Pith Number

pith:BROUFS2R

pith:2016:BROUFS2RZNCEEJXCOENQBNDSJ2

not attested not anchored not stored refs pending

Bounds on trilinear and quadrilinear exponential sums

Giorgis Petridis, Igor E. Shparlinski

arxiv:1604.08469 v4 · 2016-04-28 · math.NT · math.CA · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BROUFS2RZNCEEJXCOENQBNDSJ2}

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	2026-05-18T00:51:03.256088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c5d42cb51cb444226e2711b00b4724ebe9eaab65b6ad1bbdcb8eb594afb9f46

Aliases

arxiv: 1604.08469 · arxiv_version: 1604.08469v4 · doi: 10.48550/arxiv.1604.08469 · pith_short_12: BROUFS2RZNCE · pith_short_16: BROUFS2RZNCEEJXC · pith_short_8: BROUFS2R

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/BROUFS2RZNCEEJXCOENQBNDSJ2 \
  | 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: 0c5d42cb51cb444226e2711b00b4724ebe9eaab65b6ad1bbdcb8eb594afb9f46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdae87c8c3307b30ff920451593efab92c29bf9f2f6fc8d2f833900d28201dd2",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-04-28T15:34:11Z",
    "title_canon_sha256": "844d18cf8a869c516a5fa72ef4b5e9fa22b33bd02611f9e0c2c7a7034357c274"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.08469",
    "kind": "arxiv",
    "version": 4
  }
}