Pith Number

pith:QBHZYE6Z

pith:2026:QBHZYE6ZRVM756RXMY3PKTLXOE

not attested not anchored not stored refs pending

Long Intervals Without Distinct Multiples of the First $n$ Positive Integers

Scott Duke Kominers

arxiv:2607.10431 v1 · 2026-07-11 · math.NT · 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{QBHZYE6ZRVM756RXMY3PKTLXOE}

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	2026-07-14T01:21:15.627600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

804f9c13d98d59fefa376636f54d777123a9bd050fc7911c918329b43622562a

Aliases

arxiv: 2607.10431 · arxiv_version: 2607.10431v1 · doi: 10.48550/arxiv.2607.10431 · pith_short_12: QBHZYE6ZRVM7 · pith_short_16: QBHZYE6ZRVM756RX · pith_short_8: QBHZYE6Z

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/QBHZYE6ZRVM756RXMY3PKTLXOE \
  | 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: 804f9c13d98d59fefa376636f54d777123a9bd050fc7911c918329b43622562a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12f54400a8577da312cd5a02ae00fa473eb4fa0b4d044e89e93e6ed35bbbd6a1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-11T18:25:27Z",
    "title_canon_sha256": "36e7847b025e27b06b7cc25d295ecbcf56f2f568ad6172691b2ffd85799a8946"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10431",
    "kind": "arxiv",
    "version": 1
  }
}