Phase 24 · does the system heal itself?
Better protection, and the bill is still unpaid
AT-0191 → AT-0198. Phase 23 showed a nonlinear restoring law disturbs identity less than a matched linear one. That is not a discovery — a stiffer law is stiffer by construction. Here every run carries a third tracked sector, a memory variable, so that 'identity came back' can never be paid for by parking the debt somewhere nobody is plotting.
Current result, stated plainly
PROTECTION IMPROVED RELATIVE TO MATCHED LINEAR BASELINE. IDENTITY DISTURBANCE AND MEMORY RESIDUE REMAIN NONZERO. CORE OBJECTIVE NOT SOLVED.
A stable system can repair small disturbances. The question is whether it can protect what matters while its relationships change — and whether the repair leaves any hidden bill. In this toy model the repair works better than the linear comparison, and it still leaves a bill: identity does not return exactly, and the memory variable does not return to zero.
Lawful substantial change in genuine relational location without destructive traversal, under narrow identity tolerance, invariant preservation, bounded local propagation, pathwise reachability, near-zero complete-state debt, finite action, robustness, transfer without retuning and nontriviality.
Internal toy benchmark, seed 191: matched nonlinear versus linear identity/address system carrying a small memory variable. Across parameter perturbations of 0, 5, 10, 20 and 30 per cent around one fixed parameter set, the nonlinear arm achieved above 90 per cent address progress in all runs and held median final identity disturbance near 0.27–0.28 against roughly 0.46 for the linear baseline. Median memory residue stayed nonzero throughout, near 0.074–0.076 nonlinear against 0.134–0.141 linear. Read it correctly: nonlinear stabilisation improves the numbers, it does not eliminate identity disturbance or memory debt.
This phase sits directly on top of WHERE THE PATH BREAKS and the nonlinear frontier, and every blocker recorded in the blocker ledger still stands.
Controls
Loosening the tolerance or widening the basin makes success easy and meaningless. AT-0191 and AT-0193 exist to make that visible rather than convenient.
Integrating the three-sector system…
Research progress · evidence ladder
Where this work actually stands
Each rung means something different, and a result on one rung never counts as a result on the next. We are on rung three, working. Rungs five and six are empty and we do not pretend otherwise.
- 01Mathematical propertyreached
A statement that follows from the definitions we chose, provable or verifiable by construction.
Gain bound Γ_A ≤ 1 for L1 edge-weight perturbation; invariant-preserving displacement in the 24-D benchmark.
- 02Computational resultreached
A number produced by a specific seeded model run. Reproducible, but only about the model.
AT-0059 → AT-0071: manifold sampling, connectivity, corridor width, detour ratio, action minimisation.
- 03Robust toy-model phenomenonwe are here
A result that survives seed changes, noise, topology changes, countermodels and coarse-graining.
Partially reached: some findings persist across scales and seeds, others are flagged FRAGILE by the gate.
- 04Candidate theoretical principlenot reached
A rule general enough to state without reference to our particular graph, with derived consequences.
No candidate rule has yet survived every countermodel and scale test simultaneously.
- 05Physical predictionnot reached
A quantitative, falsifiable statement about a measurable physical quantity, with an error budget.
None. Graph observables are not mapped to any measurable physical quantity.
- 06Experimental evidencenot reached
Independent measurement agreeing with a prediction that alternatives do not make.
None, and deliberately far away.