Follow the work, not just the paper.

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.

RO-2026-0001:C1

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.

RO-2026-0001:C2

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.

RO-2026-0001:C3

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.

RO-2026-0001:C4

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.

RO-2026-0001:C5

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.

RO-2026-0001:C6

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.

RO-2026-0001:C7

For faithful finite-dimensional states and every fixed integer n >= 2, measured relative entropy on n tensor copies equals n times its one-copy value if and only if the states commute.

RO-2026-0003:C1

For every faithful noncommuting state pair, a phase-optimized rotation of two product measurement vectors has a strictly positive directional derivative of the two-copy measured relative entropy at the product optimum.

RO-2026-0003:C2

The fixed-horizon specialization of the known Li-Tan-Tomamichel adaptive bound implies that any fresh-copy measurement protocol with classical feed-forward has classical relative entropy at most n times the one-copy measured relative entropy.

RO-2026-0003:C3

For a Gibbs-prepared isolated unitary drive, the dimensionless irreversible work beta times W minus Delta F equals D(rho_tau || pi_tau).

RO-2026-0003:C4

In the faithful finite-temperature IID isolated-drive construction, strict globally optimized two-copy gain in measured relative entropy is equivalent to nonzero energetic coherence relative to the final Hamiltonian.

RO-2026-0003:C5

A calibrated positive implemented two-copy gain is a one-sided witness within the stated model, whereas a null restricted gain does not establish incoherence.

RO-2026-0003:C6

The stated faithful qubit family has a certified x-basis one-copy optimum and an explicit positive-slope two-copy rotation.

RO-2026-0003:C7

On the deterministic 453-point qubit grid, the maximum recovered globally optimized gain is 0.0214758723 nats per copy and the explicit rotation attains 0.0073100901 nats per copy at the best displayed point.

RO-2026-0003:C8

The known equality between cooling-map and low-temperature thermal-operation state-transition power for a two-level system fails at the first open dimension under the exact finite-bath, ground-state-subspace convention: every irrational parameter in the displayed qutrit family gives a cooling-map transition that is not exactly reachable by that thermal class.

RO-2026-0004:C1

At cold-limit errors 10^-4, 10^-8, and 10^-12, the theorem lower bounds are 13, 1280, and 128000, while the displayed golden Fibonacci construction dimensions are 288, 21892, and 2692538.

RO-2026-0004:C10

The exact two-subspace construction has the stated gap-calibration tolerance, while the equal-rank approximation construction is independent of temperature.

RO-2026-0004:C11

For distinct nonzero qutrit Bohr frequencies, every qutrit cooling map lies in the diamond-norm closure of exact finite-bath thermal operations initialized on their ground-state subspaces.

RO-2026-0004:C2

Every D-dimensional finite Gibbs-bath implementation of the displayed qutrit channel obeys kappa_D(a)/D^2 <= exp(-beta Delta)/4 + (12+8 sqrt(2)) epsilon.

RO-2026-0004:C3

For each fixed badly approximable target and sufficiently small combined thermal-and-error scale, the minimum bath dimension lies between explicit positive target-dependent constants times the inverse square root of that scale.

RO-2026-0004:C4

For every positive nu and Lebesgue-almost every target, the minimum dimension has an inverse-square-root lower law with the stated logarithmic loss for sufficiently small combined thermal-and-error scale.

RO-2026-0004:C5

A rational target a=p/q has an exact two-energy-subspace implementation with total dimension 2q; explicit Fibonacci choices give approximation constructions for the golden-conjugate target, while a=1/2 has dimension four.

RO-2026-0004:C6

Shellwise polar rounding and projection rigidity give a parameter-uniform linear bound on the difference between the bath projection expectation and the target mixing parameter despite population leakage.

RO-2026-0004:C7

On a joint finite-confidence event, the actual bath dimension and ground-state degeneracy obey the sharpened dimension-exclusion inequality in the Letter; a candidate dimension is excluded only when every allowed degeneracy fails it.

RO-2026-0004:C8

The rigid phase pair belongs to a one-parameter family, and the coefficient delivered by the proof is minimized when the absolute phase parameter equals one, where it is 12+8 sqrt(2).

RO-2026-0004:C9

Established driven-energy-diffusion ingredients and thermal Kramers diffusion form a density-of-states-consistent stochastic thermodynamics when deterministic protocol transport is fixed by phase-volume continuity and entropy is defined relative to the density of states.

RO-2026-0005:C1

Positive homogeneous Hamiltonians close on a gamma energy family controlled by effective degrees of freedom, while their relaxation and power scale with the homogeneity-dependent energy relaxation rate.

RO-2026-0005:C2

For the established gamma-difference thermal-exchange family, one contrast variable yields a compact all-order cumulant recurrence, incomplete-beta wrong-way probability, exact finite-time gamma-family exchange uncertainty identity, skewness, and kurtosis; the distinct total path entropy production also has a closed distribution. The contribution claimed here is this stochastic-thermodynamic parametrization and its linked identities, not priority over the general variance-gamma probability family.

RO-2026-0005:C3

A six-member finite-time cycle atlas separates imposed topology from continuous control. Otto and Carnot supply exact stochastic benchmarks; Stirling has an exact gamma-manifold contact optimum; Ericsson and Brayton are exact at the stated mean/manifold level while their general fluctuating work remains an affine Riccati functional. The smooth loop is the exact optimizer only within the declared fixed-period periodic function space and quadratic experimental budgets.

RO-2026-0005:C4

For the nonlinear graph-metric power cage, equilibrium graph dependence is determined exactly by the Laplacian pseudodeterminant, effective resistances, and Kirchhoff index for arbitrary positive homogeneity degree.

RO-2026-0005:C5

For arbitrary positive homogeneity degree, a sudden single-edge quench of the nonlinear graph cage has an exact independent beta-gamma work representation controlled by the pre-quench effective resistance and yields all work moments and fluctuation relations. Closed work and entropy-production densities, the joint heat-work transform, and the graph-surgery engine are the fully equilibrated planar quartic specialization developed here.

RO-2026-0005:C6

Global stiffness and proportional graph breathing retain exact scalar energy closure, whereas generic finite-rate graph-shape driving requires shell mixing or additional angular observables.

RO-2026-0005:C7

Within the explicitly conditional reduced model of rapid shell mixing and orbit-averaged moving-wall work, the hard-sphere configurational integral acts as a mechanical control; a uniform attractive mean field yields a nonequilibrium van der Waals correction, whereas microscopic attractive tails generally leave the scalar closure class. No trajectory-level convergence of microscopic hard-sphere dynamics to this reduced process is claimed.

RO-2026-0005:C8

For faithful finite-dimensional product hypotheses, the fully-PPT measured Pearson optimum equals the product of the one-copy optima and is attained by measuring an optimal score on each physical copy.

RO-2026-0007:C1

A faithful noncommuting state pair has a strict unrestricted joint two-copy Pearson gain over the fully-PPT product value.

RO-2026-0007:C2

For the prescribed collective score built from a faithful noncommuting pair, spectral readout adds no variance, whereas every unbiased fully-PPT readout of that same observable adds positive variance.

RO-2026-0007:C3

A moment inequality gives a necessary fully-PPT variance lower bound for the fixed collective score that can be stronger than the class-wide Pearson bound; it is not claimed to equal the unknown restricted minimum.

RO-2026-0007:C4

In the stated driven-medium model, energy dephasing removes the joint-readout Pearson gain while leaving the full two-point work distribution unchanged.

RO-2026-0007:C5

Reduced equilibrium probes in the specified separable probe-ancilla model exhibit the fixed-score readout penalty without a drive or entangled source.

RO-2026-0007:C6

With characterized input states and calibrated outcome probabilities, a Pearson value above the product limit certifies an NPT readout effect in the stated copy partition.

RO-2026-0007:C7

evidence

data/gap_identity.csv

RO-2026-0001:evidence:data/gap_identity.csv

evidence

data/gibbs_conditioning.csv

RO-2026-0001:evidence:data/gibbs_conditioning.csv

evidence

data/hardness_reduction.csv

RO-2026-0001:evidence:data/hardness_reduction.csv

evidence

data/parity_sensor.csv

RO-2026-0001:evidence:data/parity_sensor.csv

evidence

data/physical_chain.csv

RO-2026-0001:evidence:data/physical_chain.csv

evidence

data/physical_product_parameters.npy

RO-2026-0001:evidence:data/physical_product_parameters.npy

evidence

data/physical_resolution.csv

RO-2026-0001:evidence:data/physical_resolution.csv

evidence

data/resolution_raw.csv

RO-2026-0001:evidence:data/resolution_raw.csv

evidence

data/resolution_summary.csv

RO-2026-0001:evidence:data/resolution_summary.csv

evidence

data/resource_estimate.json

RO-2026-0001:evidence:data/resource_estimate.json

evidence

data/resource_operators.csv

RO-2026-0001:evidence:data/resource_operators.csv

evidence

data/saddle_landscape.npz

RO-2026-0001:evidence:data/saddle_landscape.npz

evidence

data/score_compression.csv

RO-2026-0001:evidence:data/score_compression.csv

evidence

data/tail_bound.csv

RO-2026-0001:evidence:data/tail_bound.csv

evidence

data/thermodynamic_quantization.csv

RO-2026-0001:evidence:data/thermodynamic_quantization.csv

evidence

figures/figure3.pdf

RO-2026-0001:evidence:figures/figure3.pdf

evidence

src/appendices.tex

RO-2026-0001:evidence:src/appendices.tex

evidence

src/references.bib

RO-2026-0001:evidence:src/references.bib

evidence

src/sections/03-compression.tex

RO-2026-0001:evidence:src/sections/03-compression.tex

evidence

src/sections/03-landscape.tex

RO-2026-0001:evidence:src/sections/03-landscape.tex

evidence

src/sections/05-compiler.tex

RO-2026-0001:evidence:src/sections/05-compiler.tex

evidence

src/sections/06-hardness.tex

RO-2026-0001:evidence:src/sections/06-hardness.tex

evidence

src/sections/07-numerics.tex

RO-2026-0001:evidence:src/sections/07-numerics.tex

evidence

src/sections/08-physical.tex

RO-2026-0001:evidence:src/sections/08-physical.tex

evidence

paper/candidates/r05/unpacked/code/simulate_qubit_activation.py

RO-2026-0003:evidence:paper/candidates/r05/unpacked/code/simulate_qubit_activation.py

evidence

paper/candidates/r05/unpacked/data/two_copy_sdp.csv

RO-2026-0003:evidence:paper/candidates/r05/unpacked/data/two_copy_sdp.csv

evidence

paper/candidates/r05/unpacked/data/validation.json

RO-2026-0003:evidence:paper/candidates/r05/unpacked/data/validation.json

evidence

code/generate_figures.py

RO-2026-0004:evidence:code/generate_figures.py

evidence

data/approximate_fibonacci_flags.csv

RO-2026-0004:evidence:data/approximate_fibonacci_flags.csv

evidence

data/bath_dimension_growth.csv

RO-2026-0004:evidence:data/bath_dimension_growth.csv

evidence

data/exact_fibonacci_flags.csv

RO-2026-0004:evidence:data/exact_fibonacci_flags.csv

evidence

data/polar-leakage/comparison.json

RO-2026-0004:evidence:data/polar-leakage/comparison.json

evidence

data/verification.json

RO-2026-0004:evidence:data/verification.json

evidence

paper/pdf/letter-v016.pdf

RO-2026-0004:evidence:paper/pdf/letter-v016.pdf

evidence

paper/pdf/supplement-v016.pdf

RO-2026-0004:evidence:paper/pdf/supplement-v016.pdf

evidence

code/validate_v002.py

RO-2026-0005:evidence:code/validate_v002.py

evidence

code/validate_v004.py

RO-2026-0005:evidence:code/validate_v004.py

evidence

code/validate_v005.py

RO-2026-0005:evidence:code/validate_v005.py

evidence

code/validate_v007.py

RO-2026-0005:evidence:code/validate_v007.py

evidence

code/validate_v009.py

RO-2026-0005:evidence:code/validate_v009.py

evidence

paper/pdf/paper-v1.0.pdf

RO-2026-0005:evidence:paper/pdf/paper-v1.0.pdf

Mathematical Physics

PRG-mathematical-physics

Quantum Information

PRG-quantum-information

Quantum Thermodynamics

PRG-quantum-thermodynamics

Stochastic Thermodynamics

PRG-stochastic-thermodynamics

Few-Outcome Readout of Quantum-Fisher-Optimal Measurements: Sharp Bounds and Coherent-Synthesis Hardness

RO-2026-0001

Two-Copy Onset of Strict Superadditivity for Measured Relative Entropy

RO-2026-0003

Minimum Bath Dimension for Qutrit Cooling Maps

RO-2026-0004

Stochastic Thermodynamics of Highly Underdamped Homogeneous Hamiltonian Systems

RO-2026-0005

An Exact Product Limit on Collective Quantum Readout

RO-2026-0007

source

code/generate_figures.py

code:code/generate_figures.py

source

paper/candidates/r05/unpacked/code/simulate_qubit_activation.py

code:paper/candidates/r05/unpacked/code/simulate_qubit_activation.py

source

src/qsa_core.py

code:src/qsa_core.py

source

src/simulate.py

code:src/simulate.py

source

data/physical_chain.csv

dataset:data/physical_chain.csv

source

paper/candidates/r05/unpacked/data/two_copy_sdp.csv

dataset:paper/candidates/r05/unpacked/data/two_copy_sdp.csv

source

Gibbs-flag-construction

definition:Gibbs-flag-construction

source

measured-relative-entropy

definition:measured-relative-entropy

source

qutrit-cooling-map

definition:qutrit-cooling-map

source

sequential-fresh-copy-readout

definition:sequential-fresh-copy-readout

source

Benign-Projective-Landscapes-for-Measured-Quantum-Divergences

external_result:Benign-Projective-Landscapes-for-Measured-Quantum-Divergences

source

BQP-hard-quantum-linear-systems

external_result:BQP-hard-quantum-linear-systems

source

Cable-Gu-Modi-2016-one-clean-qubit-metrology

external_result:Cable-Gu-Modi-2016-one-clean-qubit-metrology

source

finite-tracial-polar-rounding

external_result:finite-tracial-polar-rounding

source

Graf-Luschgy-2000-Theorem-6.2

external_result:Graf-Luschgy-2000-Theorem-6.2

source

isolated-drive-relative-entropy-identity

external_result:isolated-drive-relative-entropy-identity

source

Khintchine-convergence-theorem

external_result:Khintchine-convergence-theorem

source

Kramers-energy-diffusion

external_result:Kramers-energy-diffusion

source

Liu-Pages-2020-Wasserstein-root-distortion

external_result:Liu-Pages-2020-Wasserstein-root-distortion

source

matrix-tree-and-effective-resistance-identities

external_result:matrix-tree-and-effective-resistance-identities

source

Narasimhachar-Gour-2015-two-level-equality

external_result:Narasimhachar-Gour-2015-two-level-equality

source

quantum-Sylvester-solver

external_result:quantum-Sylvester-solver

source

qubitization-and-quantum-signal-processing

external_result:qubitization-and-quantum-signal-processing

source

scalar-quantization-high-rate-theory

external_result:scalar-quantization-high-rate-theory

source

Sheng-2026-Stinespring-score-intertwining-QFI-loss

external_result:Sheng-2026-Stinespring-score-intertwining-QFI-loss

source

Sheng-2026-task-dependent-syndrome-memory

external_result:Sheng-2026-task-dependent-syndrome-memory

Why a Quantum Detector Might Need Fewer Answers

STORY-2026-0001

When Two Quantum Copies Are Worth More Than Twice One

STORY-2026-0002

How a Qutrit Can Force a 128,000-Dimensional Heat Bath

STORY-2026-0003