Pith Number

pith:AO3QNX27

pith:2018:AO3QNX27RII2X54HXQXXX7EZTT

not attested not anchored not stored refs pending

An improved upper bound for the size of the multiplicative 3-Sidon sets

P\'eter P\'al Pach

arxiv:1801.08733 v1 · 2018-01-26 · 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{AO3QNX27RII2X54HXQXXX7EZTT}

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	2026-05-18T00:25:03.156023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03b706df5f8a11abf787bc2f7bfc999cd0034dd3b71fa23fc3f933a000903dd3

Aliases

arxiv: 1801.08733 · arxiv_version: 1801.08733v1 · doi: 10.48550/arxiv.1801.08733 · pith_short_12: AO3QNX27RII2 · pith_short_16: AO3QNX27RII2X54H · pith_short_8: AO3QNX27

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/AO3QNX27RII2X54HXQXXX7EZTT \
  | 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: 03b706df5f8a11abf787bc2f7bfc999cd0034dd3b71fa23fc3f933a000903dd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfe7c661bf7bdfaec7ee6b4b26e39cb6f3e221ed72a945c3fe86d1f9d9dc54c2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-01-26T09:47:10Z",
    "title_canon_sha256": "08d6a89481b65b14c6a3a04a7cd6d7478d04b81cb3445b9e19b8c51e97cbe7e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.08733",
    "kind": "arxiv",
    "version": 1
  }
}