Y7QR3FJGZ2BVAP26OMWE

not attested not anchored not stored refs pending

Homotheties and topology of tangent sphere bundles

Rui Albuquerque

arxiv:1012.4135 v3 · 2010-12-19 · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LK4YK5Y7QR3FJGZ2BVAP26OMWE}

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	2026-05-17T23:39:42.629929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ab985771f8476549b3a0d40fd79ccb12a2526dfe1fe0cfa513d55cf58928cb2

Aliases

arxiv: 1012.4135 · arxiv_version: 1012.4135v3 · doi: 10.48550/arxiv.1012.4135 · pith_short_12: LK4YK5Y7QR3F · pith_short_16: LK4YK5Y7QR3FJGZ2 · pith_short_8: LK4YK5Y7

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/LK4YK5Y7QR3FJGZ2BVAP26OMWE \
  | 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: 5ab985771f8476549b3a0d40fd79ccb12a2526dfe1fe0cfa513d55cf58928cb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb1c5cad7249a31644fa96df6e4f9513d4395824343fd259aeb72a559b27fbe2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-12-19T00:27:57Z",
    "title_canon_sha256": "e0964ad30bfa279b2162d1e4070142f91a4fdfe9b4916f215e83e489d6cb2dc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4135",
    "kind": "arxiv",
    "version": 3
  }
}