Pith Number

pith:RRANUTOA

pith:2016:RRANUTOARGG4LO7SPBSKZBDUFS

not attested not anchored not stored refs pending

Products of primes in arithmetic progressions: a footnote in parity breaking

Aled Walker, Olivier Ramar\'e

arxiv:1610.05804 v2 · 2016-10-18 · 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{RRANUTOARGG4LO7SPBSKZBDUFS}

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	2026-05-17T23:52:24.760472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c40da4dc0898dc5bbf27864ac84742cbc87faa7a4f9ac34342ce27dd652d792

Aliases

arxiv: 1610.05804 · arxiv_version: 1610.05804v2 · doi: 10.48550/arxiv.1610.05804 · pith_short_12: RRANUTOARGG4 · pith_short_16: RRANUTOARGG4LO7S · pith_short_8: RRANUTOA

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/RRANUTOARGG4LO7SPBSKZBDUFS \
  | 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: 8c40da4dc0898dc5bbf27864ac84742cbc87faa7a4f9ac34342ce27dd652d792

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3404f2c93cad562b51e4d26981d864e0da1007fa578476a2f073e07c0edd58cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-18T21:18:03Z",
    "title_canon_sha256": "8c35788583820f4beafd52c304a93f2054377f74e9be02ed988e8d946cea1a54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05804",
    "kind": "arxiv",
    "version": 2
  }
}