Pith Number

pith:4DUNWMGB

pith:2017:4DUNWMGBGAJ32RXRBO6WRTKI2N

not attested not anchored not stored refs pending

On two functions arising in the study of the Euler and Carmichael quotients

Florian Luca, Igor E. Shparlinski, Min Sha

arxiv:1705.00388 v1 · 2017-04-30 · 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{4DUNWMGBGAJ32RXRBO6WRTKI2N}

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	2026-05-18T00:45:20.512332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0e8db30c13013bd46f10bbd68cd48d344dad4bf5634b40b6a7ccb40e33c8d53

Aliases

arxiv: 1705.00388 · arxiv_version: 1705.00388v1 · doi: 10.48550/arxiv.1705.00388 · pith_short_12: 4DUNWMGBGAJ3 · pith_short_16: 4DUNWMGBGAJ32RXR · pith_short_8: 4DUNWMGB

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/4DUNWMGBGAJ32RXRBO6WRTKI2N \
  | 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: e0e8db30c13013bd46f10bbd68cd48d344dad4bf5634b40b6a7ccb40e33c8d53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8820ef97d70f00ad10e275cdf46f2e2fa69d9e71773f1f3de944e9d41aae4e28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-04-30T23:43:18Z",
    "title_canon_sha256": "c4d53fb0904cf77f2f789a9bf38393a4db0462e262f144d89061bc9daf170609"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.00388",
    "kind": "arxiv",
    "version": 1
  }
}