Pith Number

pith:XQ4IZ5RQ

pith:2018:XQ4IZ5RQXK2KZ5WKQY4MNGVWHT

not attested not anchored not stored refs pending

Higher moments of distances between consecutive Ford spheres

Alan Haynes, Kayleigh Measures

arxiv:1809.09743 v1 · 2018-09-25 · 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{XQ4IZ5RQXK2KZ5WKQY4MNGVWHT}

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	2026-05-18T00:04:43.805795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc388cf630bab4acf6ca8638c69ab63ce90d8c73a2787f9aa7a3e71158d8e874

Aliases

arxiv: 1809.09743 · arxiv_version: 1809.09743v1 · doi: 10.48550/arxiv.1809.09743 · pith_short_12: XQ4IZ5RQXK2K · pith_short_16: XQ4IZ5RQXK2KZ5WK · pith_short_8: XQ4IZ5RQ

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/XQ4IZ5RQXK2KZ5WKQY4MNGVWHT \
  | 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: bc388cf630bab4acf6ca8638c69ab63ce90d8c73a2787f9aa7a3e71158d8e874

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fb0177934885bee0e23a9df62bb58a92526344a25d392972ee36a979b0205a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-09-25T22:10:32Z",
    "title_canon_sha256": "87ce771a27d9b16dc91daced4f7b6a02836d3e9dd27cd9f4cbf9035aa61524b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.09743",
    "kind": "arxiv",
    "version": 1
  }
}