Pith Number

pith:WRYZRPV6

pith:2019:WRYZRPV6O4ZIMY2EK2QYOYWK7I

not attested not anchored not stored refs pending

Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits

Adam Bene Watts, Avishay Tal, Luke Schaeffer, Robin Kothari

arxiv:1906.08890 v1 · 2019-06-20 · quant-ph · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WRYZRPV6O4ZIMY2EK2QYOYWK7I}

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	2026-05-17T23:42:47.524164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b47198bebe773286634456a18762cafa0cd103ce24b6fc1f42c4f6400a4b9931

Aliases

arxiv: 1906.08890 · arxiv_version: 1906.08890v1 · doi: 10.48550/arxiv.1906.08890 · pith_short_12: WRYZRPV6O4ZI · pith_short_16: WRYZRPV6O4ZIMY2E · pith_short_8: WRYZRPV6

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/WRYZRPV6O4ZIMY2EK2QYOYWK7I \
  | 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: b47198bebe773286634456a18762cafa0cd103ce24b6fc1f42c4f6400a4b9931

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22a40ed5f0c4bc597c4dc601e3af11aa675d36811ad8cf8b64fb4bd742cc8116",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2019-06-20T22:53:06Z",
    "title_canon_sha256": "cf17e9e7bb9d16380154416d890b3ef98cfca8c6d5628d5e29052eecae791976"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.08890",
    "kind": "arxiv",
    "version": 1
  }
}