Pith Number

pith:Z32EO5VY

pith:2012:Z32EO5VYYETRI4ETSFDRZKTKLE

not attested not anchored not stored refs pending

Jacobsthal's function and a generalisation of Euler's totient

Fintan Costello, Paul Watts

arxiv:1209.3464 v2 · 2012-09-16 · 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{Z32EO5VYYETRI4ETSFDRZKTKLE}

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	2026-05-18T03:45:20.735376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cef44776b8c12714709391471caa6a59174e262a6446120d9ae30c72a5c459dc

Aliases

arxiv: 1209.3464 · arxiv_version: 1209.3464v2 · doi: 10.48550/arxiv.1209.3464 · pith_short_12: Z32EO5VYYETR · pith_short_16: Z32EO5VYYETRI4ET · pith_short_8: Z32EO5VY

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/Z32EO5VYYETRI4ETSFDRZKTKLE \
  | 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: cef44776b8c12714709391471caa6a59174e262a6446120d9ae30c72a5c459dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be2e56021e7247215dbf9ed13cc54ee98cee2f54abe75f9f62abf0630a077be7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-16T08:09:44Z",
    "title_canon_sha256": "d3c4031b539256770557e3f460e0d8efa88aaf7c2be2db33cc3de37f7252be90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3464",
    "kind": "arxiv",
    "version": 2
  }
}