Pith Number

pith:NIP74E57

pith:2011:NIP74E57FPO6WGFY3REZFMTUJB

not attested not anchored not stored refs pending

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

Eleni Tzanaki, Menelaos I. Karavelas

arxiv:1106.6254 v2 · 2011-06-30 · 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{NIP74E57FPO6WGFY3REZFMTUJB}

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	2026-05-18T04:11:51.330226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a1ffe13bf2bddeb18b8dc4992b274485e7f91d6fe6f65f060fb974de7a79e49

Aliases

arxiv: 1106.6254 · arxiv_version: 1106.6254v2 · doi: 10.48550/arxiv.1106.6254 · pith_short_12: NIP74E57FPO6 · pith_short_16: NIP74E57FPO6WGFY · pith_short_8: NIP74E57

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/NIP74E57FPO6WGFY3REZFMTUJB \
  | 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: 6a1ffe13bf2bddeb18b8dc4992b274485e7f91d6fe6f65f060fb974de7a79e49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a4659e1ae968dc95399fd48e4427a36ec9d5503e6ac9404e14972a613dab618",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2011-06-30T14:59:45Z",
    "title_canon_sha256": "c0913b928569af481607043f628722ff50396023e3c5da57d192eb146e79051e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.6254",
    "kind": "arxiv",
    "version": 2
  }
}