Pith Number

pith:HCHULZ4S

pith:2014:HCHULZ4SSB3KCPDQ4VMF2JJDMD

not attested not anchored not stored refs pending

On the Fixed Points of the Map x -> x^x Modulo a Prime

Florian Luca, Igor Shparlinski, P\"ar Kurlberg

arxiv:1402.4464 v1 · 2014-02-18 · math.NT · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HCHULZ4SSB3KCPDQ4VMF2JJDMD}

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	2026-05-18T02:58:43.811172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

388f45e7929076a13c70e5585d252360d03f3635cf5478d3ca5cfd5e5a0fb81b

Aliases

arxiv: 1402.4464 · arxiv_version: 1402.4464v1 · doi: 10.48550/arxiv.1402.4464 · pith_short_12: HCHULZ4SSB3K · pith_short_16: HCHULZ4SSB3KCPDQ · pith_short_8: HCHULZ4S

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/HCHULZ4SSB3KCPDQ4VMF2JJDMD \
  | 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: 388f45e7929076a13c70e5585d252360d03f3635cf5478d3ca5cfd5e5a0fb81b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "648fbc2e7573b626f699e1c32c42da9bd897caa2b5036a94cecfaa173f7218f3",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-02-18T20:21:25Z",
    "title_canon_sha256": "ee088b9f1414853a7c381659655f653e3155b9b4bb8b3c948f9d899cbea9eff0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.4464",
    "kind": "arxiv",
    "version": 1
  }
}