Pith Number

pith:RAUDTQS3

pith:2019:RAUDTQS3NU7B2ZEVG5PT2B4IWL

not attested not anchored not stored refs pending

Modular hyperbolas and bilinear forms of Kloosterman sums

Ilya D. Shkredov

arxiv:1905.00291 v1 · 2019-05-01 · math.NT · 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{RAUDTQS3NU7B2ZEVG5PT2B4IWL}

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.

Cited by

1 paper in Pith

Some remarks on products of sets in the Heisenberg group and in the affine group

Receipt and verification

First computed	2026-05-17T23:47:13.247075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

882839c25b6d3e1d6495375f3d0788b2d5c38478470d96d97fce0cff3a308ca6

Aliases

arxiv: 1905.00291 · arxiv_version: 1905.00291v1 · doi: 10.48550/arxiv.1905.00291 · pith_short_12: RAUDTQS3NU7B · pith_short_16: RAUDTQS3NU7B2ZEV · pith_short_8: RAUDTQS3

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/RAUDTQS3NU7B2ZEVG5PT2B4IWL \
  | 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: 882839c25b6d3e1d6495375f3d0788b2d5c38478470d96d97fce0cff3a308ca6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd979642cb44750aa98b03c8365d94f92006aa1f40d194ba84de4ff16dbc19cb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-05-01T12:56:28Z",
    "title_canon_sha256": "ac1d58c67070fc4759530e7361e611c20f37a0dab827458d26292e4299853fed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.00291",
    "kind": "arxiv",
    "version": 1
  }
}