Pith Number

pith:KAYG46R6

pith:2015:KAYG46R6XLYWXNM47KH3DZ65HL

not attested not anchored not stored refs pending

On products of k atoms II

Alfred Geroldinger, David J. Grynkiewicz, Pingzhi Yuan

arxiv:1503.06164 v1 · 2015-03-20 · 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{KAYG46R6XLYWXNM47KH3DZ65HL}

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	2026-05-18T02:20:48.446423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50306e7a3ebaf16bb59cfa8fb1e7dd3ad0c19444e25105f93274040931bb83fd

Aliases

arxiv: 1503.06164 · arxiv_version: 1503.06164v1 · doi: 10.48550/arxiv.1503.06164 · pith_short_12: KAYG46R6XLYW · pith_short_16: KAYG46R6XLYWXNM4 · pith_short_8: KAYG46R6

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/KAYG46R6XLYWXNM47KH3DZ65HL \
  | 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: 50306e7a3ebaf16bb59cfa8fb1e7dd3ad0c19444e25105f93274040931bb83fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c4dc5772c1f07d849c0a8d68498be32e7fa89580f6c83ae24a4a3a99816c8fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-20T17:11:26Z",
    "title_canon_sha256": "f3a46380e5c4a90609280fba88cabafcab2f8674b7280275360316498934bd31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06164",
    "kind": "arxiv",
    "version": 1
  }
}