Pith Number

pith:42M43O6P

pith:2024:42M43O6PSXCH5DSKEBC62MER3T

not attested not anchored not stored refs pending

Clustering in typical unit-distance avoiding sets

Alex Cohen, Nitya Mani

arxiv:2407.05071 v1 · 2024-07-06 · math.MG · 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{42M43O6PSXCH5DSKEBC62MER3T}

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

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

Receipt and verification

First computed	2026-07-05T08:41:07.637591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e699cdbbcf95c47e8e4a2045ed3091dcc8cff144e8a4ecc3b22be616c79234d4

Aliases

arxiv: 2407.05071 · arxiv_version: 2407.05071v1 · doi: 10.48550/arxiv.2407.05071 · pith_short_12: 42M43O6PSXCH · pith_short_16: 42M43O6PSXCH5DSK · pith_short_8: 42M43O6P

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/42M43O6PSXCH5DSKEBC62MER3T \
  | 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: e699cdbbcf95c47e8e4a2045ed3091dcc8cff144e8a4ecc3b22be616c79234d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87dc78b31d06ed787dac664e65c01d4599431ba856b09ef7d41cadd51ed5aa1c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-07-06T13:26:29Z",
    "title_canon_sha256": "c5b1078458a7f8c1824b2dd57fa29c90f8846b6f9e02ef0c5cd1eccfafca8f89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.05071",
    "kind": "arxiv",
    "version": 1
  }
}