Pith Number

pith:EOZPPH4X

pith:2017:EOZPPH4XQNC2FBGIS3D23YG4NK

not attested not anchored not stored refs pending

Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

Igor E. Shparlinski, Ilya D. Shkredov, Simon Macourt

arxiv:1701.06192 v2 · 2017-01-22 · 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{EOZPPH4XQNC2FBGIS3D23YG4NK}

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	2026-05-18T00:32:36.313004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23b2f79f978345a284c896c7ade0dc6ab1b296d51e2ef92a9b1b6cff9c5e8ca0

Aliases

arxiv: 1701.06192 · arxiv_version: 1701.06192v2 · doi: 10.48550/arxiv.1701.06192 · pith_short_12: EOZPPH4XQNC2 · pith_short_16: EOZPPH4XQNC2FBGI · pith_short_8: EOZPPH4X

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/EOZPPH4XQNC2FBGIS3D23YG4NK \
  | 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: 23b2f79f978345a284c896c7ade0dc6ab1b296d51e2ef92a9b1b6cff9c5e8ca0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a6179bdbc37c1a0a24da96ae9b8b1bfcfcd1d1243c73f43db35dc37929fbfaf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-01-22T17:23:40Z",
    "title_canon_sha256": "9c7b22d30d16ae8af932810e9583a50ee164ab7fa66864d9be91acf6b7963cb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.06192",
    "kind": "arxiv",
    "version": 2
  }
}