M01 · Manuscript
Local Evaluation and Continuous Quadratic Forms for Cardinal Spline Networks
Which calculations can be compiled out of repeated neural evaluation when the represented function and operator are known?
The technical collection
Behind the stories.
Focused papers with mathematical setup, experiments, limitations and references. All are working drafts, not submission-ready claims.
M02 · Manuscript
Function-Preserving Grid Transfer and Continuous Regularization in Spline Networks
Can a model acquire additional degrees of freedom while its pre-update input-output function remains unchanged?
M03 · Manuscript
Learning Constitutive Laws Inside Known Dynamics: Structured Identification and Out-of-Range Prediction
When the conservation structure is known, can learning only its missing material law improve extrapolation?
M04 · Manuscript
Stable State Coordinates for Compact Learned Dynamics: Aircraft Vibration and Nano-Drone Identification
What predictive capability remains when a learned dynamical model must be small enough to inspect, transmit or execute cheaply?
M05 · Manuscript
Continuous-Domain Retention in Local Spline Adaptation: Guarantees, Counterexamples, and Sparse Updates
What exactly is promised when an online model is said not to forget?
M06 · Manuscript
Frozen Visual Representations with Pooled Analytic Readouts: A Continual-Classification Case Study
How far can inexpensive readout updates go when perception has already been learned?
Companion articles: B14
M07 · Manuscript
Batched Neuroevolution with Analytic Readouts: A Finite-Parity Construction Study
Can architecture search spend its budget on representations rather than repeated readout optimization?
Companion articles: B15
M08 · Manuscript
Blockwise Reverse-Mode Differentiation and Predictive-Coding Relaxation: An Implementation-Level Comparison
What computation actually assigns credit when an update is described as local?
Companion articles: B16
M09 · Manuscript
Event-Integrated Spline Readouts and Finite-Precision Synaptic Realizations
When does continuous calculus reduce work, and when does a changed realization merely move the cost?
M10 · Manuscript
From Compact Actuator Identification to Policy Recovery: Quadratic Structure and a Matched-Controller Boundary
Can an adaptive system repair what changed without silently invalidating what its controller relies on?
M11 · Manuscript
Operator-Aware Residual Assimilation: Improved Field Recovery and a Failure of Trajectory Transfer
Does enforcing a more plausible field improve the prediction a scientist or controller actually needs?
Companion articles: B21
M12 · Manuscript
What Compressed Measurement Statistics Preserve: Fixed-Space Inverse Problems and a Walnut CT Counterexample
What future reconstruction choices remain possible after measurement data have been replaced by a compact message?
M13 · Manuscript
Portable Learned Task Automata: Exact Spline Compilation and a Thirty-Pool Capability Failure
What is missing when many agents can exchange models but their recipient still cannot solve the task?
Companion articles: B24
M14 · Manuscript
Mergeable Parameter-Dependent Objective Summaries for Stable Scalar Dynamics
Can a tiny record retain later computational choices rather than the original waveform?
M15 · Manuscript
Deferred Gaussian Time-Series Inference from Lag Summaries with Record-Specific Error Bounds
Can a scientist revise a model after capture while knowing whether the compressed record still supports the conclusion?
M16 · Manuscript
Operator-Based Activation Compression: Query Sensitivity and a KV-Cache Prototype Audit
When does a compact cache preserve the answers future attention queries require?
Companion articles: B29
M17 · Manuscript
Exact Operator Cells for Compact Option-Pricing Services: Stability, Workload, and Single-Thread Deployment
Can a precisely defined numerical inference service be useful without a large runtime or accelerator?
M18 · Manuscript
Signed-Functional Error Bounds and Independent Verification for Operator-Based Option Risk
Can a small recipient check a consequential numerical claim without trusting the model-search process?
M19 · Manuscript
Price Agreement Does Not Identify Local Risk: Thin-Layer Limits and a Bounded Market-Admission Study
What can be concluded about risk when observations admit multiple models—or none of the tested models?
M20 · Manuscript
Pole-Based Source–Filter Speech Reconstruction: A Prototype and Bitstream Audit
Which components of speech must a tiny dynamical program preserve to remain intelligible and useful?
Companion articles: B37
M21 · Manuscript
Verified Prompt Memory in a Frozen Language Model: A Paired Arithmetic Case Study
Can changing which experiences enter a prompt improve a frozen model, and what kind of improvement is it?
M22 · Manuscript
Separating Physical Constraints from Statistical Estimation in Operator-Structured Models
Which uncertainties remain after known physics is built into the representation?
Companion articles: B01