Pith Number

pith:QSPKZFLI

pith:2009:QSPKZFLISWYSKZJDWOYDKD7P7B

not attested not anchored not stored refs pending

Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes

Eleni Tzanaki, Menelaos I. Karavelas

arxiv:0911.5086 v5 · 2009-11-26 · cs.CG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QSPKZFLISWYSKZJDWOYDKD7P7B}

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	2026-05-18T04:20:13.301578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

849eac956895b1256523b3b0350feff848c8709f53cc8637c3ee74da8cbb836d

Aliases

arxiv: 0911.5086 · arxiv_version: 0911.5086v5 · doi: 10.48550/arxiv.0911.5086 · pith_short_12: QSPKZFLISWYS · pith_short_16: QSPKZFLISWYSKZJD · pith_short_8: QSPKZFLI

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/QSPKZFLISWYSKZJDWOYDKD7P7B \
  | 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: 849eac956895b1256523b3b0350feff848c8709f53cc8637c3ee74da8cbb836d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93344c443a90b2df11f8e22d1d8f280dcb9202f349a7c618b1e614d04b98e25c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2009-11-26T20:06:03Z",
    "title_canon_sha256": "659cd5552cfabb147aeae7e42b0319fa8856b85b01144431535c242540440d03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5086",
    "kind": "arxiv",
    "version": 5
  }
}