Pith Number

pith:VRHHJRSQ

pith:2017:VRHHJRSQEBPSUML5GPAOU4VVOF

not attested not anchored not stored refs pending

Natural exact covering systems and the reversion of the M\"obius series

Andrew Granville, I. P. Goulden, Jeffrey Shallit, L. Bruce Richmond

arxiv:1711.04109 v4 · 2017-11-11 · math.NT · cs.DM · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRHHJRSQEBPSUML5GPAOU4VVOF}

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	2026-05-18T00:15:37.052669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4e74c650205f2a317d33c0ea72b571791e1abd01295eed4b147e76e808a963

Aliases

arxiv: 1711.04109 · arxiv_version: 1711.04109v4 · doi: 10.48550/arxiv.1711.04109 · pith_short_12: VRHHJRSQEBPS · pith_short_16: VRHHJRSQEBPSUML5 · pith_short_8: VRHHJRSQ

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/VRHHJRSQEBPSUML5GPAOU4VVOF \
  | 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: ac4e74c650205f2a317d33c0ea72b571791e1abd01295eed4b147e76e808a963

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10449356fcbafccac3f5974254f0c5dcc6f0616d3e6ccda13f2c6f813d408ff7",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-11-11T09:40:23Z",
    "title_canon_sha256": "b6c9bc0b846532410ccf8858bcc9436e9c8aef166a98ad2d399c7b22cdc2d035"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.04109",
    "kind": "arxiv",
    "version": 4
  }
}