Pith Number

pith:PPBR6BNM

pith:2017:PPBR6BNMMNCKVNTXW5F3MLE3UB

not attested not anchored not stored refs pending

$\beta$-expansion: A Theoretical Framework for Fast and Recursive Construction of Polar Codes

Ganghua Yang, Gaoning He, Ingmar Land, Jean-Claude Belfiore, Jun Wang, Ran Zhang, Rong Li, Wen Tong, Xiaocheng Liu, Ying Chen, Yiqun Ge

arxiv:1704.05709 v1 · 2017-04-19 · cs.IT · math.IT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPBR6BNMMNCKVNTXW5F3MLE3UB}

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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

1 paper in Pith

Improved Logical Error Rate via List Decoding of Quantum Polar Codes

Receipt and verification

First computed	2026-05-18T00:46:06.728980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bc31f05ac6344aab677b74bb62c9ba04a0a9ef6006e95d03e96d7dcf6a32699

Aliases

arxiv: 1704.05709 · arxiv_version: 1704.05709v1 · doi: 10.48550/arxiv.1704.05709 · pith_short_12: PPBR6BNMMNCK · pith_short_16: PPBR6BNMMNCKVNTX · pith_short_8: PPBR6BNM

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/PPBR6BNMMNCKVNTXW5F3MLE3UB \
  | 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: 7bc31f05ac6344aab677b74bb62c9ba04a0a9ef6006e95d03e96d7dcf6a32699

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1279d079f69fe2970541584fcf4afb5abf4013ebfcbf48d49c6b83626670a08",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2017-04-19T12:41:50Z",
    "title_canon_sha256": "d34e6b2cdedc8d593d17177ab3cd5d4c4d224405948824a8229ae9276d52a316"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.05709",
    "kind": "arxiv",
    "version": 1
  }
}