Pith Number

pith:VMS5SZEJ

pith:2026:VMS5SZEJCZ7IWLMAHYCGTFTESS

not attested not anchored not stored refs pending

Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action

Ercai Chen, Xiaoyao Zhou, Yage Liu

arxiv:2605.21048 v1 · 2026-05-20 · 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{VMS5SZEJCZ7IWLMAHYCGTFTESS}

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	2026-05-21T01:05:34.028399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab25d96489167e8b2d803e0469966494b43f8620678bedf251fd3b4ac1981369

Aliases

arxiv: 2605.21048 · arxiv_version: 2605.21048v1 · doi: 10.48550/arxiv.2605.21048 · pith_short_12: VMS5SZEJCZ7I · pith_short_16: VMS5SZEJCZ7IWLMA · pith_short_8: VMS5SZEJ

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/VMS5SZEJCZ7IWLMAHYCGTFTESS \
  | 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: ab25d96489167e8b2d803e0469966494b43f8620678bedf251fd3b4ac1981369

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c4af9357e39f41a592ebff173a0c8bab827a0f3af2aa66cc50f20d54bbe6f7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-20T11:31:35Z",
    "title_canon_sha256": "b3be28425c61a82a6bd5e6418404c92fa6db13c470b272979639c4b5c9ba6b29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21048",
    "kind": "arxiv",
    "version": 1
  }
}