Pith Number

pith:DNEO4BSJ

pith:2015:DNEO4BSJEHOKUSJH7XUJMXUUKN

not attested not anchored not stored refs pending

Birkhoff sum fluctuations in substitution dynamical systems

Elliot Paquette, Younghwan Son

arxiv:1505.01428 v1 · 2015-05-06 · math.DS · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DNEO4BSJEHOKUSJH7XUJMXUUKN}

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	2026-05-18T02:16:49.382572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b48ee064921dcaa4927fde8965e9453659eaec9f71ff7c713382bf60c458b4b

Aliases

arxiv: 1505.01428 · arxiv_version: 1505.01428v1 · doi: 10.48550/arxiv.1505.01428 · pith_short_12: DNEO4BSJEHOK · pith_short_16: DNEO4BSJEHOKUSJH · pith_short_8: DNEO4BSJ

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/DNEO4BSJEHOKUSJH7XUJMXUUKN \
  | 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: 1b48ee064921dcaa4927fde8965e9453659eaec9f71ff7c713382bf60c458b4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72d1112607ce5abc907d7e3957c1aa6ae3edf4d49e7ad920128693101816d22d",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-05-06T16:46:33Z",
    "title_canon_sha256": "9aa66a83acf5b15ff4dd9c99ab45c249ab84892323ec878e7ff15e256bf90749"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01428",
    "kind": "arxiv",
    "version": 1
  }
}