Pith Number

pith:PTQA5UPJ

pith:2025:PTQA5UPJNMNJNH6MN2WZNIXLAL

not attested not anchored not stored refs pending

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras

Chengming Bai, Guilai Liu, Li Guo, Quan Zhao

arxiv:2509.09884 v1 · 2025-09-11 · math.RA · math.QA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTQA5UPJNMNJNH6MN2WZNIXLAL}

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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.

Cited by

1 paper in Pith

Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras

Receipt and verification

First computed	2026-07-05T12:09:51.406537Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ce00ed1e96b1a969fcc6ead96a2eb02d96f8b39f9469948f3584254c306acf5

Aliases

arxiv: 2509.09884 · arxiv_version: 2509.09884v1 · doi: 10.48550/arxiv.2509.09884 · pith_short_12: PTQA5UPJNMNJ · pith_short_16: PTQA5UPJNMNJNH6M · pith_short_8: PTQA5UPJ

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/PTQA5UPJNMNJNH6MN2WZNIXLAL \
  | 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: 7ce00ed1e96b1a969fcc6ead96a2eb02d96f8b39f9469948f3584254c306acf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7b7aae6bb28d7cb0b8dcd125b05c60234953a25baf536d9131b55afb58ef823",
    "cross_cats_sorted": [
      "math.QA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2025-09-11T22:45:01Z",
    "title_canon_sha256": "d074b84c16ba5cf170fa2effc3f689e85f420ea9982e80fde72505c1bdc715bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.09884",
    "kind": "arxiv",
    "version": 1
  }
}