Pith Number

pith:GLVINKWW

pith:2012:GLVINKWWW3OAKYY4N7MHAG5QFH

not attested not anchored not stored refs pending

On the periodicity of a class of arithmetic functions associated with multiplicative functions

Guoyou Qian, Qianrong Tan, Shaofang Hong

arxiv:1201.0931 v3 · 2012-01-04 · 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{GLVINKWWW3OAKYY4N7MHAG5QFH}

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	2026-05-18T03:32:57.196471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32ea86aad6b6dc05631c6fd8701bb029e1c26aa388db4addfb34dd5461a0472e

Aliases

arxiv: 1201.0931 · arxiv_version: 1201.0931v3 · doi: 10.48550/arxiv.1201.0931 · pith_short_12: GLVINKWWW3OA · pith_short_16: GLVINKWWW3OAKYY4 · pith_short_8: GLVINKWW

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/GLVINKWWW3OAKYY4N7MHAG5QFH \
  | 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: 32ea86aad6b6dc05631c6fd8701bb029e1c26aa388db4addfb34dd5461a0472e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2915e9ca1cf203b28307f37f9a4aa2aff832d051a9ff4f4633286b5cff8c935",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-04T16:06:47Z",
    "title_canon_sha256": "04c63f2d40022f6f1cdee5f601e29fe4a66e1edd2cce29d0c63df145e1d60b75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0931",
    "kind": "arxiv",
    "version": 3
  }
}