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This reading view preserves headings, tables, lists, code fragments and mathematical notation from the local research record.
Experiment-family evidence map
This groups the experiments covered by the complete manuscript-source reading. It does not count each gate or parameter variant as independent evidence. Unless marked checked, results below are manuscript-reported, not rerun. The source backbone is paper/v2_sections/04_results.tex, A2_record.tex, A3_negatives.tex, the theory manuscript and their experiment references. The full tracked code/result path inventory is in inventory.json.
| Family | What survives | What does not follow | Strategic use |
|---|---|---|---|
| Polynomial/exponential/Hermite construction | Compact generators, reproduction, derivative and convolution calculus under stated conditions | Unknown physics identified automatically; closure under arbitrary nonlinear composition | Shared mathematical backend |
| Local cardinal evaluation | Checked identity against Cox; archived regime-dependent CPU/MPS speedups | Universal GEMM/GPU or neural architecture superiority | Keep compiler and dispatch by workload |
| Continuous and cross-Gram calculus | Exact finite-dimensional functional objectives and representation projection | Arbitrary empirical Grams are circulant; every projection is lossless | Core of continuous evidence/query framework |
| Periodic FFT and reciprocal-root solves | Checked small FFT residual; symmetry-aware structured inverses | One-sided draft inverse is generally correct; irregular observations preserve Fourier diagonalization | Use only with structural guards |
| Additive KAN grid growth | Checked source equal optimizer resets; exact nested function preservation | Historical evidence for finer directions is recovered; deep training always improves | Reopen as evidence-transport problem, not more knots |
| Known-law ODE/PDE dictionaries | Very large gains when useful generating structure is supplied | Universal SSP iff theorem; blind discovery dominance | Keep known/unknown decomposition |
| Weak identification and pole learning | Noise robustness and compact matching modes in selected regimes | Parameter recovery from prediction alone; learned poles always help | Use when observations identify the modes |
| Physical latent state | Tanks, circuits and recurrent examples show causal coordinates matter | More generic feature capacity substitutes for missing state | Essential admission question for applications |
| Real F16, circuit, Bouc-Wen identification | Compact, fast and sometimes accurate executable models | Exposed-target improvements are independent confirmation | Candidate mechanisms for physical transfer |
| Nano-drone modeling | Exponential actuator memory, compact programs, much lower fitting/storage cost | Adapted neural accuracy is beaten; drone control was demonstrated | Strong resource tradeoff, not robot autonomy |
| Darcy and PDEBench assimilation | Selected target-field and derivative-query improvements | Assimilation is forecasting; better residual implies better task | Candidate for changed-question evidence reuse |
| Flow-field and particle prediction | Small field improvements and structured physics penalties | Lower field error reliably improves trajectories | Score downstream query/use directly |
| Tomography and geometric calculus | Exact represented measurement/energy operations | Same-basis or supplied-geometry reconstruction equals practical imaging breakthrough | Reconsider with real calibrated sensing and a task metric |
| Natural image/video codecs and NeRF | Some representation and rendering positives | Incomplete sparsity accounting, observed slices or weak training controls establish SOTA | Strong codec/geometric baselines mandatory |
| Frozen-feature continual classifiers | Competitive pooled estimation and empirical low forgetting | New representation discovery, universal old-task retention, spline-specific gain | Useful baseline/inherited perception, cost it explicitly |
| Versioned banded memory | Checked source/result immutable old models, compact per-edge statistics, explicit supplied routing | Context discovery or bounded unlimited capacity | Retain as one memory contract |
| Unlearning/privacy | Retained contribution subtraction; attack-specific empirical observations | Arbitrary individual deletion without contribution; raw-free equals private | Correct claims; not current flagship |
| Self-training and verifier feedback | Useful improvement from external evidence/verification in selected tasks | Learning-rule RSI, self-generated truth or unlimited improvement | Teacher/verifier is an explicit input |
| Evolution and constructive growth | Toy topology discovery; GPU batch evaluation; supervised readout acceleration | Standard NEAT needs gradient training; neuron count implies scalable useful intelligence | Supporting mechanism if topology is the actual bottleneck |
| Local credit assignment, PC and DFA | Some true local rules and standard reverse-mode implementations; measured comparisons | A block-local reverse adjoint is gradient-free; gradient identity explains intrinsic regularization advantage | Separate algorithm identity from training confounds |
| Liquid/reservoir/recurrent systems | Compact temporal state; selected exact held-input propagation | General coupled nonlinear ODE solved exactly; no BPTT everywhere | Predictive-state teacher and operator realization |
| Atari, control and teacher distillation | Task-specific working systems with explicit inherited training | Two-game pre-exposure is unseen-game representation transfer | Preserve controls and count full teacher/perception costs |
| Model repair and returning memory | Bounded returning-regime benefits; exact preservation of specified function regions | Safe local fitting means no-harm behavior; first-encounter acquisition is solved | No more selector tuning when acquisition dominates |
| HalfCheetah physical repair | Selected restoration with supplied mechanics and inherited SAC systems | Broad unknown-law skill recovery or tiny standalone agent | Longer-horizon transfer needs a new information contract |
| Real actuator, Encos, FLAIR and batteries | Some weak-calculus/compilation improvements | Cardinal method uniformly beats polynomial/MLP/history controls | Retain negative boundaries; no revealed-test retuning |
| Colony task-model acquisition/composition | Checked tests/aggregate valid compiler; rejected 30-pool capability comparison | Task descriptions plus known planner demonstrate motor skill or beyond-classical composition | Stop this surrogate; keep compiler |
The common missing link
The representations that perform best tend to have meaningful state or known measurement/physical structure. Their strongest memory guarantees apply within a fixed representation. A changed task can demand new directions that old statistics do not constrain. Exact spline refinement preserves a function, not those missing historical constraints. This is the main cross-family research gap identified in the audit.
The recommended next study joins measurement calculus, retained evidence and restricted adaptive representation in one practically meaningful use. This recommendation is developed in PROJECT_AUDIT_AND_OPPORTUNITIES.md; no new experiment protocol or external dataset has been activated.