Pith Number

pith:MDKII4D7

pith:2024:MDKII4D7SI2LPR6DQTHKHWVROT

not attested not anchored not stored refs pending

Triple sums of Kloosterman sums and the discrepancy of modular inverses

Igor E. Shparlinski, Morten S. Risager, Valentin Blomer

arxiv:2411.17823 v3 · 2024-11-26 · 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{MDKII4D7SI2LPR6DQTHKHWVROT}

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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

On denominators of consecutive $\operatorname{SL}(2,{\mathbb N})$-saturated Farey fractions

Receipt and verification

First computed	2026-07-05T11:56:51.191141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60d484707f9234b7c7c384cea3dab174ce4024598c93df4809acaaa4076a1fb1

Aliases

arxiv: 2411.17823 · arxiv_version: 2411.17823v3 · doi: 10.48550/arxiv.2411.17823 · pith_short_12: MDKII4D7SI2L · pith_short_16: MDKII4D7SI2LPR6D · pith_short_8: MDKII4D7

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/MDKII4D7SI2LPR6DQTHKHWVROT \
  | 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: 60d484707f9234b7c7c384cea3dab174ce4024598c93df4809acaaa4076a1fb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afe7731b67803dbaa7adaf01276c5dc12b248f773f7d33cf59cd1e76f1d86984",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-11-26T19:02:50Z",
    "title_canon_sha256": "6daa76899d085bbefd649bb132c63d16d354236f7a2993376f64f5422e8d5c75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.17823",
    "kind": "arxiv",
    "version": 3
  }
}