Pith Number

pith:C7BZHDXW

pith:2012:C7BZHDXWT6JRRWG4XOHOHO3MYA

not attested not anchored not stored refs pending

Behaviors of multivariable finite Euler products in probabilistic view

Takahiro Aoyama, Takashi Nakamura

arxiv:1204.4043 v1 · 2012-04-18 · math.PR · 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{C7BZHDXWT6JRRWG4XOHOHO3MYA}

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	2026-05-18T03:57:37.912594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17c3938ef69f9318d8dcbb8ee3bb6cc019c6b5065d128c3d5c6ac898b113a373

Aliases

arxiv: 1204.4043 · arxiv_version: 1204.4043v1 · doi: 10.48550/arxiv.1204.4043 · pith_short_12: C7BZHDXWT6JR · pith_short_16: C7BZHDXWT6JRRWG4 · pith_short_8: C7BZHDXW

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/C7BZHDXWT6JRRWG4XOHOHO3MYA \
  | 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: 17c3938ef69f9318d8dcbb8ee3bb6cc019c6b5065d128c3d5c6ac898b113a373

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7f98c0a5c82dfa48d68ecb737779c9151d65993128b6eaa6d48cd4f5aebcf4f",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-18T10:48:05Z",
    "title_canon_sha256": "decea3e78c7e0f152850cfc3fe836a7107f610e570dd5253ca1e1262bbb24f12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4043",
    "kind": "arxiv",
    "version": 1
  }
}