Pith Number

pith:HG3JSL4U

pith:2013:HG3JSL4UORASZLB5FSZNGFPNR3

not attested not anchored not stored refs pending

Minkowski sum of polytopes and its normality

Akihiro Higashitani

arxiv:1312.6340 v2 · 2013-12-22 · math.CO · math.AC · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HG3JSL4UORASZLB5FSZNGFPNR3}

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	2026-05-18T02:47:24.273040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39b6992f9474412cac3d2cb2d315ed8ed4264e42a6b9d25c1674d41a4eccd9b9

Aliases

arxiv: 1312.6340 · arxiv_version: 1312.6340v2 · doi: 10.48550/arxiv.1312.6340 · pith_short_12: HG3JSL4UORAS · pith_short_16: HG3JSL4UORASZLB5 · pith_short_8: HG3JSL4U

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/HG3JSL4UORASZLB5FSZNGFPNR3 \
  | 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: 39b6992f9474412cac3d2cb2d315ed8ed4264e42a6b9d25c1674d41a4eccd9b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "046ddc640b2f676b69ca27f6a90ba492920dcf4bd992f0c219be07a97f083ebc",
    "cross_cats_sorted": [
      "math.AC",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-22T03:53:21Z",
    "title_canon_sha256": "efd5e3f96b23972abd4c4ead1738651601dcebcfbb1fc078de5581a06df1cfd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6340",
    "kind": "arxiv",
    "version": 2
  }
}