Pith Number

pith:WNTKIUW2

pith:2013:WNTKIUW2JUBY2QRVIFIULELQQR

not attested not anchored not stored refs pending

A family of rotation numbers for discrete random dynamics on the circle

Christian S. Rodrigues, Paulo R. C. Ruffino

arxiv:1308.1349 v2 · 2013-08-06 · 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{WNTKIUW2JUBY2QRVIFIULELQQR}

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	2026-05-18T02:25:40.543269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b366a452da4d038d42354151459170846b111cc57ef9f76df5a9a10b5c267234

Aliases

arxiv: 1308.1349 · arxiv_version: 1308.1349v2 · doi: 10.48550/arxiv.1308.1349 · pith_short_12: WNTKIUW2JUBY · pith_short_16: WNTKIUW2JUBY2QRV · pith_short_8: WNTKIUW2

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/WNTKIUW2JUBY2QRVIFIULELQQR \
  | 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: b366a452da4d038d42354151459170846b111cc57ef9f76df5a9a10b5c267234

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6628f2e4bc5ff278285ae4cf57768935d483253a7c509297d9fc612532e18d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-08-06T17:05:47Z",
    "title_canon_sha256": "f0871c39f0fb7cd10c138faad7341b9158d6c74594e62eb849a5123bfbcf525b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1349",
    "kind": "arxiv",
    "version": 2
  }
}