Pith Number

pith:5RHPLWKZ

pith:2015:5RHPLWKZP6PBA5FVBSCWH2FAUN

not attested not anchored not stored refs pending

Multifractal analysis of the divergence points of Birkhoff averages in $beta$-dynamical systems

Xiaojun Zhao, Yuanhong Chen, Zhenliang Zhang

arxiv:1512.09205 v1 · 2015-12-31 · 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{5RHPLWKZP6PBA5FVBSCWH2FAUN}

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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	2026-05-18T01:23:32.996630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec4ef5d9597f9e1074b50c8563e8a0a36e2ebb871f5633d6384b9950e4d91478

Aliases

arxiv: 1512.09205 · arxiv_version: 1512.09205v1 · doi: 10.48550/arxiv.1512.09205 · pith_short_12: 5RHPLWKZP6PB · pith_short_16: 5RHPLWKZP6PBA5FV · pith_short_8: 5RHPLWKZ

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/5RHPLWKZP6PBA5FVBSCWH2FAUN \
  | 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: ec4ef5d9597f9e1074b50c8563e8a0a36e2ebb871f5633d6384b9950e4d91478

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98e9f5a1a33bd1624343aff3bfa85af90ba1c65220c9eb25b81de1ebcd8f57c6",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-12-31T03:10:32Z",
    "title_canon_sha256": "709e132c48b3c69c94cab41082f385e2028efa4b5a6e29f9a754f6e6a5ef7c2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09205",
    "kind": "arxiv",
    "version": 1
  }
}