Pith Number

pith:4LQPGIAF

pith:1996:4LQPGIAFXLFRXFBHUHAQYQIH5B

not attested not anchored not stored refs pending

Concatenated Quantum Codes

Emanuel Knill, Raymond Laflamme

arxiv:quant-ph/9608012 v1 · 1996-08-08 · 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{4LQPGIAFXLFRXFBHUHAQYQIH5B}

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

5 papers in Pith

Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation

Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction

Coupled-Layer Construction of Quantum Product Codes

Fault-Tolerant One-Shot Entanglement Generation with Constant-Sized Quantum Devices in the Plane

Learning to Concatenate Quantum Codes

Receipt and verification

First computed	2026-07-04T14:47:05.144727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2e0f32005bacb1b9427a1c10c4107e87581adda6b539bb9abc20137a3f4ff04

Aliases

arxiv: quant-ph/9608012 · arxiv_version: quant-ph/9608012v1 · doi: 10.48550/arxiv.quant-ph/9608012 · pith_short_12: 4LQPGIAFXLFR · pith_short_16: 4LQPGIAFXLFRXFBH · pith_short_8: 4LQPGIAF

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/4LQPGIAFXLFRXFBHUHAQYQIH5B \
  | 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: e2e0f32005bacb1b9427a1c10c4107e87581adda6b539bb9abc20137a3f4ff04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4099c4af7cb745e33d229cecac7cf0896ee29090746633e8076f773ca6f20a0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1996-08-08T23:13:46Z",
    "title_canon_sha256": "ebc511219009156310cc7a2773ee71cb5daf84ed449da4f2a236a432db021d4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9608012",
    "kind": "arxiv",
    "version": 1
  }
}