Pith Number

pith:PXO4H3YR

pith:2026:PXO4H3YRYOKCJZWX5S5FQMSTP7

not attested not anchored not stored refs pending

Character sums over smooth numbers

Max Wenqiang Xu, Seth Hardy

arxiv:2607.00592 v1 · 2026-07-01 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PXO4H3YRYOKCJZWX5S5FQMSTP7}

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	2026-07-02T01:17:48.458342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dddc3ef11c39424e6d7ecba5832537ffb2e840d15002cf93b5e75d497edb178

Aliases

arxiv: 2607.00592 · arxiv_version: 2607.00592v1 · doi: 10.48550/arxiv.2607.00592 · pith_short_12: PXO4H3YRYOKC · pith_short_16: PXO4H3YRYOKCJZWX · pith_short_8: PXO4H3YR

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/PXO4H3YRYOKCJZWX5S5FQMSTP7 \
  | 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: 7dddc3ef11c39424e6d7ecba5832537ffb2e840d15002cf93b5e75d497edb178

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcf4fd06c2dbb001777960f60eacf116810a4131babb9a112feca769c5cb3cd5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-01T08:17:56Z",
    "title_canon_sha256": "ce769785b8910cb1284b8b6460e66d24227bed26e99ee4d7be4cf924f5d70aa2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00592",
    "kind": "arxiv",
    "version": 1
  }
}