Pith Number

pith:HG5E6N6D

pith:2011:HG5E6N6DJ7H74ZJHAEE4CPMLE4

not attested not anchored not stored refs pending

Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization

Leonid G. Fel

arxiv:1108.0957 v1 · 2011-08-03 · 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{HG5E6N6DJ7H74ZJHAEE4CPMLE4}

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	2026-05-18T04:16:13.318121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39ba4f37c34fcffe65270109c13d8b2707ae23fbaa0a6a6bd3a9139f5ad3dc21

Aliases

arxiv: 1108.0957 · arxiv_version: 1108.0957v1 · doi: 10.48550/arxiv.1108.0957 · pith_short_12: HG5E6N6DJ7H7 · pith_short_16: HG5E6N6DJ7H74ZJH · pith_short_8: HG5E6N6D

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/HG5E6N6DJ7H74ZJHAEE4CPMLE4 \
  | 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: 39ba4f37c34fcffe65270109c13d8b2707ae23fbaa0a6a6bd3a9139f5ad3dc21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58560f1a688139c8d9d1bbaf6377c3a63142a607e7872f9dd54deab65091d47c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-03T22:59:07Z",
    "title_canon_sha256": "6d9ffcc076e7c389bb4b6cc34ac0e924baf3ea8237f03ae59a2c0c12c7a69923"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0957",
    "kind": "arxiv",
    "version": 1
  }
}