Pith Number

pith:67MTPOGK

pith:2018:67MTPOGKV2NYDUZM5XEW4SRKVA

not attested not anchored not stored refs pending

Counting integers with a smooth totient

C. Pomerance, I. E. Shparlinski, J. B. Friedlander, W. D. Banks

arxiv:1809.01214 v1 · 2018-09-04 · 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{67MTPOGKV2NYDUZM5XEW4SRKVA}

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	2026-05-18T00:06:31.378763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7d937b8caae9b81d32cedc96e4a2aa839bb1439055c9cf557388407d6526354

Aliases

arxiv: 1809.01214 · arxiv_version: 1809.01214v1 · doi: 10.48550/arxiv.1809.01214 · pith_short_12: 67MTPOGKV2NY · pith_short_16: 67MTPOGKV2NYDUZM · pith_short_8: 67MTPOGK

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/67MTPOGKV2NYDUZM5XEW4SRKVA \
  | 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: f7d937b8caae9b81d32cedc96e4a2aa839bb1439055c9cf557388407d6526354

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "819306b5b756a6f14a0fd9fec0056a3786da371c467ff797d3466b155f0c5ec9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-09-04T19:27:12Z",
    "title_canon_sha256": "d2e3c566492054b584ccd2b4d513a1d5fe2ccd210ad7119ff1229beaf1b23783"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.01214",
    "kind": "arxiv",
    "version": 1
  }
}