Pith Number

pith:U4TFTRJQ

pith:2018:U4TFTRJQNFC45J36LK3W7ZRAI6

not attested not anchored not stored refs pending

Smooth squarefree and square-full integers in arithmetic progressions

Igor E. Shparlinski, Kam Hung Yau, Marc Munsch

arxiv:1810.02573 v2 · 2018-10-05 · 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{U4TFTRJQNFC45J36LK3W7ZRAI6}

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	2026-05-17T23:51:49.072424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a72659c5306945cea77e5ab76fe62047b41baf731c4985c554e3b2bb1617a62b

Aliases

arxiv: 1810.02573 · arxiv_version: 1810.02573v2 · doi: 10.48550/arxiv.1810.02573 · pith_short_12: U4TFTRJQNFC4 · pith_short_16: U4TFTRJQNFC45J36 · pith_short_8: U4TFTRJQ

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/U4TFTRJQNFC45J36LK3W7ZRAI6 \
  | 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: a72659c5306945cea77e5ab76fe62047b41baf731c4985c554e3b2bb1617a62b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc10a73e9b8ad401dfcba482c5a262ab3ba288e05cab309f5442e4effafadaab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-05T09:04:39Z",
    "title_canon_sha256": "58ecfa2e39e7aa18a7c287a8556a243b0231e82c970579f83f6a02fcdfb91e14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.02573",
    "kind": "arxiv",
    "version": 2
  }
}