Pith Number

pith:WUK6KQRP

pith:2026:WUK6KQRPCJTWVAUW72ATUPPEWB

not attested not anchored not stored refs pending

Complex Analysis of Channel Polarization on Discrete BMS Channels

Dongxiao Xu, Holger Boche, Moritz Wiese

Complex analysis yields exact Bhattacharyya parameters for polarized bit-channels on any discrete BMS channel.

arxiv:2605.03805 v2 · 2026-05-05 · cs.IT · math.IT

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\pithnumber{WUK6KQRPCJTWVAUW72ATUPPEWB}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

CE systematically derives analytic expressions for the Bhattacharyya parameters of the bit-channels of a given discrete BMS channel at arbitrary polarization levels.

C2weakest assumption

That the Bhattacharyya parameter admits a natural and useful extension to a broader class of complex-valued channel functionals that preserves the key polarization properties and allows closed-form recursion.

C3one line summary

A new complex-analytic framework derives analytic expressions for Bhattacharyya parameters of polarized bit-channels on discrete BMS channels and provides evidence for extremality of BEC and BSC.

Receipt and verification

First computed	2026-05-20T00:05:45.940980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b515e5422f12676a8296fe813a3de4b043781adc91359d3a225c277a76e7bf3e

Aliases

arxiv: 2605.03805 · arxiv_version: 2605.03805v2 · doi: 10.48550/arxiv.2605.03805 · pith_short_12: WUK6KQRPCJTW · pith_short_16: WUK6KQRPCJTWVAUW · pith_short_8: WUK6KQRP

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/WUK6KQRPCJTWVAUW72ATUPPEWB \
  | 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: b515e5422f12676a8296fe813a3de4b043781adc91359d3a225c277a76e7bf3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b06612b6926e2e24e04968d30ca2d9c9064670075df8b3fd20b74f059c6b560b",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-05T14:31:11Z",
    "title_canon_sha256": "5cd7436b70f4220c98885b12d32b2a949dd9f14bc56965d1c37a27311bed8fb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03805",
    "kind": "arxiv",
    "version": 2
  }
}