Pith Number

pith:YF57X57F

pith:2026:YF57X57F55CLKYIQBYFX7IEBUL

not attested not anchored not stored refs pending

Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning

Andrzej Cichocki, Piergiulio Tempesta

arxiv:2603.08651 v2 · 2026-03-09 · cs.LG · hep-th · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YF57X57F55CLKYIQBYFX7IEBUL}

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	2026-06-01T02:03:36.742913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c17bfbf7e5ef44b561100e0b7fa081a2d655164821d816904f820c1d6f23aedd

Aliases

arxiv: 2603.08651 · arxiv_version: 2603.08651v2 · doi: 10.48550/arxiv.2603.08651 · pith_short_12: YF57X57F55CL · pith_short_16: YF57X57F55CLKYIQ · pith_short_8: YF57X57F

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/YF57X57F55CLKYIQBYFX7IEBUL \
  | 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: c17bfbf7e5ef44b561100e0b7fa081a2d655164821d816904f820c1d6f23aedd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dfc150808fcad505f11d10cc15c3eb0ab7e8c57148dfebffbe8ad88d78d5365",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-09T17:31:03Z",
    "title_canon_sha256": "134918d0e75c727f1017542956f4ef657244d15e32b27a02357c0148d7b8d37d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.08651",
    "kind": "arxiv",
    "version": 2
  }
}