Pith Number

pith:2UXOU6C7

pith:2026:2UXOU6C76ELFNVIRIIHQRBI7LT

not attested not anchored not stored refs pending

Structure of Clifford groups of composite finite quantum systems

Ji\v{r}\'i Tolar, Miroslav Korbel\'a\v{r}

arxiv:2606.08215 v1 · 2026-06-06 · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2UXOU6C76ELFNVIRIIHQRBI7LT}

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	2026-06-09T01:05:30.298800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d52eea785ff11656d511420f08851f5cdc667a1120e152f10d721b0dd0e92c5e

Aliases

arxiv: 2606.08215 · arxiv_version: 2606.08215v1 · doi: 10.48550/arxiv.2606.08215 · pith_short_12: 2UXOU6C76ELF · pith_short_16: 2UXOU6C76ELFNVIR · pith_short_8: 2UXOU6C7

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/2UXOU6C76ELFNVIRIIHQRBI7LT \
  | 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: d52eea785ff11656d511420f08851f5cdc667a1120e152f10d721b0dd0e92c5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc238a142e698408c5891c9542848d90a10c294ccfdd1aeb7a5f428d11e9580f",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-06T14:58:46Z",
    "title_canon_sha256": "8838c4facf421341723056d34e8dcded32541d6665d1914a1313d8c876e40ec7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08215",
    "kind": "arxiv",
    "version": 1
  }
}