Pith Number

pith:3LWFCQMQ

pith:2011:3LWFCQMQ3SWOR4Y6N6MUO25ZR6

not attested not anchored not stored refs pending

On the Cycle Structure of Repeated Exponentiation Modulo a Prime Power

Min Sha

arxiv:1101.3482 v2 · 2011-01-18 · 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{3LWFCQMQ3SWOR4Y6N6MUO25ZR6}

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	2026-05-18T04:15:04.124030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daec514190dcace8f31e6f99476bb98f968a1e82eb6627d230ed8294522115f3

Aliases

arxiv: 1101.3482 · arxiv_version: 1101.3482v2 · doi: 10.48550/arxiv.1101.3482 · pith_short_12: 3LWFCQMQ3SWO · pith_short_16: 3LWFCQMQ3SWOR4Y6 · pith_short_8: 3LWFCQMQ

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/3LWFCQMQ3SWOR4Y6N6MUO25ZR6 \
  | 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: daec514190dcace8f31e6f99476bb98f968a1e82eb6627d230ed8294522115f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47b4f6d4ee2d7fdcc6edbced8d9f14e81d23829a1e7df7c8b3193664dc85e0ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-18T15:50:05Z",
    "title_canon_sha256": "62bfb73a64e5881ec0a69e01b498d0a1e2806594fac0dfbe7e39dfd4c88c68e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3482",
    "kind": "arxiv",
    "version": 2
  }
}