Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot select basis action eq perm”; the hypotheses and conclusion in the code panel fix its exact scope. The two selected system bits are XORed with the selector, while the sector, selector, and coefficient wires are unchanged.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The two selected system bits are XORed with the selector, while the sector, selector, and coefficient wires are unchanged.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:28. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot select program eval”; the hypotheses and conclusion in the code panel fix its exact scope. Exact matrix semantics of the physical XOR SELECT program.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. Exact matrix semantics of the physical XOR SELECT program.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:39. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot select program no oracle calls”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:65. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot control wires ne target”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:72. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot amplitude angle eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:102. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot amplitude ry eq rotation”; the hypotheses and conclusion in the code panel fix its exact scope. Every exact angle denotes the corresponding T2 amplitude rotation.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. Every exact angle denotes the corresponding T2 amplitude rotation.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:113. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot context index bijective”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:139. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot context equiv apply”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:149. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot middle bits equiv apply”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:161. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot select basis action middle index”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:169. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot select program eval reindexed”; the hypotheses and conclusion in the code panel fix its exact scope. Matrix-level SELECT refinement under the exact middle-register reindex.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. Matrix-level SELECT refinement under the exact middle-register reindex.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:190. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot controlled ry eq amplitude lift”; the hypotheses and conclusion in the code panel fix its exact scope. The generic five-control multiplexor is exactly the T2 amplitude lift after the explicit little-endian product-register reindexing.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The generic five-control multiplexor is exactly the T2 amplitude lift after the explicit little-endian product-register reindexing.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:217. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot selector high low eq prepare”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:270. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin four slot bits equiv symm pack”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:285. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot low context iff”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:291. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot high context iff”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:300. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot selector low eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:309. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot selector high eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:334. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot selector prepare circuit eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:359. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot selector unprepare circuit eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:381. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot amplitude program eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:403. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot amplitude circuit eval reindexed”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:416. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive middle eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:432. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot pair coordinate circuit eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:457. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot pair coordinate basis equiv involutive”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:485. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot symmetry context iff”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:491. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot symmetry prepare circuit eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:505. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot symmetry unprepare circuit eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:534. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive pair eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:554. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive eval reindexed pair”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:582. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot original bits equiv index”; the hypotheses and conclusion in the code panel fix its exact scope. The physical pair-coordinate convention agrees with the original Robin system order and the repository-wide six-wire little-endian convention.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The physical pair-coordinate convention agrees with the original Robin system order and the repository-wide six-wire little-endian convention.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:600. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive eval eq flat unitary”; the hypotheses and conclusion in the code panel fix its exact scope. Exact T3 refinement root: the primitive '{X, RY, RZ, CX}' circuit denotes the XOR four-slot T2 unitary after the explicit little-endian reindexing.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. Exact T3 refinement root: the primitive '{X, RY, RZ, CX}' circuit denotes the XOR four-slot T2 unitary after the explicit little-endian reindexing.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:618. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive program eval”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:644. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive clean block”; the hypotheses and conclusion in the code panel fix its exact scope. The executable primitive circuit has the required exact clean block.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The executable primitive circuit has the required exact clean block.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:662. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive unitary”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:675. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive no oracle calls”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:680. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive resource faithful”; the hypotheses and conclusion in the code panel fix its exact scope. Resource ownership is definitional: no handwritten gate or depth tuple is used by the promoted candidate.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. Resource ownership is definitional: no handwritten gate or depth tuple is used by the promoted candidate.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:699. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. Lean checks the proposition indexed as “warm robin xor four slot primitive block contains target proof”; the hypotheses and conclusion in the code panel fix its exact scope.

Formal status. Compiled theorem in the default ASPBE import surface; the displayed Lean signature is the authoritative claim.

Why it is in this chapter. Paper-facing backend models, source-specific Hermite constructions, and concrete State Preparation / Robin example artifacts.

Technical source note. The source declaration has no docstring. The reader cue above is generated from its kind and name and does not replace the Lean signature.

Declaration kind. theorem.

Source: QuantumBlockEncoding/Robin/SymmetryXorFourSlotPrimitive.lean:711. A commit-pinned external link is added by the publication build when the source exists at the published ref.