Pith Number

pith:S3ZKYFEZ

pith:2011:S3ZKYFEZDWBS5JUQIONJCMWVP2

not attested not anchored not stored refs pending

On a problem of Arnold: the average multiplicative order of a given integer

Carl Pomerance, Par Kurlberg

arxiv:1108.5209 v1 · 2011-08-25 · 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{S3ZKYFEZDWBS5JUQIONJCMWVP2}

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	2026-05-18T04:14:38.741408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96f2ac14991d832ea690439a9132d57e81cc47ba0dfaf1b83154f68dd6e46b9a

Aliases

arxiv: 1108.5209 · arxiv_version: 1108.5209v1 · doi: 10.48550/arxiv.1108.5209 · pith_short_12: S3ZKYFEZDWBS · pith_short_16: S3ZKYFEZDWBS5JUQ · pith_short_8: S3ZKYFEZ

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/S3ZKYFEZDWBS5JUQIONJCMWVP2 \
  | 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: 96f2ac14991d832ea690439a9132d57e81cc47ba0dfaf1b83154f68dd6e46b9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f855ae8a34313fce3c42242b52756cf7805665432387bfcb7a437c089a0ea50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-25T22:10:42Z",
    "title_canon_sha256": "603dde31c3e9f246cc9b8f5444f03bbed866b0779f497e4dd52d8f54d4785404"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5209",
    "kind": "arxiv",
    "version": 1
  }
}