Pith Number

pith:DUUCBD5Q

pith:2024:DUUCBD5QOQQISMTLXOYNIRURJW

not attested not anchored not stored refs pending

On lower bounds of the density of planar periodic sets without unit distances

Alexander Tolmachev

arxiv:2411.13248 v2 · 2024-11-20 · math.MG · cs.LG · 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{DUUCBD5QOQQISMTLXOYNIRURJW}

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	2026-07-05T10:47:33.634907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d28208fb0742089326bbbb0d446914d9329a7afeb1d517868bd7841b42dc52f

Aliases

arxiv: 2411.13248 · arxiv_version: 2411.13248v2 · doi: 10.48550/arxiv.2411.13248 · pith_short_12: DUUCBD5QOQQI · pith_short_16: DUUCBD5QOQQISMTL · pith_short_8: DUUCBD5Q

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/DUUCBD5QOQQISMTLXOYNIRURJW \
  | 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: 1d28208fb0742089326bbbb0d446914d9329a7afeb1d517868bd7841b42dc52f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e44a44ea470e642ae9fd3659fa5cd1c8555fc0c4c9f0ce1cf2cea8726131ec42",
    "cross_cats_sorted": [
      "cs.LG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-11-20T12:07:19Z",
    "title_canon_sha256": "c409b2b25ba7bc779688a46faf800f3f82b3e92598fab2446763fd9ea78b6d95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.13248",
    "kind": "arxiv",
    "version": 2
  }
}