Pith Number

pith:MIQ56OL7

pith:2018:MIQ56OL7B3QH2Q4KNMAER24TI5

not attested not anchored not stored refs pending

Stronger sum-product inequalities for small sets

George Shakan, Ilya Shkredov, Misha Rudnev

arxiv:1808.08465 v4 · 2018-08-25 · math.CO · math.NT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MIQ56OL7B3QH2Q4KNMAER24TI5}

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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	2026-05-18T00:04:44.472021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6221df397f0ee07d438a6b0048eb9347471d11a7ace449ed884a934abf53b143

Aliases

arxiv: 1808.08465 · arxiv_version: 1808.08465v4 · doi: 10.48550/arxiv.1808.08465 · pith_short_12: MIQ56OL7B3QH · pith_short_16: MIQ56OL7B3QH2Q4K · pith_short_8: MIQ56OL7

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/MIQ56OL7B3QH2Q4KNMAER24TI5 \
  | 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: 6221df397f0ee07d438a6b0048eb9347471d11a7ace449ed884a934abf53b143

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "236dac35f0c7b9f303c69078408726d947a4a88899c8a2af71652b746fa88e08",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-25T20:03:17Z",
    "title_canon_sha256": "e0d32098e0033af8d3906de38f4e0b55d789a0b391ac3593c062fec61dcb48d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.08465",
    "kind": "arxiv",
    "version": 4
  }
}