Pith Number

pith:GTYB4LZK

pith:2016:GTYB4LZKK4WQC7E2YZKVHVTCXT

not attested not anchored not stored refs pending

Free ergodic $\mathbb{Z}^2$-systems and complexity

Bryna Kra, Van Cyr

arxiv:1602.03439 v1 · 2016-02-10 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTYB4LZKK4WQC7E2YZKVHVTCXT}

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	2026-05-18T01:20:59.935417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34f01e2f2a572d017c9ac65553d662bcc00a48525e024b1a5de832f438d835e4

Aliases

arxiv: 1602.03439 · arxiv_version: 1602.03439v1 · doi: 10.48550/arxiv.1602.03439 · pith_short_12: GTYB4LZKK4WQ · pith_short_16: GTYB4LZKK4WQC7E2 · pith_short_8: GTYB4LZK

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/GTYB4LZKK4WQC7E2YZKVHVTCXT \
  | 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: 34f01e2f2a572d017c9ac65553d662bcc00a48525e024b1a5de832f438d835e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6da0f08ee972d76d9729c43ca6f987912a84ffc81790f5f4c22456fb096ed7d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-02-10T16:45:51Z",
    "title_canon_sha256": "804f9d9bb28951f6fde8818007fe97ea51312d9db2f796f137fa76bb3a9a2049"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.03439",
    "kind": "arxiv",
    "version": 1
  }
}