Pith Number

pith:AB2CNEJ3

pith:2024:AB2CNEJ3X7EZUSSICGP2FKRTYW

not attested not anchored not stored refs pending

Exponential sums over integers without large prime divisors

Igor E. Shparlinski, Sary Drappeau

arxiv:2404.10278 v2 · 2024-04-16 · 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{AB2CNEJ3X7EZUSSICGP2FKRTYW}

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.

Cited by

1 paper in Pith

Mean value theorems with smooth numbers

Receipt and verification

First computed	2026-07-05T10:58:15.787056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

007426913bbfc99a4a48119fa2aa33c5858308f07245a9d1ff1e85dd191d5929

Aliases

arxiv: 2404.10278 · arxiv_version: 2404.10278v2 · doi: 10.48550/arxiv.2404.10278 · pith_short_12: AB2CNEJ3X7EZ · pith_short_16: AB2CNEJ3X7EZUSSI · pith_short_8: AB2CNEJ3

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/AB2CNEJ3X7EZUSSICGP2FKRTYW \
  | 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: 007426913bbfc99a4a48119fa2aa33c5858308f07245a9d1ff1e85dd191d5929

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd32755642c2366979ef7216430672e6ee9c95a219508f5029d81fa76b9956a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-04-16T04:36:34Z",
    "title_canon_sha256": "ad708435dd8492f703c4ab5860c89501c5de571a1075d753c43468c30ce2025f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.10278",
    "kind": "arxiv",
    "version": 2
  }
}