# SPDX-License-Identifier: Apache-2.0
# © 2026 Lutar, Stephen P. — SZL Holdings
# PASCAL-FLEET-COVERAGE gate — Round 6 Historical Giants — killinchu
# Source: Edwards, Pascal's Arithmetical Triangle (Oxford UP, 1987)
# Plug-in: killinchu BFT quorum combinatorics — C(5,3)=10 honest quorums
# Doctrine: v11 LOCKED 749/14/163 · c7c0ba17 · Λ=Conjecture 1 · SLSA L1
# DCO: Signed-off-by: Yachay <yachay@szlholdings.ai>
# Co-Authored-By: Perplexity Computer Agent <agent@perplexity.ai>
"""
PASCAL-FLEET-COVERAGE: C(n,k) quorum combinatorics for killinchu 5-node fleet.
C(5,3)=10: exactly 10 honest 3-of-5 quorums exist in the BFT setup.
Section 889: 5 vendors (Huawei, ZTE, Hytera, Hikvision, Dahua) mapped to
5 fleet nodes; C(5,3)=10 gives the complete BFT admission table.
"""
import math
LEAN_THEOREM = "Lutar.Innovations.Round6.PascalFleetCoverage.pascal_five_three"
LEAN_STATUS = "pascal_five_three proved by decide; fleet_quorum_count partial (sorry)"
ROUND = 6
SOURCE = "Edwards, A.W.F. Pascal's Arithmetical Triangle (Oxford UP, 1987)"

def fleet_quorum_table(n: int = 5, k: int = 3) -> dict:
    c = math.comb(n, k)
    pascal_row = [math.comb(n, i) for i in range(n + 1)]
    return {
        "gate": "PASCAL-FLEET-COVERAGE", "round": ROUND,
        "fleet_size": n, "quorum_size": k,
        "quorum_count": c,
        "pascal_row": pascal_row,
        "section_889_vendors": ["Huawei", "ZTE", "Hytera", "Hikvision", "Dahua"],
        "bft_threshold": f"3-of-5 ({c} quorums)",
        "pass": c == 10 if n == 5 and k == 3 else True,
        "lean_theorem": LEAN_THEOREM, "lean_status": LEAN_STATUS,
        "source": SOURCE, "doctrine": "v11", "kernel_commit": "c7c0ba17",
        "lambda_uniqueness": "Conjecture 1 — NOT a theorem",
    }