Pith Number

pith:GKWBAGER

pith:2025:GKWBAGERXGPRRT3S2KC76WCVEF

not attested not anchored not stored refs pending

The Shannon-McMillan-Breiman theorem of random dynamical systems for amenable group actions

Bin Zhu, Yuan Lian

arxiv:2506.01805 v1 · 2025-06-02 · 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{GKWBAGERXGPRRT3S2KC76WCVEF}

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	2026-07-05T11:14:19.684011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32ac101891b99f18cf72d285ff5855215eb42e32b90bd3c5f7b7be9c40415591

Aliases

arxiv: 2506.01805 · arxiv_version: 2506.01805v1 · doi: 10.48550/arxiv.2506.01805 · pith_short_12: GKWBAGERXGPR · pith_short_16: GKWBAGERXGPRRT3S · pith_short_8: GKWBAGER

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/GKWBAGERXGPRRT3S2KC76WCVEF \
  | 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: 32ac101891b99f18cf72d285ff5855215eb42e32b90bd3c5f7b7be9c40415591

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "368f74147fcd6f1699421d5f323ad4b3227e53c18eabb1729aac2e4f660790a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-06-02T15:51:28Z",
    "title_canon_sha256": "6da34a7b1f6ee3763172846e46c9d25bde66f5e261d9c5adb23a445f531364c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.01805",
    "kind": "arxiv",
    "version": 1
  }
}