One control parameter drags a system's spectrum between the universal fixed points of random matrix theory. I measure that statement with the same instruments on two substrates: freely vibrating plates and training neural networks — and I publish the hypothesis before the test, the gates with the numbers, and the negatives with the positives.

Six preprints, published as one arc: a falsifiable physics hypothesis, its full open-source test campaign, the quantitative transfer to neural networks, the formal unification — and the payoff: the program's diagnostic turned into a metrological figure of merit.

→ Read the illustrated program report — how the six papers relate, a reading guide, the predictions scoreboard (what held, what broke), and the D₂ bridge, with figures from the papers.

1 · Why Rosenzweig–Porter? Evanescent coupling and a random matrix hypothesis for intermediate statistics in freely vibrating plates    The mechanism (H = H₀ + λV from free-edge evanescent coupling), eight testable predictions, and a preregistered eigenvector fractal dimension D₂ = 0.76 ± 0.15.

2 · Open-source finite-element tests of the Rosenzweig–Porter hypothesis: preliminary results    Twenty preregistered experiment campaigns executing the registered program: the boundary-controlled transition confirmed; a three-tier boundary-adaptedness hierarchy; the D₂ signature exposed as a truncation-protocol artifact, with a real, ordered multifractal residue in its place; a mechanical GOE→GUE crossover with its antiunitary protection theorem, completing at ≈1,500 RPM for a decimeter silicone disk; and a designed plate assembly whose fabricated D₂ lands inside the neural-network band.

3 · A random-matrix account of structure formation in neural networks    The same account, quantitative on the AI side: level repulsion is absent in dense nets but fabricable under forced sector cooperation (causal dose–response, capacity-attenuation law); two routes to the unitary class (the causal mask, exactly; a directional task, genuinely); and the fabricated transition is genuine Rosenzweig–Porter multifractality — D₂ = 0.76, co-transitioning with the spacing statistic on the same Hessian.

4 · Effective-rank collapse marks the semantic phase transition in neural networks    The transferring spectral signature as an order parameter — from frozen transformer heads to a trained 7B (weights, live activations, training) — with a grokking decoupling and a label-corruption dose–response: the coupling, not the magnitude, is the semantic signature.

5 · The dynamic selector and the formal operad are one object    The bridge made literal: instantiating the random-matrix model with an integer Clifford algebra's grades, kernels, and gate, the signatures survive and the composition laws are machine-checked (Coq/Rocq, re-verified at runtime).

6 · Multifractality as a sensing resource: a D2 figure of merit for Rosenzweig-Porter systems, and a lattice platform    The payoff: composing F_Q = 4·chi_f with Kravtsov's exact RP result makes D₂ an operational sensing figure of merit — QFI enhancement exponent 1 − D₂ for multifractal random states under local couplings, confirmed at 4/4 preregistered gates, its boundaries measured (geometric fractality alone: no effect; critical PBRM: extends), with an operator design rule and a constructed cold-atom platform.

plates-rp-fem — the full FEM campaign behind paper 2: certified Argyris / C⁰ interior-penalty eigensolvers, the preregistered experiment registry (E1–E20, frozen readings committed before each run — the git history is the preregistration trail), and the manuscript. Python, CPU-only.

rp-qfi-sensing — companion of paper 6: the gRP/PBRM/Sierpinski fidelity-susceptibility experiments with frozen readings and certified eigensolvers.

rmt-signatures — code + derived-data companion of papers 3–5: per-phase experiment scripts, findings records, and figures — including the machine-checked operad proof (operad_osynth_mech.v: 56 Qed, 0 Admitted, one typing parameter; coqchk-verified).

• Preregistration as a workflow, not a form — every experiment ships with a frozen reading in its header before it runs; amendments are declared, dated, and diffed in git.
• Measurement-based accuracy gates — two-mesh, cross-instrument, and penalty-robustness certification decide what counts, not asymptotic hope.
• Negatives are first-class results — the strongest finding of the campaign is a claim that failed under the true operator, and exactly how.
• Formal claims are machine-checked — if a paper says "proved," there is a .v file and a kernel re-checker exit code you can reproduce.

Neurosymbolic substrate and a quaternionic logic framework — the program that led here.

Triadic Neurosymbolic Engine · repo · doi:10.5281/zenodo.19205805 Prime factorisation as a neurosymbolic bridge: subsumption, composition, and abduction as exact integer operations.

TriadicGPT · repo · doi:10.5281/zenodo.19206545 The projection learned end-to-end in a generative LM (triadic-head on PyPI).

reptimeline · repo · doi:10.5281/zenodo.19208672 Tooling for tracking representation evolution across training.

Layered Ontology of Semantic Duality · repo · doi:10.5281/zenodo.19375167 Empirical evidence for layered semantic duality in transformers.

Quaternionic Logic series · repo · doi:10.5281/zenodo.19562014 · t-norm · synthesis · pre-logical A G-lattice on [0,1]×[−1,1]³ with an SU(2) context action unifying Boolean, fuzzy, modal, trivalent, ordinal, and probabilistic logics.

The program spans random matrix theory, wave chaos, elastodynamics, deep-learning theory, Clifford algebra, and formal verification — no single community covers all of it. If you want to verify a proof, challenge a gate, test a prediction (the 1,500-RPM silicone rotor is waiting for a lab), or connect this to your own work: critical engagement is welcome.

Seeking arXiv endorsement — as an independent researcher I am looking for endorsement to cross-post in cond-mat.stat-mech, nlin.CD, cs.LG, and math.LO. If you endorse in these areas and the work holds up to your reading, it would be much appreciated.

📧 arturoornelas62@gmail.com · ✖️ @Ornelord