Pith Number

pith:3M2L7PRM

pith:2018:3M2L7PRMDIUKU6UYKZB3F332YZ

not attested not anchored not stored refs pending

On growth rate in $SL_2(\mathbf{F}_p)$, the affine group and sum-product type implications

Ilya D. Shkredov, Misha Rudnev

arxiv:1812.01671 v3 · 2018-12-04 · math.CO

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3M2L7PRMDIUKU6UYKZB3F332YZ}

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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	2026-05-17T23:52:39.370703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db34bfbe2c1a28aa7a985643b2ef7ac650d506dc54f3a7c761d5ad6269db3d60

Aliases

arxiv: 1812.01671 · arxiv_version: 1812.01671v3 · doi: 10.48550/arxiv.1812.01671 · pith_short_12: 3M2L7PRMDIUK · pith_short_16: 3M2L7PRMDIUKU6UY · pith_short_8: 3M2L7PRM

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/3M2L7PRMDIUKU6UYKZB3F332YZ \
  | 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: db34bfbe2c1a28aa7a985643b2ef7ac650d506dc54f3a7c761d5ad6269db3d60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80b9dd3dac054c1ccdf19bf00a80a0a37a193719de831901a4196f6d658825c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-12-04T20:36:43Z",
    "title_canon_sha256": "e1364d56abe6dda0290ed3b8a869dfa62d1f5c275901f7091af9d6a27d774b63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.01671",
    "kind": "arxiv",
    "version": 3
  }
}