Plain-English reading. This definition gives the library's named construction or computation for “task id”. Task identifier used by the retrieval and verifier ledgers.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Task identifier used by the retrieval and verifier ledgers.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:25. 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 “requested epsilon”. User-requested error tolerance '1e-10'.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. User-requested error tolerance '1e-10'.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:28. 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 “grid point”. Grid point 'x_j = j / 2^n'.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Grid point 'x_j = j / 2^n'.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:31. 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 “cubic amplitude”. Cubic amplitude 'f(x_j) = x_j^3'.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Cubic amplitude 'f(x_j) = x_j^3'.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.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 definition gives the library's named construction or computation for “cubic operator”. The rank-one operator 'O_n = |v_n><0^n|'.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. The rank-one operator 'O_n = |v_n><0^n|'. In column-vector convention this maps the input basis state '|0^n>' to the unnormalized vector with entries '(j / 2^n)^3', and maps every other input basis state to zero.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:43. 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 “cubic norm sq”. Exact rational squared norm of the unnormalized target vector.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Exact rational squared norm of the unnormalized target vector. The analytic normalizer is its square root; this rational quantity is the cheap diagnostic used before any approximate rotation-synthesis route is accepted.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:51. 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 “conservative normalizer”. A conservative rational normalizer.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. A conservative rational normalizer. It is not intended to be optimal; it is a stable placeholder until the approximate synthesis backend proves a sharper normalizer and error bound.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:60. 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 “cubic target”. Operator-first target record used by the ABEIS harness.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Operator-first target record used by the ABEIS harness.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:64. 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 “default required cost”. Resource floor used for the first Scenario 2 run.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Resource floor used for the first Scenario 2 run.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:77. 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 “default policy”. Adaptive search policy for the cubic benchmark.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Adaptive search policy for the cubic benchmark. The zero gate/depth fields in 'defaultRequiredCost' deliberately mean "discover a concrete candidate and then rank it"; the active search is expected to relax from exact to approximate construction after a small exact-search stall window.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:89. 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 “arithmetic cubic default precision”. First arithmetic-route precision seed for Scenario 2.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. First arithmetic-route precision seed for Scenario 2.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:100. 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 “arithmetic cubic layout”. Register layout for the first arithmetic-transduction candidate route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Register layout for the first arithmetic-transduction candidate route. The single signal qubit is the clean block selector. The pure workspace keeps an address copy, reversible square/cube work registers, and fixed-point precision workspace. This is a candidate interface only; it does not certify the arithmetic or rotation subroutines.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:110. 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 “arithmetic cubic circuit”. Oracle-level transcript for the scalable cubic route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Oracle-level transcript for the scalable cubic route. The clean branch is intended to compute 'j / 2^n', reversibly form the cubic fixed-point amplitude, apply one amplitude-transduction rotation, and uncompute the arithmetic workspace. Each label remains a semantic proof obligation.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:122. 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 “arithmetic cubic resource”. Local resource count for the unexpanded oracle-level 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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Local resource count for the unexpanded oracle-level transcript.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:133. 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 “arithmetic cubic normalizer”. Normalizer used by the first arithmetic-transduction route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Normalizer used by the first arithmetic-transduction route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:137. 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 “arithmetic cubic cost”. Candidate score extracted from the arithmetic-route layout and 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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Candidate score extracted from the arithmetic-route layout and transcript.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:141. 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 “arithmetic cubic resource tuple”. Resource tuple in QBE candidate-population order.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Resource tuple in QBE candidate-population order.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:147. 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 “arithmetic cubic claim”. Human-facing construction claim for the first scalable route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Human-facing construction claim for the first scalable route. This claim is an unproved candidate record, not a certified block encoding.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:170. 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 “arithmetic rank one cubic layout”. Rank-one wrapper layout for the arithmetic cubic route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Rank-one wrapper layout for the arithmetic cubic route. The extra pure workspace is reserved for a zero-input filter and row-generation wrapper. This is still an oracle-level interface: it repairs the register shape of the candidate transcript, but it does not certify the wrapper semantics.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:192. 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 “arithmetic rank one cubic circuit”. Rank-one candidate transcript around the arithmetic middle block.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Rank-one candidate transcript around the arithmetic middle block. The first two calls are the missing wrapper from 'CUBIC-CAND-SHAPE-001': reject nonzero input columns from the clean branch, then generate the output row register on the zero-input branch. The final call is a placeholder cleanup for the zero-input filter. The row-generation step is intentionally not uncomputed, because the output row is the system output of the rank-one operator.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:206. 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 “arithmetic rank one cubic resource”. Oracle-level resource count for the rank-one wrapped 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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Oracle-level resource count for the rank-one wrapped transcript.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:214. 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 “arithmetic rank one cubic normalizer”. Normalizer used by the rank-one wrapped arithmetic route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Normalizer used by the rank-one wrapped arithmetic route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:218. 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 “arithmetic rank one cubic cost”. Candidate score for the rank-one wrapped arithmetic route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Candidate score for the rank-one wrapped arithmetic route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:222. 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 “arithmetic rank one cubic resource tuple”. Resource tuple in QBE candidate-population order for the wrapped route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Resource tuple in QBE candidate-population order for the wrapped route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:228. 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 “arithmetic rank one cubic claim”. Human-facing construction claim for the rank-one wrapped scalable route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Human-facing construction claim for the rank-one wrapped scalable route. This still records obligations, not a verified block-encoding certificate.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:258. 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 “hadamard counting cubic workspace”. Workspace seed for the Hadamard-counting mutation.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Workspace seed for the Hadamard-counting mutation. This is an oracle-level interface budget for the reversible cube/comparator workspace. It is not a gate-level implementation of multiplication.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:280. 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 “hadamard counting cubic layout”. Register layout for the exact Hadamard-counting candidate.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Register layout for the exact Hadamard-counting candidate. The signal qubit is the reject flag. Pure ancillas are the nonzero-input flag, the 'R,T' path registers of total width '4*n', and the reversible cube/comparator workspace. Nonzero input columns set the reject signal before the 'nz' cleanup, so the clean projection cannot leak identity entries.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:291. 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 “hadamard counting cubic circuit”. Oracle-level transcript for the Hadamard-counting route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Oracle-level transcript for the Hadamard-counting route. The row XOR is not uncomputed, because it writes the output system row for the rank-one operator. The separate nonzero-column reject signal is applied before the 'nz' cleanup, so nonzero input columns keep a clean-projection rejection witness. The Hadamard layers and reversible arithmetic are still semantic obligations at this interface tier.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:305. 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 “hadamard counting cubic resource”. Oracle-level resource count for the Hadamard-counting route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Oracle-level resource count for the Hadamard-counting route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:336. 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 “hadamard counting cubic normalizer”. Normalizer used by the Hadamard-counting route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Normalizer used by the Hadamard-counting route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:340. 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 “hadamard counting cubic cost”. Candidate score for the Hadamard-counting route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Candidate score for the Hadamard-counting route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:344. 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 “hadamard counting cubic resource tuple”. Resource tuple in QBE candidate-population order.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Resource tuple in QBE candidate-population order.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:350. 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 “hadamard counting cubic claim”. Human-facing construction claim for the Hadamard-counting exact route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Human-facing construction claim for the Hadamard-counting exact route. This is an unproved candidate record, not a certified block encoding.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:378. 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 “hard mode upper agent schedule”. Hard Mode panel escalation schedule.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Hard Mode panel escalation schedule. The four entries are the planned parallel-agent counts for levels 0 through 3. Upper agents should only move to the next level after the active proof leaf has stalled and the reviewer has confirmed that the blocker is not just stale memory.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:401. 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 “hard mode middle agent schedule”.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

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. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:403. 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 “hard mode lower agent schedule”.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

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. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:405. 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 “hard mode exact stall window”. Number of consecutive cycles without a closed leaf before the first escalation.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Number of consecutive cycles without a closed leaf before the first escalation.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:408. 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 “hard mode construction stall window”. Number of consecutive cycles without an improving certified or finite candidate before the next Hard Mode level is considered.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Number of consecutive cycles without an improving certified or finite candidate before the next Hard Mode level is considered.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:414. 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 “hard mode level cycle budget”. Per-level cycle budgets before the upper panel must explicitly review progress.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Per-level cycle budgets before the upper panel must explicitly review progress.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:417. 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 “relaxed epsilon ladder”. Scenario 2 epsilon ladder.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Scenario 2 epsilon ladder. The first entry is the user-requested tolerance. Later entries are relaxed exploratory waypoints used only if the exact or requested-epsilon search stalls; a relaxed waypoint is not a substitute for a certificate at 'requestedEpsilon'.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:425. 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 “initial expected phase”. Current expected phase.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Current expected phase. This is a planning declaration, not a proof of impossibility: it records that exact finite gate synthesis should not consume the full budget before approximate arithmetic/state-preparation search starts.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:448. 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 “rank one clean block contract”. Entrywise clean-block contract for a rank-one cubic candidate.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Entrywise clean-block contract for a rank-one cubic candidate. The first field states the scaled clean first column. The second field states that all other input columns vanish in the clean block. This is a semantic obligation for a future unitary/circuit proof, not a proof that the current oracle labels already realize the contract.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:471. 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 “arithmetic rank one cubic clean block contract”. Candidate-specific clean-block contract for the repaired rank-one route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Candidate-specific clean-block contract for the repaired rank-one route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:478. 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 “hadamard counting cubic clean block contract”. Candidate-specific clean-block contract for the Hadamard-counting route.

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. State-preparation and exact rational Householder developments for the cubic benchmark family.

Technical source note. Candidate-specific clean-block contract for the Hadamard-counting route.

Declaration kind. def.

Source: QuantumBlockEncoding/CubicStatePreparation.lean:515. A commit-pinned external link is added by the publication build when the source exists at the published ref.