Pith Number

pith:RZZ2GM4H

pith:2015:RZZ2GM4HSBUPAIEKZ3GLFZJBGF

not attested not anchored not stored refs pending

Deformed Covariant Quantum Phase Spaces as Hopf Algebroids

Jerzy Lukierski, Mariusz Woronowicz, Zoran Skoda

arxiv:1507.02612 v4 · 2015-07-09 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RZZ2GM4HSBUPAIEKZ3GLFZJBGF}

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	2026-05-18T01:31:10.711343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e73a333879068f0208aceccb2e5213165779876b73a6941556080a36d1fae3a

Aliases

arxiv: 1507.02612 · arxiv_version: 1507.02612v4 · doi: 10.48550/arxiv.1507.02612 · pith_short_12: RZZ2GM4HSBUP · pith_short_16: RZZ2GM4HSBUPAIEK · pith_short_8: RZZ2GM4H

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/RZZ2GM4HSBUPAIEKZ3GLFZJBGF \
  | 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: 8e73a333879068f0208aceccb2e5213165779876b73a6941556080a36d1fae3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1cda0f695db89182058d24d48be6d814e3e6823c96a1f44f663973c9dcccd91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2015-07-09T17:39:28Z",
    "title_canon_sha256": "18b8b5cd0c8864e0f7a4bf03380c87c6d904ddd7053203d2d435213b8795cc5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02612",
    "kind": "arxiv",
    "version": 4
  }
}