Pith Number

pith:5UGFJOUP

pith:2010:5UGFJOUP32DDRV4QJ45V622KQ2

not attested not anchored not stored refs pending

Elementary Trigonometric Sums related to Quadratic Residues

A. Laradji, M. Mignotte, N. Tzanakis

arxiv:1001.2638 v3 · 2010-01-15 · 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{5UGFJOUP32DDRV4QJ45V622KQ2}

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	2026-05-18T03:55:23.728760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed0c54ba8fde8638d7904f3b5f6b4a86b559f0fb16a4938e6039b76d0913410e

Aliases

arxiv: 1001.2638 · arxiv_version: 1001.2638v3 · doi: 10.48550/arxiv.1001.2638 · pith_short_12: 5UGFJOUP32DD · pith_short_16: 5UGFJOUP32DDRV4Q · pith_short_8: 5UGFJOUP

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/5UGFJOUP32DDRV4QJ45V622KQ2 \
  | 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: ed0c54ba8fde8638d7904f3b5f6b4a86b559f0fb16a4938e6039b76d0913410e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8bc6cfff976da65f6a242f9824855805da78eab7790add718e4e31581c93029",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-01-15T09:14:48Z",
    "title_canon_sha256": "1ceb6b50abecc00e70215f5ad0f4f5c737eb728c06763a5d0213285f982cfd0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.2638",
    "kind": "arxiv",
    "version": 3
  }
}