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RO-2026-0001 C1
For any occupied spectral partition of an SLD-regular one-parameter quantum model, the Fisher-information loss equals the state-weighted within-bin SLD score variance and is at most one quarter of the state-weighted squared bin diameters; consequently any occupied bins of diameter at most delta lose at most delta squared divided by four.
Open →claim · RO-2026-0001:C2RO-2026-0001 C2
The optimal few-outcome SLD readout admits a dimension-free central-plus-tail bound, is stable under Wasserstein-2 perturbations of the state-weighted score measure, has a dense-spectrum high-rate quantization window, and crosses exactly to zero distortion once the bin count reaches the finite score-support size.
Open →claim · RO-2026-0001:C3RO-2026-0001 C3
For a rank-one projective measurement, the quantum-Fisher loss equals the rho-weighted squared residual between its induced score operator and the SLD, providing an exact projective-search stopping certificate; the broader local-to-global and pair-rotation geometry is an imported companion result.
Open →claim · RO-2026-0001:C4RO-2026-0001 C4
For an actual parameter-independent initialized isometry V with exhaustive ordinary, boundary, leakage, and failure labels, a bounded label-score observable C, and an approximate Hermitian SLD L-tilde, the uniform score-intertwining defect xi = norm(CV - V L-tilde) controls the actual POVM Fisher loss by (eta + xi)^2. If the actual controlled-score gadget has label-block error chi at scale s, its reconstructed signal operator differs from the exact SLD by at most eta + xi + chi/s.
Open →claim · RO-2026-0001:C5RO-2026-0001 C5
Producing a coherent SLD score instrument that satisfies the declared score-intertwining and signal-block interface at inverse-polynomial accuracy is BQP-hard for a faithful, trace-normalized, full-support metrological embedding with polynomial state conditioning, inverse-polynomial zero-score margin, inverse-polynomial quantum Fisher information, and inverse-polynomial coherent application success, even though the sensor-state score histogram is independent of the encoded linear-system right-hand side.
Open →claim · RO-2026-0001:C6RO-2026-0001 C6
The parity-coherence sensing family has constant condition number three, quantum Fisher information n divided by four, exactly n plus one SLD scores, and logarithmic score-register size, while Gibbs access obeys the rescaling-invariant conditioning obstruction exp(beta times energy span) and the archived finite-size beta proportional to one over n family has bounded conditioning together with the reported rescaled sensitivity.
Open →claim · RO-2026-0001:C7RO-2026-0001 C7
In the archived frustrated four-spin sensor benchmark, the best product projective readout found by the archived heuristic search retains 48.55 percent of the quantum Fisher information, whereas globally optimized contiguous seven- and eight-bin SLD score readouts retain 98.34 percent and 99.26 percent respectively.
Open →literature · RO-2026-0001:literature:C1Literature audit for RO-2026-0001:C1
The candidate gives a support-aware specialization to regular SLD-score measures, a uniform spectral-diameter corollary, and integration with the later compiler and hardness interface; it does not claim priority for the conditional-variance identity or the one-quarter variance constant.
Open →literature · RO-2026-0001:literature:C2Literature audit for RO-2026-0001:C2
The defensible contribution is the exact mapping from SLD-score loss to scalar distortion, the explicit tail construction, the changing-resolution Wasserstein transfer, and its combination with the exact finite-support crossover. Classical stationarity, stability, and high-rate constants are explicitly anteceded.
Open →literature · RO-2026-0001:literature:C3Literature audit for RO-2026-0001:C3
The candidate imports and applies the companion projective-landscape theorem as an exact residual certificate; it does not re-claim that theorem as a new self-contained result.
Open →literature · RO-2026-0001:literature:C4Literature audit for RO-2026-0001:C4
Sheng anteceded the generic Stinespring score-intertwining loss identity. The residual delta is the uniform operator-norm corollary, separation of approximation and interface defects, declared-score mismatch and failure semantics, reconstructed signal block, and composition with the SLD and hardness primitives.
Open →literature · RO-2026-0001:literature:C5Literature audit for RO-2026-0001:C5
The candidate narrows the hardness result to coherent selected-input synthesis under full-support metrological promises and explicitly separates that interface from ordinary sampling, histogram estimation, and stronger classical access models.
Open →literature · RO-2026-0001:literature:C6Literature audit for RO-2026-0001:C6
Cable, Gu, and Modi anteceded the parity-coherence state family and extensive sensitivity scaling. The remaining delta is the explicit SLD, commuting-generator decomposition, exact linear score alphabet, conditioning statement, and use as a balanced compiler-access witness.
Open →literature · RO-2026-0001:literature:C7Literature audit for RO-2026-0001:C7
This is a deterministic four-spin numerical readout benchmark and resource diagnostic, not an experiment or a claim of a globally optimized product measurement.
Open →program · PRG-mathematical-physicsMathematical Physics
Reusable proof infrastructure and obstruction-led work on hard structural problems.
Open →program · PRG-quantum-informationQuantum Information
Auditable mathematical structures for information processing, recovery, and statistical distinguishability.
Open →program · PRG-quantum-thermodynamicsQuantum Thermodynamics
Rigorous, operational statements connecting quantum dynamics, records, and thermodynamic inference.
Open →research object · RO-2026-0001Few-Outcome Readout of Quantum-Fisher-Optimal Measurements: Sharp Bounds and Coherent-Synthesis Hardness
A quantum-Fisher-optimal measurement may resolve exponentially many eigenvectors even when its information-bearing score needs only a small outcome alphabet. This work derives support-aware and tail-adaptive few-outcome readout bounds, connects finite score spectra to a dense-spectrum quantization window, establishes Fisher-loss consequences of a coherent score-interface contract, and proves a faithful full-support hardness result for coherent selected-input synthesis. Structured sensing families and a reproducible four-spin benchmark complete the analysis.
Open →review finding · RO-2026-0001:review:F-R1-001RO-2026-0001 review finding F-R1-001
The proven Fisher-loss statement concerns an exact PVM of the Hermitian approximation, not the delivered finite-precision instrument. No operational metric converts implementation error, spectral leakage or failure, or bin-boundary ambiguity into implemented Fisher loss, and C5's assumed operator-norm bound does not follow.
Open →review finding · RO-2026-0001:review:F-R1-002RO-2026-0001 review finding F-R1-002
The explicit full-cost assumption conflicts with a partial proxy that leaves solver cost unresolved and omits composed square-root, Sylvester, access, precision-allocation, and amplification costs.
Open →review finding · RO-2026-0001:review:F-R1-003RO-2026-0001 review finding F-R1-003
Polynomial sample cost in the beta-equals-c-over-n window lacks a uniform nonasymptotic quantum-Fisher-information lower bound with a controlled remainder.
Open →review finding · RO-2026-0001:review:F-R1-004RO-2026-0001 review finding F-R1-004
Direct antecedents contain consecutive spectral binning, quantization optimization, within-bin variance loss, general SLD clustering, and Wasserstein quantization stability; the current originality boundary is not yet reliable.
Open →review finding · RO-2026-0001:review:F-R1-005RO-2026-0001 review finding F-R1-005
The artificial hardness construction, classically structured scalable sensor, and four-spin example do not yet bridge into the broad physical impact asserted by the candidate framing.
Open →review finding · RO-2026-0001:review:F-R1-006RO-2026-0001 review finding F-R1-006
The isolated regeneration supports C7, but the official validator does not recompute the advertised quantities and the pinned clean-room contract remains incomplete.
Open →review finding · RO-2026-0001:review:F-R1-007RO-2026-0001 review finding F-R1-007
Optimized product measurement can imply a certified optimum, while the supported statement is the best product PVM found by the archived heuristic search.
Open →review finding · RO-2026-0001:review:F-R1-008RO-2026-0001 review finding F-R1-008
The C1 computation path misses the direct diameter tests, figure and table counts conflict with generated data, and the Sheng dependency metadata require current digest binding.
Open →review finding · RO-2026-0001:review:F-R1-009RO-2026-0001 review finding F-R1-009
The companion result is accessible at a pinned commit and supports the imported specialization, but lacks its planned stable scholarly identifier; the reproducibility DOI is also absent.
Open →review finding · RO-2026-0001:review:F-R2-001RO-2026-0001 review finding F-R2-001
The integrated toolkit did not meet the separate exceptional broad-impact threshold.
Open →review finding · RO-2026-0001:review:F-R2-002RO-2026-0001 review finding F-R2-002
The score interface was a contract rather than a primitive-to-error and end-to-end cost theorem.
Open →review finding · RO-2026-0001:review:F-R2-003RO-2026-0001 review finding F-R2-003
The supplement named absent build and checksum files, and claim paths were not fully rebound to the candidate.
Open →review finding · RO-2026-0001:review:F-R2-004RO-2026-0001 review finding F-R2-004
Anteceded identities and imported geometry required tighter, claim-level attribution.
Open →review finding · RO-2026-0001:review:F-R2-005RO-2026-0001 review finding F-R2-005
Stable identifiers and inspected isolated-container evidence were absent.
Open →review finding · RO-2026-0001:review:F-R3-001RO-2026-0001 review finding F-R3-001
The score-intertwining Fisher-loss identity is correct under the declared isometry contract.
Open →review finding · RO-2026-0001:review:F-R3-002RO-2026-0001 review finding F-R3-002
The reconstructed-signal inequality is a valid consequence of the accepted interface assumptions.
Open →review finding · RO-2026-0001:review:F-R3-003RO-2026-0001 review finding F-R3-003
The full-support embedding and metrological promises support the restricted coherent selected-input hardness statement.
Open →review finding · RO-2026-0001:review:F-R3-004RO-2026-0001 review finding F-R3-004
All seven claims are valid, package-local, resolvable, and bound to the accepted archive.
Open →review finding · RO-2026-0001:review:F-R3-005RO-2026-0001 review finding F-R3-005
Fresh complete and smoke runs passed all 34 declared checks in all 12 families.
Open →review finding · RO-2026-0001:review:F-R3-006RO-2026-0001 review finding F-R3-006
The exact contiguous-bin optima reproduce and the product value is correctly limited to a heuristic-search baseline.
Open →story · STORY-2026-0001Why a Quantum Detector Might Need Fewer Answers
Quantum sensors are prized for exquisite sensitivity. But their mathematically perfect measurements can demand a bewildering number of outcomes. A new analysis asks which distinctions matter—and why shrinking the display does not simplify the machine behind it.
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