Pith Number

pith:G7CW5NAP

pith:2015:G7CW5NAP76W5DYKDSGRMANCBSE

not attested not anchored not stored refs pending

Salem sets with no arithmetic progressions

Pablo Shmerkin

arxiv:1510.07596 v3 · 2015-10-26 · math.CA · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G7CW5NAP76W5DYKDSGRMANCBSE}

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	2026-05-18T00:07:24.008088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37c56eb40fffadd1e14391a2c034419134affa5f904c555644d4a8f007e23247

Aliases

arxiv: 1510.07596 · arxiv_version: 1510.07596v3 · doi: 10.48550/arxiv.1510.07596 · pith_short_12: G7CW5NAP76W5 · pith_short_16: G7CW5NAP76W5DYKD · pith_short_8: G7CW5NAP

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/G7CW5NAP76W5DYKDSGRMANCBSE \
  | 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: 37c56eb40fffadd1e14391a2c034419134affa5f904c555644d4a8f007e23247

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca6535e65784cfc037ef2f4cdd48a2a4cf83954d04a24c9c144fe8839e17c876",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-10-26T19:05:38Z",
    "title_canon_sha256": "abf4481c0fe7885e4ca1e89add5871e7c0e379246aa445731bced191ee5bbbce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07596",
    "kind": "arxiv",
    "version": 3
  }
}