BDL26 Random Seed Embedding: seed qubit density

Proved

QEC.Coding.BDL26RandomSeedEmbedding.seed_qubit_density

by marwahaha · Nov 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-qecert-4a64933quantum-computingquantum-error-correction

The BDL26 Random Seed Embedding construction uses the seed qubit density property established by this source lemma. The formal statement records the complete hypotheses and conclusion.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Coding/FiniteAlternatingConstruction/RandomPerturbation/SeedEmbedding.lean#L98-L101

Preamble

import Definitions.Def_QEC_Coding_FiniteAlternatingConstruction_RandomPerturbation_PhysicalLocality
import Definitions.Def_QEC_Coding_FiniteAlternatingConstruction_RandomPerturbation_RandomizedEmbeddingStep
import Definitions.Def_QEC_Coding_FiniteAlternatingConstruction_RandomPerturbation_SeedEmbedding
set_option autoImplicit false
noncomputable section
open QEC QEC.Coding QEC.Coding.BDL26RandomSeedEmbedding
open Classical BDL26FiniteTannerSquare BDL26DecodingGraph BDL26ReplacementEmbedding
open BDL26RandomPerturbation BDL26RandomPhysicalLocality BDL26CSSHamiltonian
open Semantics Semantics.Davies
open QEC.Coding.ProbabilisticConstruction.SphericalCap

Formal statement

theorem QEC.Coding.BDL26RandomSeedEmbedding.seed_qubit_density (S : OddScale) (c : Space) :
    ((qubitHits (state S 0).presentation (seedPoint S) (Metric.closedBall c 1)).card : ℝ) ≤ 5 := by sorry

Source

https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Coding/FiniteAlternatingConstruction/RandomPerturbation/SeedEmbedding.lean#L98-L101

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