Pith Number

pith:7OUZMALF

pith:2012:7OUZMALF3WX4TS42LQIQV3BBEN

not attested not anchored not stored refs pending

The maximum number of faces of the Minkowski sum of three convex polytopes

Christos Konaxis, Eleni Tzanaki, Menelaos I. Karavelas

arxiv:1211.6089 v1 · 2012-11-26 · 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{7OUZMALF3WX4TS42LQIQV3BBEN}

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	2026-05-18T03:39:53.525149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fba9960165ddafc9cb9a5c110aec21234b6e84dfe056c83fe160a617e65a0459

Aliases

arxiv: 1211.6089 · arxiv_version: 1211.6089v1 · doi: 10.48550/arxiv.1211.6089 · pith_short_12: 7OUZMALF3WX4 · pith_short_16: 7OUZMALF3WX4TS42 · pith_short_8: 7OUZMALF

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/7OUZMALF3WX4TS42LQIQV3BBEN \
  | 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: fba9960165ddafc9cb9a5c110aec21234b6e84dfe056c83fe160a617e65a0459

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83e51663636bbd0ca560311324518a232af01b559d1d22e01f9990907adadd42",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2012-11-26T20:47:25Z",
    "title_canon_sha256": "3ba831780fe6c14df8d732e358e6419a98d55fdc00b04e31bf42c63a8c620249"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6089",
    "kind": "arxiv",
    "version": 1
  }
}