Plain-English reading. This type lists the allowed alternatives for “reconstruction protocol”; its constructors are the cases that downstream code must handle. Whether the natural-language reconstruction was produced without seeing the source prose.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. Whether the natural-language reconstruction was produced without seeing the source prose.

Declaration kind. inductive.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:35. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This type lists the allowed alternatives for “semantic slot”; its constructors are the cases that downstream code must handle. ASPBE-specific theorem slots whose meaning must survive formalization.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. ASPBE-specific theorem slots whose meaning must survive formalization.

Declaration kind. inductive.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:41. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This type lists the allowed alternatives for “fidelity verdict”; its constructors are the cases that downstream code must handle. Slotwise verdict for the complete source-to-Lean-to-text round trip.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. Slotwise verdict for the complete source-to-Lean-to-text round trip.

Declaration kind. inductive.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:58. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This type lists the allowed alternatives for “repair status”; its constructors are the cases that downstream code must handle. Review state of a proposed clarification or theorem repair.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. Review state of a proposed clarification or theorem repair.

Declaration kind. inductive.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:68. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This record groups the data and proof fields needed for “semantic delta”. A proposition-valued field is a requirement until a constructor supplies it. One explicit semantic discrepancy between the source reading and blind reconstruction.

Formal status. Data contract in the default import surface; proposition-valued fields are obligations, not automatically established facts.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. One explicit semantic discrepancy between the source reading and blind reconstruction.

Declaration kind. structure.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:76. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This record groups the data and proof fields needed for “repair proposal”. A proposition-valued field is a requirement until a constructor supplies it. A non-destructive replacement candidate.

Formal status. Data contract in the default import surface; proposition-valued fields are obligations, not automatically established facts.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. A non-destructive replacement candidate. It never mutates 'RoundTripAudit.originalText'.

Declaration kind. structure.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:84. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This record groups the data and proof fields needed for “round trip audit”. A proposition-valued field is a requirement until a constructor supplies it. A theorem-fidelity certificate record.

Formal status. Data contract in the default import surface; proposition-valued fields are obligations, not automatically established facts.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. A theorem-fidelity certificate record. 'originalText' is immutable evidence. 'reconstructedText' must come from the Lean declaration and imported definitions under 'blindLeanOnly'. Any suggested repair is stored separately and requires an independent reviewer.

Declaration kind. structure.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:97. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “admissible”. Minimal admission contract for a publishable semantic round-trip record.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. Minimal admission contract for a publishable semantic round-trip record.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:115. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “published statement”. The statement exposed as source evidence remains the original, never an automatic repair.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. The statement exposed as source evidence remains the original, never an automatic repair.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:127. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “proposed statement”. The repair candidate is available separately for human/source review.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. The repair candidate is available separately for human/source review.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:131. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “requires human review”. Mismatches and underspecified statements must enter the independent review queue.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. Mismatches and underspecified statements must enter the independent review queue.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:135. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “verified operator block encoding round trip”. **Equivalent after elaboration.** The source contract says that a verified exact operator block encoding consists of a candidate unitary plus proofs of unitarity and clean-block containment.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. **Equivalent after elaboration.** The source contract says that a verified exact operator block encoding consists of a candidate unitary plus proofs of unitarity and clean-block containment. The blind reconstruction recovers the same claim while making target dimensions, normalizer, layout, circuit, resources, and 'layoutMatches' explicit. No repair is proposed.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:156. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “approximate block encoding norm round trip”. **Lean conclusion is weaker than the public analytic formula.** The public route states '‖A - α Π U Π†‖ ≤ ε' in a declared norm and register convention.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. **Lean conclusion is weaker than the public analytic formula.** The public route states '‖A - α Π U Π†‖ ≤ ε' in a declared norm and register convention. The current Lean interface stores 'epsilon' and an arbitrary proposition 'approximationBound'; it deliberately does not yet identify that proposition with a concrete norm, projector, or register order. The repair proposal lists what must be fixed before a theorem is advertised as an analytic approximate block encoding.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:184. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “verified state preparation round trip”. **Equivalent after elaboration.** State preparation is reconstructed as a proof that the target is normalized, the candidate matrix is unitary, and its first computational-basis column equals the target amplitudes.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. **Equivalent after elaboration.** State preparation is reconstructed as a proof that the target is normalized, the candidate matrix is unitary, and its first computational-basis column equals the target amplitudes. This is exactly the finite-matrix form of 'U |0…0⟩ = |ψ⟩'; no extra assumption or weakened conclusion appears.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:227. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “one term robin claim round trip”. **Paper theorem is not yet reconstructed as a proved block encoding.** The GHL source-facing branch records the one-term Robin claim, normalizer, register and resource formulas, and the full theorem-facing transcript.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. **Paper theorem is not yet reconstructed as a proved block encoding.** The GHL source-facing branch records the one-term Robin claim, normalizer, register and resource formulas, and the full theorem-facing transcript. The blind reconstruction also sees the explicit repository boundary: matrix-level oracle correctness and the claimed resource theorem are not yet proved, and the active seven-gate backend is not identical to the full source transcript. The proposed repair prevents a compiled skeleton from being described as a completed paper theorem.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:256. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “candidate improvement round trip”. **Source wording is underspecified without a correctness fibre.** 'BlockEncodingCost.betterThan' proves only a lexicographic comparison of gate count, depth, auxiliary qubits, and unresolved oracle calls.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. **Source wording is underspecified without a correctness fibre.** 'BlockEncodingCost.betterThan' proves only a lexicographic comparison of gate count, depth, auxiliary qubits, and unresolved oracle calls. It does not say that two candidates encode the same target under the same normalization, projection/error convention, or that both candidates are semantically certified. Any natural-language claim that one algorithm is better must add those assumptions.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:307. A commit-pinned external link is added by the publication build when the source exists at the published ref.

Plain-English reading. This definition gives the library's named construction or computation for “semantic round trip registry”. The initial public semantic-fidelity registry shown as declaration leaves in the Underlying Lean Graph.

Formal status. Compiled declaration in the default ASPBE import surface; its kind and displayed Lean type determine how it may be used.

Why it is in this chapter. Typed controller state, agent contracts, literature memory, open-problem records, and source-to-Lean semantic-fidelity audits.

Technical source note. The initial public semantic-fidelity registry shown as declaration leaves in the Underlying Lean Graph. Two core contracts round-trip faithfully; three records enter the review queue because an analytic norm bridge, a paper theorem closure, or a same-target premise is still required.

Declaration kind. def.

Source: QuantumBlockEncoding/SemanticFidelityEvidence.lean:343. A commit-pinned external link is added by the publication build when the source exists at the published ref.