Pith Number

pith:A4NKVR5D

pith:2022:A4NKVR5DWD2D27CYSHIB2EFWKV

not attested not anchored not stored refs pending

Random quantum circuits are approximate unitary $t$-designs in depth $O\left(nt^{5+o(1)}\right)$

Jonas Haferkamp

arxiv:2203.16571 v3 · 2022-03-30 · 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{A4NKVR5DWD2D27CYSHIB2EFWKV}

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

Long-range nonstabilizerness of topologically encoded states from mutual information

Receipt and verification

First computed	2026-07-05T04:57:06.215355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

071aaac7a3b0f43d7c5891d01d10b6555a4549fc465622ec76855aea77b09ace

Aliases

arxiv: 2203.16571 · arxiv_version: 2203.16571v3 · doi: 10.48550/arxiv.2203.16571 · pith_short_12: A4NKVR5DWD2D · pith_short_16: A4NKVR5DWD2D27CY · pith_short_8: A4NKVR5D

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/A4NKVR5DWD2D27CYSHIB2EFWKV \
  | 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: 071aaac7a3b0f43d7c5891d01d10b6555a4549fc465622ec76855aea77b09ace

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d39bf447aca86f1a05db9c6d1f48a25e40bd540a28933f7c704944b7284b7131",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2022-03-30T18:02:08Z",
    "title_canon_sha256": "a73f810eb1da880260c51537adb72e00a66cb72e5525f722da57a4e02409221b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.16571",
    "kind": "arxiv",
    "version": 3
  }
}