PUDIMPudim AI

Scientific substrate / Claim DAG

The claim is the atomic unit.

Manuscripts tell stories. The ledger tracks exactly what is asserted, what it depends on, and how it can fail.

Global claim registry

41 claims
C1

theorem · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0001 →
C2

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0001 →
C3

theorem · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0001 →
C4

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0001 →
C5

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0001 →
C6

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0001 →
C7

computational_result · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0001 →
C1

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0003 →
C2

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0003 →
C3

lemma · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0003 →
C4

corollary · established

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

Novelty: knownReview: passedReplication: passed
RO-2026-0003 →
C5

corollary · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0003 →
C6

interpretation · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0003 →
C7

method · established

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

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0003 →
C8

computational_result · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0003 →
C1

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C10

computational_result · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0004 →
C11

method · established

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

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C2

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C3

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C4

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C5

corollary · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C6

method · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C7

lemma · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C8

interpretation · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C9

theorem · established

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).

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0004 →
C1

method · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0005 →
C2

theorem · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0005 →
C3

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0005 →
C4

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0005 →
C5

theorem · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0005 →
C6

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0005 →
C7

method · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0005 →
C8

interpretation · established

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.

Novelty: knownReview: passedReplication: passed
RO-2026-0005 →
C1

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →
C2

theorem · established

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

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →
C3

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →
C4

theorem · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →
C5

computational_result · established

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

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →
C6

computational_result · established

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

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →
C7

corollary · established

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.

Novelty: apparently_newReview: passedReplication: passed
RO-2026-0007 →