Pith Number

pith:BYWE6L4E

pith:2003:BYWE6L4EXAOPR27BRX4OPB6KQN

not attested not anchored not stored refs pending

Bounds on the Power of Constant-Depth Quantum Circuits

Frederic Green, Stephen Fenner, Steven Homer, Yong Zhang

arxiv:quant-ph/0312209 v2 · 2003-12-28 · 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{BYWE6L4EXAOPR27BRX4OPB6KQN}

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

Witnessing the architecture of quantum circuits

Receipt and verification

First computed	2026-07-04T14:46:29.572851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e2c4f2f84b81cf8ebe18df8e787ca835debd22ba4178613fb8f439a20b67706

Aliases

arxiv: quant-ph/0312209 · arxiv_version: quant-ph/0312209v2 · doi: 10.48550/arxiv.quant-ph/0312209 · pith_short_12: BYWE6L4EXAOP · pith_short_16: BYWE6L4EXAOPR27B · pith_short_8: BYWE6L4E

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/BYWE6L4EXAOPR27BRX4OPB6KQN \
  | 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: 0e2c4f2f84b81cf8ebe18df8e787ca835debd22ba4178613fb8f439a20b67706

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d0dbcf5d66cc1ee15f8a96a00264580c6d0ad3cd049f32815ac85a7f9315756",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2003-12-28T20:34:58Z",
    "title_canon_sha256": "e1d2730f35234b63127b6b0b3ce9d8e37f9c35374caa3d569a324c1ea28e677b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0312209",
    "kind": "arxiv",
    "version": 2
  }
}