Prove2Me

BDL26 Random Seed Embedding: seed face image

Proved
QEC.Coding.BDL26RandomSeedEmbedding.seed_face_image

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 face image 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#L40-L42

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_face_image (S : OddScale) (f : (state S 0).presentation.Face) :
    tannerFaceImage (state S 0).presentation (seedPoint S) f = {(0 : Space)} := by sorry
Source
https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Coding/FiniteAlternatingConstruction/RandomPerturbation/SeedEmbedding.lean#L40-L42

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