{
  "schema_version": 1,
  "query": "",
  "route_id": "spw-uncompute",
  "truth_boundary": "Curated retrieval packet, not an execution result or Lean implication. Hyperedge tails are conjunctive. Check exact source, input/oracle/phase/norm/resource contracts before reuse.",
  "families": [
    {
      "id": "family:reachable-branch-recovery",
      "label": "Recoverable history on reachable states",
      "domains": [
        "concept:complexity",
        "concept:verification"
      ],
      "tags": [
        "uncompute",
        "divsteps",
        "history",
        "reachable",
        "proof digestion"
      ],
      "question": "When can a computation recover its branch decisions without a full history stack?",
      "formula": "b=\\operatorname{bit}_{j-1}(g_v^\\prime q^{-1}\\bmod 2^j)",
      "mechanism": "Recover a branch only after a global reachable-state invariant makes the post-step state distinguish the alternatives. Compile and clear the decoder separately.",
      "assumptions": [
        "Pinned initialization and exact signed recurrence",
        "Full invariant and decoder dependencies; odd modulus and valuation conditions are not disposable",
        "Physical register refinement, phase/cleanup and actual gate costs remain separate"
      ],
      "proof_steps": [
        "Audit Appendix A and existing upstream proofs, preserving their actual hypotheses.",
        "Check invariant preservation and low-bit decoding as distinct suppliers.",
        "Connect the decoded bit to inverse control and ancilla cleanup in the actual circuit; then count costs."
      ],
      "lean_refs": [],
      "source_ids": [
        "gu-kemeny-yelin-lukin-2026-uncompute",
        "uncompute-upstream-64b5a13"
      ],
      "boundary": "Proposed local intake; existing upstream proof names are not new ASPBE certificates, and recurrence correctness is not a whole quantum circuit theorem.",
      "technical_card": {
        "id": "tl-reachable-branch-recovery",
        "source_ids": [
          "gu-kemeny-yelin-lukin-2026-uncompute",
          "uncompute-upstream-64b5a13"
        ],
        "statement": "Use a proved reachable-state invariant to recover a prior branch from the updated state; supply the gate-level inverse/cleanup bridge separately.",
        "lean_decl": [],
        "lean_status": "obligation",
        "used_by": [
          "spw-uncompute"
        ],
        "dependencies": [
          "family:matrix-contract",
          "family:charged-access"
        ],
        "next_action": "Audit full upstream Recovery.lean and its imports, then compile an isolated Lean4.33.0 adaptation with explicit provenance before local admission.",
        "tags": [
          "uncompute",
          "reachable invariant",
          "source-first"
        ],
        "failure_modes": [
          "Applying the decoder to arbitrary unreachable states.",
          "Reading a branch bit correctly but failing to clear its temporary register.",
          "Counting external Lean proofs as local compilation or whole-circuit resource closure."
        ]
      }
    },
    {
      "id": "family:matrix-contract",
      "label": "Finite matrices, norms and registers",
      "domains": [
        "concept:matrix-analysis"
      ],
      "tags": [
        "norm",
        "adjoint",
        "matrix",
        "register",
        "normalization"
      ],
      "question": "Are dimensions, basis order, scalar field and selected subspace fixed?",
      "formula": "U^† U=I,\\qquad \\Pi U\\Pi^†=A/\\alpha",
      "mechanism": "Use matrix-entry and state-action contracts before optimizing circuits. A first column and an entire projected block are different targets.",
      "assumptions": [
        "Finite dimensions and explicit little-/big-endian conversion",
        "Positive normalizer; selected input and output ancilla states",
        "Named vector/operator norm and exact versus approximate tolerance"
      ],
      "proof_steps": [
        "Name the basis equivalence and the clean projector.",
        "Prove unitarity independently of the target action.",
        "Evaluate all requested entries, not only a finite diagnostic subset."
      ],
      "lean_refs": [
        "QuantumBlockEncoding.VerifiedStatePreparation"
      ],
      "source_ids": [],
      "boundary": "A structure accepting a proposition is an interface, not an unconditional construction theorem."
    },
    {
      "id": "family:charged-access",
      "label": "Charged access and finite-precision compilation",
      "domains": [
        "concept:complexity",
        "concept:matrix-analysis"
      ],
      "tags": [
        "QRAM",
        "QROM",
        "oracle",
        "T-count",
        "precision",
        "lower-bound",
        "cost",
        "classical"
      ],
      "question": "Does a query or symbolic gate hide the dominant work?",
      "formula": "T_{\\rm total}=T_{\\rm preprocessing}+Q\\,T_{\\rm oracle}+T_{\\rm synthesis}+T_{\\rm readout}",
      "mechanism": "Separate descriptions, arithmetic operations, bit operations, logical rotations, T/Toffoli gates, depth, connectivity and ancillas. Compare only matching models.",
      "assumptions": [
        "Input encoding and precision specified",
        "One cost model for both upper and lower bounds",
        "Initialization, maintenance, amplification and measurements charged"
      ],
      "proof_steps": [
        "Freeze the access model before optimizing.",
        "Bind costs to actual data producers and primitive lists.",
        "Budget each numerical error and then sum compositional errors."
      ],
      "lean_refs": [
        "QuantumBlockEncoding.HermiteFiniteNorm.norm_arithmetic_budget"
      ],
      "source_ids": [
        "zhang-yuan-2024",
        "yuan-zhang-2023"
      ],
      "boundary": "The local norm theorem is only a substrate. It is not the entire displayed end-to-end cost decomposition certified in Lean."
    }
  ],
  "routes": [
    {
      "id": "spw-uncompute",
      "title": "Uncompute: digesting discovered reversible circuits",
      "priority": 0,
      "status": "research-target",
      "setting_id": "setting:pinned-kickmix-clean-phase-trajectory",
      "formula": "\\text{reachable invariant}\\;\\land\\;\\text{branch decoder}\\;\\land\\;\\text{circuit refinement}\\;\\Longrightarrow\\;\\text{clean reversible implementation}",
      "goal": "First research priority: digest the whole pinned paper and its existing proofs into readable, audited mechanisms, then use them in controlled SP/BE construction-evolution experiments. Start with Appendix A branch recovery and the DQI theorem boundary, then connect real circuit semantics, error and resources; do not stop at a toy arithmetic identity or claim a resource improvement before a matched-contract comparison.",
      "motivation": "A circuit can output correct bits yet fail coherently through a wrong phase or dirty workspace. Explain the reusable construction before exposing the implementation proof forest.",
      "input_model": "Pinned paper v1 and author code commit 64b5a13aa249f1360846657392e6c66817b26d0f. Explicit bit widths, registers, signed arithmetic, phase, measurement records, allowed input subspace, failure distribution and actual emitted operations. Each SP/BE experiment additionally freezes the target state/operator, oracle access, error norm, precision, success probability and comparison baseline before proposing circuits.",
      "assumptions": [
        "Keep Lean 4.33.0 locally; upstream 4.32.2 and 4.33.1 proofs need explicit compatibility checks.",
        "Reachable-state invariants must be proved from initialization, not added as convenient final circuit hypotheses.",
        "Do not replace phase and cleanup checks by output-bit tests, or random tests by universal certificates.",
        "Retain separate native-certificate trust, primality, code-distance, collision, statistical and circuit-to-oracle obligations.",
        "Workers never modify the trusted verifier, acceptance anchors, scoring, benchmark split or historical logs. Workflow variants require controlled experiments.",
        "A distribution-dependent failure allowance or small error on one initial state is not a uniform operator-norm block-encoding guarantee."
      ],
      "target_bound": "First deliver a source-faithful, independently reviewed 4.33.0 adaptation and exact source-to-Lean crosswalk; subsequently certify the missing gate/record/cleanup and cost bridges. Then evaluate actual SP/BE candidates under matched contracts and preserve both improvements and negative results. Author results remain author results; no new best-known circuit is promised.",
      "known_boundary": "No new ASPBE Lean closure yet. Upstream recurrence/DQI proofs do not certify all eight circuit tasks. A 590-step worst-case result does not accept the 533-step failure-budget circuit. TQ is a paper objective, not a replacement for ASPBE correctness-first resource contracts.",
      "families": [
        "family:reachable-branch-recovery",
        "family:matrix-contract",
        "family:charged-access"
      ],
      "source_ids": [
        "gu-kemeny-yelin-lukin-2026-uncompute",
        "uncompute-upstream-64b5a13"
      ],
      "lean_refs": [],
      "steps": [
        {
          "id": "upstream-adaptation",
          "target": "Pin and audit the actual upstream theorem interfaces before adapting them to Lean4.33.0.",
          "acceptance": "Compile exact adapted modules; audit axioms, binders, definitions, licenses and source graph; preserve author credit and publish the compatibility delta."
        },
        {
          "id": "reachable-decoder",
          "target": "Close the Appendix A reachability-to-decoder chain, then its actual reversible register implementation.",
          "acceptance": "Initialization/step, determinant/parity and window suppliers discharge the decoder premises. Include zero/frozen/signed cases and exact cleanup; no arbitrary-state strengthening."
        },
        {
          "id": "dqi-bridge",
          "target": "Audit DQI strict-distance and boundary regimes and connect the implementation to their oracle hypotheses.",
          "acceptance": "Keep strict inequality, clean relocation, record leakage, collision and profile residual distinct. Prove the circuit-to-oracle refinement instead of assuming the desired output."
        },
        {
          "id": "case-family",
          "target": "Digest numerical evaluation, chemistry SELECT/QROM and lattice-group constructions in dependency-ready batches.",
          "acceptance": "Every claimed result has source coverage, exact finite-bit/error/resource contract, checked Lean scope and independently reproduced executable evidence."
        },
        {
          "id": "function-oracle-spbe",
          "target": "Planned first construction loop: finite-bit function oracle -> controlled amplitude transduction -> uncompute -> state preparation or diagonal block encoding. Choose one source-backed HHL, Gaussian or Coulomb case after checking existing library interfaces.",
          "acceptance": "Prove the actual output action, coherent relative phase, domain/scaling and workspace restoration. Charge finite-bit arithmetic and rotation synthesis; for SP also retain normalization, success probability and amplification cost. A function evaluator alone does not close SP or BE."
        },
        {
          "id": "prepare-select-lab",
          "target": "Planned second construction loop: proof-guided LCU PREPARE-SELECT optimization, using the paper's alias-SELECT case as a source-backed entry point rather than assuming an entire chemistry algorithm is certified.",
          "acceptance": "Freeze coefficients, normalization, oracle contracts and error; compare real alias/QROM/selection/cleanup variants without changing that target. Supply PREPARE, SELECT and unprepare dependencies internally and retain the full resource tuple."
        },
        {
          "id": "reader",
          "target": "Publish a compressed construction spine with lossless source and proof drill-down.",
          "acceptance": "Independent reader can recover registers, phases, cleanup, error, cost tier and remaining obligations; no declaration-count or sample-pass proxy."
        }
      ],
      "next": "Complete independent source-topology and source/formal reconciliation for the fixed upstream modules, retaining separate compatibility-build evidence. Freeze one dependency-ready SP/BE experiment and its baseline before proposal search; no production proof-tree changes until the current bindings are stable.",
      "lower_bound": {
        "status": "model-definition-pending",
        "task": "Paper resource improvements are instance/model comparisons, not universal optimality or a poly(n) state-preparation theorem.",
        "comparison_key": "setting:pinned-kickmix-clean-phase-trajectory"
      },
      "benchmarks": [
        "Appendix A: reachable negative-counter nonswap, including frozen and signed cases",
        "DQI: strict dual distance versus the Reed-Solomon boundary; no global-isometry shortcut",
        "Methods: correct bits with incorrect phase or dirty record must fail"
      ],
      "reading_layers": [
        {
          "title": "01 · The question",
          "summary": "How can an automatically proposed circuit become a trustworthy SP/BE construction?",
          "items": [
            "Follow data, phase and garbage separately. Start with the contract, not theorem names.",
            "The planned laboratory follows a visible loop: freeze the contract -> propose a circuit -> independently check and cost it -> prove its symbolic guarantees -> compare -> mutate or cross over a named mechanism."
          ]
        },
        {
          "title": "02 · The mechanisms",
          "summary": "Route data through a shared kernel; recover history from a proved invariant; account for permitted failure.",
          "items": [
            "These are techniques to audit under their own promises, not automatic substitutions into a state-preparation route.",
            "Conditional routing shares an arithmetic kernel; branch recovery reconstructs a decision from a proved reachable-state invariant; measurement-based cleanup needs its own feedback and phase semantics.",
            "A mutation changes one specified mechanism. A crossover combines compatible verified interfaces; concatenating two proposals does not transfer a certificate."
          ]
        },
        {
          "title": "03 · The mathematical suppliers",
          "summary": "Read the source construction and its complete AND dependencies.",
          "items": [
            "Appendix A: initialization and step -> determinant/parity and window invariant -> decoder -> finite-dependence/depth-two consumers.",
            "Termination is a separate certificate branch; it is not a prerequisite for the local decoder.",
            "SP/diagonal BE needs function evaluation AND amplitude transduction AND uncomputation AND the relevant error/success guarantees. LCU needs PREPARE AND SELECT AND unprepare, with coefficient/phase and normalization conventions. These are planned integration chains, not newly certified graph edges."
          ]
        },
        {
          "title": "04 · The evidence",
          "summary": "Open upstream Lean first, then the local compatibility and independent acceptance records as they become available.",
          "items": [
            "Upstream 4.32.2/4.33.1 is not local 4.33.0 acceptance. An isolated compatibility compile is not local publication admission or a circuit certificate.",
            "Circuit refinement, statistical confidence, instance constants and resource counts retain separate open gates.",
            "Correctness is a gate before resource comparison. Record oracle construction/calls, classical preprocessing/storage, Toffoli and other gates, depth, peak qubits, cleanup, precision and SP success/amplification. TQ alone is not the objective.",
            "Compare only matched domains, error norms, precision, failure budgets and oracle assumptions. Preserve failed candidates, lineage and available wall-clock/model-call/token telemetry; unknown measurements stay unknown."
          ]
        }
      ]
    }
  ],
  "hyperedges": [
    {
      "id": "transport:diagonal-filter-state",
      "label": "Diagonal block + prepared input + success contract",
      "tails": [
        "family:diagonal-postselection",
        "family:state-action",
        "family:charged-access"
      ],
      "heads": [
        "concept:state-preparation"
      ],
      "formula": "|\\psi\\rangle\\longmapsto D|\\psi\\rangle/\\|D\\psi\\|,\\quad p=\\|D\\psi\\|^2/\\alpha^2",
      "mechanism": "Specialize the existing BE-to-SP consumer to a diagonal filter; retain input preparation and successful-branch normalization as AND inputs.",
      "hypothesis_map": "Literal source dilation, bounded diagonal, known success sector, nonzero output, charged inverse/control and matched error metric.",
      "conclusion_map": "A conditional state and model-specific space–depth–accuracy/resource comparison.",
      "failure_boundary": "Neither a diagonal function description nor a compiled nearby fixed-size example certifies a scalable supplier; this is not SP-to-BE inclusion.",
      "source_ids": [
        "zylberman-et-al-2025-diagonal",
        "lin-wiebe-2026-qasc"
      ],
      "lean_refs": [],
      "status": "proposal",
      "review": "Source-planning edge; independent conceptual review pending; no local transport theorem"
    },
    {
      "id": "transport:envelope-structured",
      "label": "Sampling envelope meets function structure",
      "tails": [
        "family:envelope-reweight",
        "family:bounded-memory",
        "family:charged-access"
      ],
      "heads": [
        "concept:state-preparation"
      ],
      "formula": "\\kappa_{\\rm env}=C\\|g\\|_2/\\|f\\|_2",
      "mechanism": "Search for an envelope with both a provable ratio bound and a constructive small representation.",
      "hypothesis_map": "Support domination, ratio degree/rank, phase access and charged reference preparation.",
      "conclusion_map": "A model-specific success and end-to-end cost target.",
      "failure_boundary": "A good classical envelope need not have a cheap coherent preparation; no universal cure for dimensionality.",
      "source_ids": [
        "quantum-rejection-2013",
        "multivariate-2025"
      ],
      "lean_refs": [],
      "status": "proposal",
      "review": "independent review pending"
    },
    {
      "id": "transport:fourier-pde",
      "label": "Harmonic analysis to quantum evolution",
      "tails": [
        "family:harmonic-lift",
        "family:matrix-contract",
        "family:state-action"
      ],
      "heads": [
        "concept:block-encoding"
      ],
      "formula": "H_{\\rm Sch}=D_p\\otimes A_1-I\\otimes A_2",
      "mechanism": "The prepared auxiliary profile is one supplier; operator access and recovery remain separate.",
      "hypothesis_map": "Hermitian components, Fourier sign, finite grid and norm/recovery budget.",
      "conclusion_map": "Candidate Hamiltonian-access route for Schrödingerisation.",
      "failure_boundary": "SP certification alone proves neither the Hamiltonian block encoding nor end-to-end PDE accuracy.",
      "source_ids": [],
      "lean_refs": [],
      "status": "proposal",
      "review": "independent review pending"
    },
    {
      "id": "transport:hermite-compression",
      "label": "Exact function structure to bounded memory",
      "tails": [
        "family:hermite-bernstein",
        "family:matrix-contract"
      ],
      "heads": [
        "family:bounded-memory"
      ],
      "formula": "\\{\\text{degree and subdivision},\\text{bit/branch contract}\\}\\Longrightarrow R\\le2k+6",
      "mechanism": "Keep local polynomial updates and branch routing together; neither alone proves the sampled source.",
      "hypothesis_map": "Endpoint jets, grid coordinate, boundary ownership and bit order agree.",
      "conclusion_map": "The finite core contraction equals the literal sampled Hermite function.",
      "failure_boundary": "A degree statement alone does not account for an arbitrary number of pieces.",
      "source_ids": [
        "holmes-matsuura-2020"
      ],
      "lean_refs": [
        "QuantumBlockEncoding.HermiteFiniteChain.sourceChain_contract"
      ],
      "status": "curated-transport",
      "review": "independent conceptual review pending; local Lean roots have their own build evidence"
    }
  ],
  "sources": [
    {
      "id": "gu-kemeny-yelin-lukin-2026-uncompute",
      "title": "Discovering state-of-the-art quantum circuits with large language models",
      "authors": "Andi Gu, Alek H. Kemeny, Susanne F. Yelin, Mikhail D. Lukin",
      "year": 2026,
      "url": "https://arxiv.org/abs/2610.22367v1",
      "status": "primary-text-checked",
      "anchor": "v1: design principles; Methods Eqs. (10)-(22); Appendix A, A.1-A.8 (PDF pp. 44-46). Other case studies remain a queued source audit.",
      "scope": "Priority intake for reversible computation and proof digestion. First batch audits existing branch-recovery and DQI proof interfaces; full paper and circuit/resource closure remain open.",
      "formal_status": "No new local certificate. Existing author proofs are separately pinned and must be adapted to Lean 4.33.0 before local admission."
    },
    {
      "id": "uncompute-upstream-64b5a13",
      "title": "uncompute: pinned author circuit, evaluator and Lean artifacts",
      "authors": "Andi Gu and contributors; retain upstream attribution",
      "year": 2026,
      "url": "https://github.com/andigu/uncompute/tree/64b5a13aa249f1360846657392e6c66817b26d0f",
      "status": "primary-text-checked",
      "anchor": "Commit 64b5a13aa249f1360846657392e6c66817b26d0f; lean/divsteps/README.md, lean/dqi/README.md; selected Recovery.lean and Complete.lean theorem interfaces; not yet a whole-module audit or local build.",
      "scope": "Observed pins: divsteps Lean/Mathlib4.32.2; DQI Lean/Mathlib4.33.1. Apache-2.0 repository; divsteps also retains MIT safegcd-bounds attribution. Upstream source and claimed builds are not ASPBE acceptance.",
      "formal_status": "External proof assets, not local certificates: Hddivsteps.ladder/ladder_det/finite_dependence/j2_law and Dqi.dqi_end_to_end. Full compiler, binder, definition, source and trust audit pending."
    },
    {
      "id": "zylberman-et-al-2025-diagonal",
      "title": "Efficient Quantum Circuits for Non-Unitary and Unitary Diagonal Operators with Space-Time-Accuracy trade-offs",
      "authors": "Julien Zylberman; Ugo Nzongani; Andrea Simonetto; Fabrice Debbasch",
      "url": "https://arxiv.org/abs/2404.02819v4",
      "requested_version": "https://arxiv.org/pdf/2404.02819v4",
      "year": 2025,
      "status": "primary-text-checked",
      "anchor": "arXiv v4, 21 January 2025; checked 29 September 2026: II.1, III.1–III.2, IV.1 Eqs. (15)–(16), V.1 Eqs. (19)–(21), VI A, VIII.1 and Tables I–II. Figure 4 signal-sector and III.2/VIII.1 accounting ambiguities remain explicit source obligations.",
      "scope": "Parallel scheduling trades ancillas for depth, not automatically total size. Table I uses spectral-norm error; Eq. (18) bounds normalized-block error delta, corresponding to total-scale times delta in the unscaled-operator convention. Exact-block success in source notation is ||D psi||^2/(alpha^2 dmax^2); alpha>1 controls the transformed-angle derivative in smooth approximation. No local source theorem or resolution of source ambiguities is claimed.",
      "formal_status": "planned-formalization"
    },
    {
      "id": "holmes-matsuura-2020",
      "title": "Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions",
      "authors": "Adam Holmes; A. Y. Matsuura",
      "url": "https://arxiv.org/abs/2005.04351",
      "requested_version": "https://arxiv.org/html/2005.04351v1",
      "year": 2020,
      "status": "primary-metadata-checked",
      "anchor": "Abstract: explicit function to MPS to circuit; requested v1 HTML was unavailable in this audit",
      "scope": "Prior art for function-to-MPS preparation. The ASPBE Hermite specialization must not be credited with inventing polynomial-to-MPS or sequential MPS preparation.",
      "formal_status": "external-reference"
    },
    {
      "id": "yuan-zhang-2023",
      "title": "Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits",
      "authors": "Pei Yuan; Shengyu Zhang",
      "url": "https://quantum-journal.org/papers/q-2023-03-20-956/",
      "year": 2023,
      "status": "primary-metadata-checked",
      "anchor": "Abstract and publication version notice: published arXiv v2; later v3 exists",
      "scope": "Baseline for arbitrary and controlled state preparation and ancilla/depth trade-offs. Pin a version and gate model before comparing bounds.",
      "formal_status": "external-reference"
    },
    {
      "id": "zhang-yuan-2024",
      "title": "Circuit complexity of quantum access models for encoding classical data",
      "authors": "Xiao-Ming Zhang; Xiao Yuan",
      "url": "https://www.nature.com/articles/s41534-024-00835-8",
      "year": 2024,
      "status": "primary-text-checked",
      "anchor": "Results: circuit complexity lower bound; construction of LCU-based block-encoding; Methods: state preparation",
      "scope": "Explicit access construction is not a free oracle. PREPARE together with SELECT and uncomputation can supply a block encoding; a single prepared state alone does not determine an arbitrary operator.",
      "formal_status": "external-reference"
    },
    {
      "id": "multivariate-2025",
      "title": "Quantum state preparation for multivariate functions",
      "authors": "See primary source",
      "url": "https://quantum-journal.org/papers/q-2025-04-09-1703/",
      "year": 2025,
      "status": "primary-metadata-checked",
      "anchor": "Abstract and article record",
      "scope": "Multivariate preparation baseline; a tensor-product coefficient count is not automatically polynomial in dimension.",
      "formal_status": "external-reference"
    },
    {
      "id": "quantum-rejection-2013",
      "title": "Quantum Rejection Sampling",
      "authors": "Maris Ozols; Martin Roetteler; Jérémie Roland",
      "url": "https://www.microsoft.com/en-us/research/publication/quantum-rejection-sampling/",
      "year": 2013,
      "status": "primary-metadata-checked",
      "anchor": "Authors' publication page: quantum state generation, query characterization and matching lower bound",
      "scope": "Prior art for coherent amplitude reweighting. Novelty must be in an explicit structured envelope, guarantees, implementation or model-matched bound, not in rejection sampling itself.",
      "formal_status": "external-reference"
    },
    {
      "id": "lin-wiebe-2026-qasc",
      "title": "Quantum Algorithms for Scientific Computation",
      "authors": "Lin Lin; Nathan Wiebe",
      "url": "https://math.berkeley.edu/~linlin/qasc/live_notes_0429.pdf",
      "year": 2026,
      "status": "primary-text-checked",
      "anchor": "29 April 2026 public 447-page edition; PDF SHA256 56825000d53025dea4c2998dd6a061592b8fb2b9a446c3194c5f408183327599. First bounded source slice: Chapter 9 Section 9.1, printed pages 141–143, equations (9.2), (9.9), (9.10), (9.12); standing partial-application convention Definition 2.25, page 37. Parts I–IV remain curriculum anchors, not completed formalisation.",
      "scope": "Peer Part IV curriculum anchor, reusing existing ASPBE state-preparation/block-encoding APIs. New Chapter 9 adapters, operator-norm approximation, scientific constructions and resource certificates still require separate production admission. No whole-section/book completion is claimed.",
      "formal_status": "external-reference"
    }
  ],
  "required_handoff": [
    "frozen target and access model",
    "exact reused declarations",
    "bounded mathematical delta",
    "assumption differences",
    "independent round-trip evidence",
    "graph contribution and residual boundary"
  ]
}