Pith Number

pith:Q3U4BJW6

pith:2013:Q3U4BJW63N3TMNW4UPDFJ45EIV

not attested not anchored not stored refs pending

The distribution of r-free numbers in arithmetic progressions

Jason Gibson

arxiv:1302.5976 v1 · 2013-02-25 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q3U4BJW63N3TMNW4UPDFJ45EIV}

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	2026-05-18T03:12:11.791087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b

Aliases

arxiv: 1302.5976 · arxiv_version: 1302.5976v1 · doi: 10.48550/arxiv.1302.5976 · pith_short_12: Q3U4BJW63N3T · pith_short_16: Q3U4BJW63N3TMNW4 · pith_short_8: Q3U4BJW6

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/Q3U4BJW63N3TMNW4UPDFJ45EIV \
  | 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: 86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2c255bd5ca1f72864c05e24f95224bb98937eca13b0407440483191786f03de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-25T02:10:34Z",
    "title_canon_sha256": "bc9374f102312b956b7edf38b1780c673b7ce8921afa7c0e1aa0e675ce21b00c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5976",
    "kind": "arxiv",
    "version": 1
  }
}