Pith Number

pith:UAHHDFQY

pith:2026:UAHHDFQYO3PL2T6KGEYYSKQRMY

not attested not anchored not stored refs pending

Emergence of Gamma-Type Upward-Phase Statistics in the Collatz Map: An Effective Poisson Process Mechanism

Weicheng Fu, Xiaobin Liu, Yisen Wang

arxiv:2606.26811 v1 · 2026-06-25 · nlin.CD · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UAHHDFQYO3PL2T6KGEYYSKQRMY}

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	2026-06-26T01:16:00.546900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a00e71961876debd4fca3131892a116629dee6b478ab2311957a2c9c3a9730dd

Aliases

arxiv: 2606.26811 · arxiv_version: 2606.26811v1 · doi: 10.48550/arxiv.2606.26811 · pith_short_12: UAHHDFQYO3PL · pith_short_16: UAHHDFQYO3PL2T6K · pith_short_8: UAHHDFQY

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/UAHHDFQYO3PL2T6KGEYYSKQRMY \
  | 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: a00e71961876debd4fca3131892a116629dee6b478ab2311957a2c9c3a9730dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecb0eda0761d64afed5ba92062e0a215f7c26900882b1326e3487e3a43a9bfa8",
    "cross_cats_sorted": [
      "physics.data-an"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.CD",
    "submitted_at": "2026-06-25T09:51:49Z",
    "title_canon_sha256": "f6113d3ad7e43599b99f083519125cfe4e156a7b3e77a9e5df488f1141f7a16a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26811",
    "kind": "arxiv",
    "version": 1
  }
}