Pith Number

pith:FB22E5FX

pith:2003:FB22E5FXMPKZN3IQU2Z6EGCSAI

not attested not anchored not stored refs pending

A Simple Proof that Toffoli and Hadamard are Quantum Universal

Dorit Aharonov

arxiv:quant-ph/0301040 v1 · 2003-01-09 · 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{FB22E5FXMPKZN3IQU2Z6EGCSAI}

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

10 papers in Pith

On the Complexity of the Circuit Width Problem

From Pauli Strings to Quantum Dynamics: A Unified Characterization

A sharp interaction-degree threshold for simulating QAOA

Ancilla-Error-Transparent Controlled Beam Splitter Gate

AutoQ 2.0: From Verification of Quantum Circuits to Verification of Quantum Programs (Technical Report)

Receipt and verification

First computed	2026-07-04T14:46:05.751211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2875a274b763d596ed10a6b3e2185202362e5cacb418e18f846b26c3fc8c26c8

Aliases

arxiv: quant-ph/0301040 · arxiv_version: quant-ph/0301040v1 · doi: 10.48550/arxiv.quant-ph/0301040 · pith_short_12: FB22E5FXMPKZ · pith_short_16: FB22E5FXMPKZN3IQ · pith_short_8: FB22E5FX

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/FB22E5FXMPKZN3IQU2Z6EGCSAI \
  | 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: 2875a274b763d596ed10a6b3e2185202362e5cacb418e18f846b26c3fc8c26c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4269c82546fc77b19d5123b90e1e3101a6ec058b2d54e4d617c2a1eeb7a93204",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2003-01-09T23:13:49Z",
    "title_canon_sha256": "41656e00ff03f081d15a3e7fddb2b814a6d8d16d2ea9fcaa22ff2e58fd953317"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0301040",
    "kind": "arxiv",
    "version": 1
  }
}