Pith Number

pith:GDTU5JJQ

pith:2015:GDTU5JJQVIYMDYZJIX35VXNECX

not attested not anchored not stored refs pending

A geometric approach for the upper bound theorem for Minkowski sums of convex polytopes

Eleni Tzanaki, Menelaos I. Karavelas

arxiv:1502.02265 v2 · 2015-02-08 · 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{GDTU5JJQVIYMDYZJIX35VXNECX}

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	2026-05-18T02:25:55.508713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30e74ea530aa30c1e32945f7dadda415f5df19e5a2b7ae71eafef9004d974974

Aliases

arxiv: 1502.02265 · arxiv_version: 1502.02265v2 · doi: 10.48550/arxiv.1502.02265 · pith_short_12: GDTU5JJQVIYM · pith_short_16: GDTU5JJQVIYMDYZJ · pith_short_8: GDTU5JJQ

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/GDTU5JJQVIYMDYZJIX35VXNECX \
  | 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: 30e74ea530aa30c1e32945f7dadda415f5df19e5a2b7ae71eafef9004d974974

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d8bb44c598c28a9eb600a09b072181d509d34054cd7a8a692a7e8d857934d9d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2015-02-08T15:54:48Z",
    "title_canon_sha256": "b8158f390f046cb77fee78c8ee3ab963af72e155a4ec904afb4789b4aff9ab0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02265",
    "kind": "arxiv",
    "version": 2
  }
}