Pith Number

pith:4EEHR7YC

pith:1996:4EEHR7YCAFWTCCGQRBRJVHYN7T

not attested not anchored not stored refs pending

Group Representations, Error Bases and Quantum Codes

E. Knill

arxiv:quant-ph/9608049 v1 · 1996-08-29 · 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{4EEHR7YCAFWTCCGQRBRJVHYN7T}

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

3 papers in Pith

Communication Advantages from Quantum Dense Network Coding

Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory

Mutually Unbiased Bases in Composite Dimensions -- A Review

Receipt and verification

First computed	2026-07-04T14:47:05.326651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e10878ff02016d3108d088629a9f0dfccd48d29fca0343eb2c7e54caa816c235

Aliases

arxiv: quant-ph/9608049 · arxiv_version: quant-ph/9608049v1 · doi: 10.48550/arxiv.quant-ph/9608049 · pith_short_12: 4EEHR7YCAFWT · pith_short_16: 4EEHR7YCAFWTCCGQ · pith_short_8: 4EEHR7YC

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/4EEHR7YCAFWTCCGQRBRJVHYN7T \
  | 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: e10878ff02016d3108d088629a9f0dfccd48d29fca0343eb2c7e54caa816c235

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83beedc8a28bdadc8825dae6dd57ba23e756174f35bbc7d9777bf000796160df",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1996-08-29T19:32:40Z",
    "title_canon_sha256": "69be53735330eb70e39239fd0555e82b17ec90f522532a39097fa0094e1f3b81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9608049",
    "kind": "arxiv",
    "version": 1
  }
}