Pith Number

pith:IZIOBJS2

pith:2018:IZIOBJS2GNDM5VIYSKD2PMJJM5

not attested not anchored not stored refs pending

Cayley sums and Minkowski sums of lattice polytopes

Akiyoshi Tsuchiya

arxiv:1804.10538 v4 · 2018-04-27 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IZIOBJS2GNDM5VIYSKD2PMJJM5}

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.

Cited by

1 paper in Pith

Toric ideals of Minkowski sums of unit simplices

Receipt and verification

First computed	2026-07-05T06:30:22.346352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4650e0a65a3346ced5189287a7b1296773305ee6874c1b2261c3fb621403ad21

Aliases

arxiv: 1804.10538 · arxiv_version: 1804.10538v4 · doi: 10.48550/arxiv.1804.10538 · pith_short_12: IZIOBJS2GNDM · pith_short_16: IZIOBJS2GNDM5VIY · pith_short_8: IZIOBJS2

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/IZIOBJS2GNDM5VIYSKD2PMJJM5 \
  | 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: 4650e0a65a3346ced5189287a7b1296773305ee6874c1b2261c3fb621403ad21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8e692633ce5a28393dc05ca53fce4e412664831ec39d5d0458006a4b1d1ff23",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-27T14:49:14Z",
    "title_canon_sha256": "719edcef613ef639749731769f3afd29f29b863121f176a70b0897c3f1a7dc4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.10538",
    "kind": "arxiv",
    "version": 4
  }
}