Pith Number

pith:SIQQYLUL

pith:2013:SIQQYLULSA3YXQXVFPU2LXRHVC

not attested not anchored not stored refs pending

Exponential Sums over Points of Elliptic Curves

Igor E. Shparlinski, Omran Ahmadi

arxiv:1302.4210 v3 · 2013-02-18 · 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{SIQQYLULSA3YXQXVFPU2LXRHVC}

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	2026-05-18T03:15:20.767589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92210c2e8b90378bc2f52be9a5de27a899a21f91d1862ceaa61a7e6bf6d4231b

Aliases

arxiv: 1302.4210 · arxiv_version: 1302.4210v3 · doi: 10.48550/arxiv.1302.4210 · pith_short_12: SIQQYLULSA3Y · pith_short_16: SIQQYLULSA3YXQXV · pith_short_8: SIQQYLUL

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/SIQQYLULSA3YXQXVFPU2LXRHVC \
  | 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: 92210c2e8b90378bc2f52be9a5de27a899a21f91d1862ceaa61a7e6bf6d4231b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7265ddb5e19e72731a6075d41a7330e69aef3ca575c67f423d043ba60eefbdbb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-18T10:19:34Z",
    "title_canon_sha256": "5a461797e145bd1f9c9939d090059597ba0eb973cb648ffb133846181c11a40c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4210",
    "kind": "arxiv",
    "version": 3
  }
}