Pith Number

pith:DKSKCPL6

pith:2026:DKSKCPL6RPM764IEOQ5Z3AP3SZ

not attested not anchored not stored refs pending

The natural extension of the $(-\beta)$-transformation

Hiroaki Ito, Hiromi Ei, Shigeki Akiyama

arxiv:2606.23097 v1 · 2026-06-22 · 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{DKSKCPL6RPM764IEOQ5Z3AP3SZ}

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	2026-06-23T03:14:09.719492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1aa4a13d7e8bd9ff7104743b9d81fb9647f2c60b618836b2b42dad170cb4db0e

Aliases

arxiv: 2606.23097 · arxiv_version: 2606.23097v1 · doi: 10.48550/arxiv.2606.23097 · pith_short_12: DKSKCPL6RPM7 · pith_short_16: DKSKCPL6RPM764IE · pith_short_8: DKSKCPL6

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/DKSKCPL6RPM764IEOQ5Z3AP3SZ \
  | 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: 1aa4a13d7e8bd9ff7104743b9d81fb9647f2c60b618836b2b42dad170cb4db0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f13357f308c691ac477031fe7f77b8b78d23693b7a9459120a40974507efb267",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-22T09:41:53Z",
    "title_canon_sha256": "a25bc47ee4f3d484875a161bfca85fbe0cec7ba345f73da16b26d8c48ca9574b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23097",
    "kind": "arxiv",
    "version": 1
  }
}