Pith Number

pith:24QIY3WO

pith:2026:24QIY3WONMCZSFHYUWG5EGWA6K

not attested not anchored not stored refs pending

Asymptotic formulas for sums of elements from a multiplicative group

Florian Luca, Jan-Hendrik Evertse, K\'alm\'an Gy\H{o}ry, Lajos Hajdu, L\'aszl\'o Remete

arxiv:2605.28973 v1 · 2026-05-27 · 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{24QIY3WONMCZSFHYUWG5EGWA6K}

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	2026-05-29T01:04:42.101402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7208c6ece6b059914f8a58dd21ac0f2825bad66640c04227d78f8f9e68bc687

Aliases

arxiv: 2605.28973 · arxiv_version: 2605.28973v1 · doi: 10.48550/arxiv.2605.28973 · pith_short_12: 24QIY3WONMCZ · pith_short_16: 24QIY3WONMCZSFHY · pith_short_8: 24QIY3WO

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/24QIY3WONMCZSFHYUWG5EGWA6K \
  | 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: d7208c6ece6b059914f8a58dd21ac0f2825bad66640c04227d78f8f9e68bc687

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b0cb631ed71495ceb78e2899e812c642165b559c042c2e507a172515ac930e6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-27T18:22:59Z",
    "title_canon_sha256": "62e5c689219b2af288a3383e7922adda7723eb2c634cd9bba9c28fa62147b172"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.28973",
    "kind": "arxiv",
    "version": 1
  }
}