Pith Number

pith:7FPAS3U2

pith:2015:7FPAS3U2SXZ3LNEZCZAXQXNIHD

not attested not anchored not stored refs pending

Rotational beta expansion: Ergodicity and Soficness

Jonathan Caalim, Shigeki Akiyama

arxiv:1502.01793 v3 · 2015-02-06 · math.DS · 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{7FPAS3U2SXZ3LNEZCZAXQXNIHD}

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	2026-05-18T01:33:06.341752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f95e096e9a95f3b5b4991641785da838f51a75c4dea7e4940daa2fb89da4f352

Aliases

arxiv: 1502.01793 · arxiv_version: 1502.01793v3 · doi: 10.48550/arxiv.1502.01793 · pith_short_12: 7FPAS3U2SXZ3 · pith_short_16: 7FPAS3U2SXZ3LNEZ · pith_short_8: 7FPAS3U2

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/7FPAS3U2SXZ3LNEZCZAXQXNIHD \
  | 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: f95e096e9a95f3b5b4991641785da838f51a75c4dea7e4940daa2fb89da4f352

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0058476cd111434998c992cd12def54fc4f94d683073bdeaa9cb17a0e2af21e0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-02-06T04:54:25Z",
    "title_canon_sha256": "aa77e57011bcf6940b49046a29ac1cd869bc7f4c4e84a582ea56bc8c2148639b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01793",
    "kind": "arxiv",
    "version": 3
  }
}