Pith Number

pith:BR4UTAHZ

pith:2018:BR4UTAHZ64R5ZT4F5N76ZXF6WZ

not attested not anchored not stored refs pending

Difference between families of weakly and strongly maximal integral lattice-free polytopes

Gennadiy Averkov

arxiv:1807.06327 v2 · 2018-07-17 · math.CO · math.AG · math.MG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BR4UTAHZ64R5ZT4F5N76ZXF6WZ}

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	2026-05-18T00:10:27.513265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c794980f9f723dccf85eb7fecdcbeb6450aba513c18473cce73e8110db2166b

Aliases

arxiv: 1807.06327 · arxiv_version: 1807.06327v2 · doi: 10.48550/arxiv.1807.06327 · pith_short_12: BR4UTAHZ64R5 · pith_short_16: BR4UTAHZ64R5ZT4F · pith_short_8: BR4UTAHZ

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/BR4UTAHZ64R5ZT4F5N76ZXF6WZ \
  | 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: 0c794980f9f723dccf85eb7fecdcbeb6450aba513c18473cce73e8110db2166b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29049996cb9fff2691538e26a4c9e1467249d7b1a19a7b037c4b52a2da4b786c",
    "cross_cats_sorted": [
      "math.AG",
      "math.MG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-17T10:40:08Z",
    "title_canon_sha256": "e49b9fbd78b699163ec85000f09be35cbaee190f3cbaefd89b020fec13e2f8aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.06327",
    "kind": "arxiv",
    "version": 2
  }
}