Pith Number

pith:U74OBOTQ

pith:2007:U74OBOTQGJ435S2KS2HN2RMOIL

not attested not anchored not stored refs pending

Semi-Clifford operations, structure of $\mathcal{C}_k$ hierarchy, and gate complexity for fault-tolerant quantum computation

Bei Zeng, Isaac L. Chuang, Xie Chen

arxiv:0712.2084 v2 · 2007-12-13 · 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{U74OBOTQGJ435S2KS2HN2RMOIL}

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	2026-07-04T17:22:57.979422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7f8e0ba703279becb4a968edd458e42c71f8cc110a69bed7995ad8b174b25be

Aliases

arxiv: 0712.2084 · arxiv_version: 0712.2084v2 · doi: 10.48550/arxiv.0712.2084 · pith_short_12: U74OBOTQGJ43 · pith_short_16: U74OBOTQGJ435S2K · pith_short_8: U74OBOTQ

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/U74OBOTQGJ435S2KS2HN2RMOIL \
  | 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: a7f8e0ba703279becb4a968edd458e42c71f8cc110a69bed7995ad8b174b25be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3281576566a4ec83058645f80a99b71970dee80d5a5a1e808bc9077ed90f62e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2007-12-13T04:59:28Z",
    "title_canon_sha256": "15e22ebb58f133b86fa996aa7a6c47cf07d1530310982356333985513ba4cc9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.2084",
    "kind": "arxiv",
    "version": 2
  }
}