Pith Number

pith:WAEI3ADC

pith:2018:WAEI3ADCBEZET7VI7XR5N62JFX

not attested not anchored not stored refs pending

Multiplicative dependence among iterated values of rational functions modulo finitely generated groups

Alina Ostafe, Attila B\'erczes, Igor E. Shparlinski, Joseph H. Silverman

arxiv:1811.04971 v1 · 2018-11-12 · 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{WAEI3ADCBEZET7VI7XR5N62JFX}

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	2026-05-18T00:00:45.602403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0088d8062093249fea8fde3d6fb492deae86f35522359b82a7104fced456c41

Aliases

arxiv: 1811.04971 · arxiv_version: 1811.04971v1 · doi: 10.48550/arxiv.1811.04971 · pith_short_12: WAEI3ADCBEZE · pith_short_16: WAEI3ADCBEZET7VI · pith_short_8: WAEI3ADC

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/WAEI3ADCBEZET7VI7XR5N62JFX \
  | 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: b0088d8062093249fea8fde3d6fb492deae86f35522359b82a7104fced456c41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17b864de4e94f24a2da1c6dd5204f45526a2c5c3986eb3a10ef6e660923a3176",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-12T19:23:21Z",
    "title_canon_sha256": "80fc5b7653af2d4f7bfd4a806ea96b5363a95a07244e1ca13ff55e6979c51ff8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.04971",
    "kind": "arxiv",
    "version": 1
  }
}