Pith Number

pith:IBDVNJAN

pith:2015:IBDVNJANGRBZBRPMR2LJEMZNI3

not attested not anchored not stored refs pending

Average Multiplicative Order of Finitely Generated Subgroup of Rational Numbers Over Primes

Cihan Pehlivan

arxiv:1504.01550 v2 · 2015-04-07 · 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{IBDVNJANGRBZBRPMR2LJEMZNI3}

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	2026-05-18T01:21:23.097020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

404756a40d344390c5ec8e9692332d46efbcb278af4d2cad58369fc22285de38

Aliases

arxiv: 1504.01550 · arxiv_version: 1504.01550v2 · doi: 10.48550/arxiv.1504.01550 · pith_short_12: IBDVNJANGRBZ · pith_short_16: IBDVNJANGRBZBRPM · pith_short_8: IBDVNJAN

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/IBDVNJANGRBZBRPMR2LJEMZNI3 \
  | 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: 404756a40d344390c5ec8e9692332d46efbcb278af4d2cad58369fc22285de38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e574fdde1dbffa955aa581e94943c1c1e6cec36db044c67cb04bb63ed81288a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-07T11:14:55Z",
    "title_canon_sha256": "60e60f97858a57c1d92abce610be1ab0dc1427e9164451ff3528ed94012864aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01550",
    "kind": "arxiv",
    "version": 2
  }
}