Pith Number

pith:2SWDDZEX

pith:2011:2SWDDZEXIXYYQ7KZHCOQNC7JK5

not attested not anchored not stored refs pending

The monomial representations of the Clifford group

David Gross, D.M. Appleby, Ingemar Bengtsson, Jan-{\AA}ke Larsson, Markus Grassl, Stephen Brierley

arxiv:1102.1268 v2 · 2011-02-07 · quant-ph · 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{2SWDDZEXIXYYQ7KZHCOQNC7JK5}

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.

Cited by

1 paper in Pith

Quantum randomness beyond projective measurements

Receipt and verification

First computed	2026-07-05T04:05:08.753540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4ac31e49745f1887d59389d068be95773afa09a7b5d206f026735d594b595fd

Aliases

arxiv: 1102.1268 · arxiv_version: 1102.1268v2 · doi: 10.48550/arxiv.1102.1268 · pith_short_12: 2SWDDZEXIXYY · pith_short_16: 2SWDDZEXIXYYQ7KZ · pith_short_8: 2SWDDZEX

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/2SWDDZEXIXYYQ7KZHCOQNC7JK5 \
  | 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: d4ac31e49745f1887d59389d068be95773afa09a7b5d206f026735d594b595fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8eaf24cf67edca000623628e6ae8505fde8ed306eb82495dbc5ae4668fa1e21",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-02-07T10:39:37Z",
    "title_canon_sha256": "136abb4ffa473c69bfcfd5bfce4fb10eaff5580212974c6af24b38f985dc1f5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1268",
    "kind": "arxiv",
    "version": 2
  }
}