The next paper pass should lead with generator discovery, symbolic verification, and corrected GlobalMOO/CASCADE simulations. Claims that depend on bigeometric derivatives now distinguish the elasticity diagnostic L_BG from the multiplicative derivative D_BG.
Publish the generator discovery demo as the bridge between NNC, sparse model discovery, and constraint-preserving GlobalMOO optimization.
Open demo →Keep symbolic checks, log-space regularization, CFD shock detection, and CASCADE boundary search, but normalize terminology and metrics across pages.
Quantum unitarity and cosmology tension claims stay as limitations or negative results unless a corrected generator or conservation law is proven.
| paper | title | status | next correction |
|---|---|---|---|
| New | Generator Discovery and Coordinate Regime Selection | Draft first | Use the new demo as the empirical front door: exponential, power-law, logistic, sparse dynamics, and constrained GlobalMOO wrappers. |
| P12 | Symbolic Verification | Keep as anchor | Use this to state the corrected L_BG versus D_BG identities before any singularity claims. |
| P03 | GlobalMOO CFD / Shu-Osher | Revise metrics | Keep the real L_BG shock detector result, but reconcile all improvement percentages on the site. |
| P13/P14 | CASCADE Boundary Search | Reframe | Present as transformed search near hard regions, not as a proof that singular fields become finite. |
| P02 | Log-Space Regularization | Strengthen | Tie to Box-Cox limits, bigeometric elasticity, and positivity-preserving parameterizations. |
| P05 | Quantum Geometry | Limit claim | State that naive bigeometric evolution is not unitary unless normalization or a valid generator is added. |
| P06 | Cosmology H0/S8 | Negative result | Keep as falsification: uniform k does not solve the tensions. |
Use these statements before singularity-adjacent simulations or demos.
L_BG[r^n] = n and D_BG[r^n] = exp(n) for r > 0 and positive fields.
L_BG[1/r] = -1, while D_BG[1/r] = exp(-1), not -1.
The transformed diagnostic is bounded; the original field can still diverge.
Direct papers and docs used to position the corrected work.
Brunton, Proctor, and Kutz
Sparse governing-equation discovery baseline.
Williams, Kevrekidis, and Rowley
Lifted-coordinate dynamics and dictionary selection context.
Box and Cox
Classical precedent for transform selection as statistical modeling.
Deb, Pratap, Agarwal, and Meyarivan
Canonical Pareto search reference for multiobjective optimization.
GlobalMOO
API framing for ask-tell style constrained model search.
Add generator discovery first, then wire the GlobalMOO constraint wrapper into the simulator surface, then reconcile CFD and CASCADE metrics.
Draft the new generator discovery paper, update P12 and P03 terminology, and keep P05/P06 as bounded or negative results until the math supports stronger claims.