Pith Number

pith:6TOKQKTB

pith:2006:6TOKQKTBGLXLCEOHTG6OBKHP2S

not attested not anchored not stored refs pending

Time Optimal Unitary Operations

Akio Hosoya, Alberto Carlini, Tatsuhiko Koike, Yosuke Okudaira

arxiv:quant-ph/0608039 v4 · 2006-08-04 · 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{6TOKQKTBGLXLCEOHTG6OBKHP2S}

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	2026-05-18T02:32:31.815929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4dca82a6132eeb111c799bce0a8efd4891e54a7c596df00a3d1f98bce0c69a2

Aliases

arxiv: quant-ph/0608039 · arxiv_version: quant-ph/0608039v4 · doi: 10.48550/arxiv.quant-ph/0608039 · pith_short_12: 6TOKQKTBGLXL · pith_short_16: 6TOKQKTBGLXLCEOH · pith_short_8: 6TOKQKTB

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/6TOKQKTBGLXLCEOHTG6OBKHP2S \
  | 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: f4dca82a6132eeb111c799bce0a8efd4891e54a7c596df00a3d1f98bce0c69a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a55b96c8dbbac114a0c2c523b358ee27d8cb928d7f0072fba99e37a4dfa349c8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2006-08-04T07:44:46Z",
    "title_canon_sha256": "ee99661ba13950b324dc7b0544c79bd62c3d1b58895b36a8ad404e92b77002a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0608039",
    "kind": "arxiv",
    "version": 4
  }
}