Pith Number

pith:JTLJ4XM5

pith:2017:JTLJ4XM5GCL2AD2P6Y7ZXQID5R

not attested not anchored not stored refs pending

A Note on the Birkhoff Ergodic Theorem

Nikola Sandri\'c

arxiv:1704.03681 v1 · 2017-04-12 · 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{JTLJ4XM5GCL2AD2P6Y7ZXQID5R}

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	2026-05-18T00:46:27.144437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cd69e5d9d3097a00f4ff63f9bc103ec42d846f2486e6f9418529859597002c3

Aliases

arxiv: 1704.03681 · arxiv_version: 1704.03681v1 · doi: 10.48550/arxiv.1704.03681 · pith_short_12: JTLJ4XM5GCL2 · pith_short_16: JTLJ4XM5GCL2AD2P · pith_short_8: JTLJ4XM5

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/JTLJ4XM5GCL2AD2P6Y7ZXQID5R \
  | 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: 4cd69e5d9d3097a00f4ff63f9bc103ec42d846f2486e6f9418529859597002c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c427c5a47bc88edd771819ae38db7383eb3041a48850ff91acef0bb83adcc35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-04-12T09:57:47Z",
    "title_canon_sha256": "dcccf5c9d0ba5887a46ca0bc829a827ef11b2f9e41ecc5a3351608b66dc554a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.03681",
    "kind": "arxiv",
    "version": 1
  }
}