Pith Number

pith:VHBNF2WN

pith:2004:VHBNF2WNGTLKTBYO57RTXDUXGD

not attested not anchored not stored refs pending

Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs

Hartmut Klauck (U Calgary), Robert Spalek (CWI), Ronald de Wolf (CWI)

arxiv:quant-ph/0402123 v2 · 2004-02-18 · 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{VHBNF2WNGTLKTBYO57RTXDUXGD}

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	2026-07-04T14:46:31.668838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9c2d2eacd34d6a9870eefe33b8e9730d3a3766173f3396ff4463547e6554a44

Aliases

arxiv: quant-ph/0402123 · arxiv_version: quant-ph/0402123v2 · doi: 10.48550/arxiv.quant-ph/0402123 · pith_short_12: VHBNF2WNGTLK · pith_short_16: VHBNF2WNGTLKTBYO · pith_short_8: VHBNF2WN

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/VHBNF2WNGTLKTBYO57RTXDUXGD \
  | 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: a9c2d2eacd34d6a9870eefe33b8e9730d3a3766173f3396ff4463547e6554a44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec4bf6c06dc2539dc51fef8952849083c99ed3cdd47abb7a3f12a3212cf7e503",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2004-02-18T15:05:15Z",
    "title_canon_sha256": "4f08ec093f5cd5a39b4408dff4a13ca8c9980848eae94b5ef6578cb7a815edd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0402123",
    "kind": "arxiv",
    "version": 2
  }
}