Pith Number

pith:L2PW5C66

pith:2011:L2PW5C66PKKUSDYXX6S6JKVDP3

not attested not anchored not stored refs pending

Tight lower bounds on the number of faces of the Minkowski sum of convex polytopes via the Cayley trick

Eleni Tzanaki, Menelaos I. Karavelas

arxiv:1112.1535 v1 · 2011-12-07 · 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{L2PW5C66PKKUSDYXX6S6JKVDP3}

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	2026-05-18T04:06:54.394623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e9f6e8bde7a95490f17bfa5e4aaa37ee438d70d8cbe9c2a1bc031d7854815b1

Aliases

arxiv: 1112.1535 · arxiv_version: 1112.1535v1 · doi: 10.48550/arxiv.1112.1535 · pith_short_12: L2PW5C66PKKU · pith_short_16: L2PW5C66PKKUSDYX · pith_short_8: L2PW5C66

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/L2PW5C66PKKUSDYXX6S6JKVDP3 \
  | 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: 5e9f6e8bde7a95490f17bfa5e4aaa37ee438d70d8cbe9c2a1bc031d7854815b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf3c781a7deb9dd75217ed95241bb497edcb2d2d68265692e425d985c20011aa",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2011-12-07T12:00:03Z",
    "title_canon_sha256": "04f64799eae9010aef1143b1cf57be46904143cb34ba3d40cb8c111e81616e00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1535",
    "kind": "arxiv",
    "version": 1
  }
}