Pith Number

pith:MHMWD44J

pith:2016:MHMWD44JY5TJ656EL6GWJ5LH5D

not attested not anchored not stored refs pending

The probability that two random integers are coprime

Julien Bureaux (MODAL'X), LPMA), Nathana\"el Enriquez (MODAL'X

arxiv:1612.03700 v1 · 2016-12-12 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHMWD44JY5TJ656EL6GWJ5LH5D}

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	2026-05-18T00:55:18.547195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61d961f389c7669f77c45f8d64f567e8c69fbd6d46b192415d4cfff3add9dfd0

Aliases

arxiv: 1612.03700 · arxiv_version: 1612.03700v1 · doi: 10.48550/arxiv.1612.03700 · pith_short_12: MHMWD44JY5TJ · pith_short_16: MHMWD44JY5TJ656E · pith_short_8: MHMWD44J

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/MHMWD44JY5TJ656EL6GWJ5LH5D \
  | 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: 61d961f389c7669f77c45f8d64f567e8c69fbd6d46b192415d4cfff3add9dfd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e051be55040b5a8901926bb893105172ff0909080dab38fa3b384c5e6227594c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-12T14:22:05Z",
    "title_canon_sha256": "7ced14d199b6b0991480b348d1a34a2cb6d8e2cf899422c09cfefe9469634e6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03700",
    "kind": "arxiv",
    "version": 1
  }
}