Pith Number

pith:KDZ4XTAI

pith:2011:KDZ4XTAIMPBGV5HNAKBZ2KU5XP

not attested not anchored not stored refs pending

On additive and multiplicative arithmetical functions

Masood Aryapoor

arxiv:1106.5320 v1 · 2011-06-27 · 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{KDZ4XTAIMPBGV5HNAKBZ2KU5XP}

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	2026-05-18T04:19:13.802619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50f3cbcc0863c26af4ed02839d2a9dbbfcf779723b2a8e32c25e5126811ede47

Aliases

arxiv: 1106.5320 · arxiv_version: 1106.5320v1 · doi: 10.48550/arxiv.1106.5320 · pith_short_12: KDZ4XTAIMPBG · pith_short_16: KDZ4XTAIMPBGV5HN · pith_short_8: KDZ4XTAI

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/KDZ4XTAIMPBGV5HNAKBZ2KU5XP \
  | 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: 50f3cbcc0863c26af4ed02839d2a9dbbfcf779723b2a8e32c25e5126811ede47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71f65b384bd71aa81c83f931a1166acf26e9db98365f15cac128a4af0d1b53eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-06-27T07:40:13Z",
    "title_canon_sha256": "6584d75cfd3b6ff00c8fceca933de36d37fe4bb990ddccdb466c338c45480659"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5320",
    "kind": "arxiv",
    "version": 1
  }
}