Pith Number

pith:HACBHJSF

pith:2011:HACBHJSFS5IDO2PA2L5U3RFQLB

not attested not anchored not stored refs pending

The least common multiple of random sets of positive integers

Ana Zumalac\'arregui, Javier Cilleruelo, Juanjo Ru\'e, Paulius \v{S}arka

arxiv:1112.3013 v2 · 2011-12-13 · 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{HACBHJSFS5IDO2PA2L5U3RFQLB}

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	2026-05-18T03:04:50.157696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

380413a64597503769e0d2fb4dc4b0586ae7b8260332139d24cc4fef85b5cd35

Aliases

arxiv: 1112.3013 · arxiv_version: 1112.3013v2 · doi: 10.48550/arxiv.1112.3013 · pith_short_12: HACBHJSFS5ID · pith_short_16: HACBHJSFS5IDO2PA · pith_short_8: HACBHJSF

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/HACBHJSFS5IDO2PA2L5U3RFQLB \
  | 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: 380413a64597503769e0d2fb4dc4b0586ae7b8260332139d24cc4fef85b5cd35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3aae60c88ba4bf1de24bf5584412f7d86379c013f61c19f64e4630bf9701e5ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-13T20:12:18Z",
    "title_canon_sha256": "354e974c2173955c6ec7a0645f3776510645f2ff8bc5ea120a41688459d1cc25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3013",
    "kind": "arxiv",
    "version": 2
  }
}