# 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.