Pith Number

pith:76VQ3AWN

pith:2026:76VQ3AWNIANTXL5FLHCBWDEJNT

not attested not anchored not stored refs pending

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers

Amit Sahai, Xinjie He

arxiv:2608.06681 v1 · 2026-08-07 · 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{76VQ3AWNIANTXL5FLHCBWDEJNT}

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	2026-08-10T01:11:41.483338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffab0d82cd401b3bafa559c41b0c896ccf6a8914e4909abe0d9441cb199b90ee

Aliases

arxiv: 2608.06681 · arxiv_version: 2608.06681v1 · doi: 10.48550/arxiv.2608.06681 · pith_short_12: 76VQ3AWNIANT · pith_short_16: 76VQ3AWNIANTXL5F · pith_short_8: 76VQ3AWN

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/76VQ3AWNIANTXL5FLHCBWDEJNT \
  | 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: ffab0d82cd401b3bafa559c41b0c896ccf6a8914e4909abe0d9441cb199b90ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1de0b424e9ca248e6560062c5fce6cc84159ea93af83b7a367c3968480fa339f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-08-07T01:06:46Z",
    "title_canon_sha256": "bde994708553e3bf5cbcd2d72f843893fd9db96bc62ac043714ceefb4cfbc55e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06681",
    "kind": "arxiv",
    "version": 1
  }
}