Pith Number

pith:7I4ZXYVY

pith:2024:7I4ZXYVYMTPXLB7AIMKYXEXKUP

not attested not anchored not stored refs pending

On averages of completely multiplicative functions over co-prime integer pairs

Biao Wang

arxiv:2406.09243 v2 · 2024-06-13 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7I4ZXYVYMTPXLB7AIMKYXEXKUP}

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	2026-06-09T01:05:03.437700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa399be2b864df7587e043158b92eaa3d267f120f40ff3e790de551f428e2d54

Aliases

arxiv: 2406.09243 · arxiv_version: 2406.09243v2 · doi: 10.48550/arxiv.2406.09243 · pith_short_12: 7I4ZXYVYMTPX · pith_short_16: 7I4ZXYVYMTPXLB7A · pith_short_8: 7I4ZXYVY

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/7I4ZXYVYMTPXLB7AIMKYXEXKUP \
  | 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: fa399be2b864df7587e043158b92eaa3d267f120f40ff3e790de551f428e2d54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56d6476e457073ed6777801d8f5498d0c15e55ef085aae59ac4fdf16e847579b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-06-13T15:46:41Z",
    "title_canon_sha256": "877199e804452e85af38d48b543bb7e2540b1498895510848452674b404ed839"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2406.09243",
    "kind": "arxiv",
    "version": 2
  }
}