Pith Number

pith:B5BDMF3W

pith:2026:B5BDMF3WQMHH3VYXBGJN7HNN6Y

not attested not anchored not stored refs pending

Asymmetry of Entropy Invariants for Generic Mixing $Z^n$-Actions

Mikhail V. Engelgardt, Valery V. Ryzhikov

arxiv:2606.05619 v1 · 2026-06-04 · 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{B5BDMF3WQMHH3VYXBGJN7HNN6Y}

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	2026-06-05T01:14:56.630526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f42361776830e7dd7170992df9dadf60b21c939cc033b0262a07488c3557912

Aliases

arxiv: 2606.05619 · arxiv_version: 2606.05619v1 · doi: 10.48550/arxiv.2606.05619 · pith_short_12: B5BDMF3WQMHH · pith_short_16: B5BDMF3WQMHH3VYX · pith_short_8: B5BDMF3W

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/B5BDMF3WQMHH3VYXBGJN7HNN6Y \
  | 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: 0f42361776830e7dd7170992df9dadf60b21c939cc033b0262a07488c3557912

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f849f9c41272f5dad6bf1b1c5fe0ec45e6874b97f49272bee853daf8da4856b8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-04T02:43:30Z",
    "title_canon_sha256": "2bacbdf0816bf5660d56f12240e8651b68c0da168d66f55aede1b43ce22429d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05619",
    "kind": "arxiv",
    "version": 1
  }
}