Pith Number

pith:NVMVA7GW

pith:2026:NVMVA7GWRZV2RM7CINFYTIOCGC

not attested not anchored not stored refs pending

Sharp omega results for the divisor and circle problems

Youness Lamzouri

arxiv:2605.21476 v1 · 2026-05-20 · 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{NVMVA7GWRZV2RM7CINFYTIOCGC}

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	2026-05-21T02:05:39.033266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d59507cd68e6ba8b3e2434b89a1c230bcb94d5ce1ba80a5ada91790cbadfcbc

Aliases

arxiv: 2605.21476 · arxiv_version: 2605.21476v1 · doi: 10.48550/arxiv.2605.21476 · pith_short_12: NVMVA7GWRZV2 · pith_short_16: NVMVA7GWRZV2RM7C · pith_short_8: NVMVA7GW

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/NVMVA7GWRZV2RM7CINFYTIOCGC \
  | 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: 6d59507cd68e6ba8b3e2434b89a1c230bcb94d5ce1ba80a5ada91790cbadfcbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8374d1f284e8018df66dcef7c3e7b8a291e9b9318a1d773458faad95ee6a0197",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-20T17:56:12Z",
    "title_canon_sha256": "076597f505b2934135147f547efc0af083648c37136d052c9d8008d5e425088c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21476",
    "kind": "arxiv",
    "version": 1
  }
}