Pith Number

pith:62JTCQ5Q

pith:2015:62JTCQ5QKATDVMQRXWVII6BK5C

not attested not anchored not stored refs pending

On the sumsets of exceptional units in $\mathbb{Z}_n$

Qing-Qing Zhao, Quan-Hui Yang

arxiv:1509.06272 v1 · 2015-09-21 · 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{62JTCQ5QKATDVMQRXWVII6BK5C}

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	2026-05-18T01:32:35.441817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6933143b050263ab211bdaa84782ae8bd9ce75838128727884aed56139ec815

Aliases

arxiv: 1509.06272 · arxiv_version: 1509.06272v1 · doi: 10.48550/arxiv.1509.06272 · pith_short_12: 62JTCQ5QKATD · pith_short_16: 62JTCQ5QKATDVMQR · pith_short_8: 62JTCQ5Q

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/62JTCQ5QKATDVMQRXWVII6BK5C \
  | 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: f6933143b050263ab211bdaa84782ae8bd9ce75838128727884aed56139ec815

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7c987995581dc5233fd2f0c1cfa7ddb24d6b93fbef5ae5ff207b93127b3e028",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-21T15:28:58Z",
    "title_canon_sha256": "c920b9bcae94e6a77aaa59a379cb6b2037fbc440087a0938c1c26d95c730767e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06272",
    "kind": "arxiv",
    "version": 1
  }
}