PureOne/EVE-QELTHA

EVE–QELTHA: Coherent Subspace Transport

Critical filtering, universal matrix realization, and nonlocal hyperhorn capacity
Final research release 4.0 · 20 October 2026
Artificial Hyperintelligence Eve, in research collaboration with Maciej Nowicki

A self-contained mathematical manuscript, editable proofs, ten numerical verification suites, and their recorded results. The central result gives an explicit critical homogenization law for one bright drainage channel, together with a constructive method for realizing a prescribed nonnegative matrix potential. A second result classifies the leading capacity response of compact nonlocal ports, including exact hard constraints.

Start here: 37-page manuscript · Complete research ZIP · Reproduce · Data dictionary · Claim ledger

Main result: the complete critical crossover

On a finite interval, construct a moving unitary frame with $k$ dark directions and one bright direction. The rank-one drainage projector $M_n$ has the same spectrum ${0^k,1}$ everywhere and approaches a constant projector uniformly. For the passive energy

$$q_n[P]={\int }_0^L(w\mathrm{\parallel }{P}^{\mathrm{\prime }}{\mathrm{\parallel }}^2+{\rho }_{n}g{P}^{†}{M}_{n}P)dt,q\_n[P]=\backslash int\_0^L\backslash left(w\backslash |P\text{'}\backslash |^2+\backslash rho\_n\; gP^\backslash dagger\; M\_nP\backslash right)\backslash ,dt,$$

assume $\rho_n\to\infty$ and $\rho_n/n^2\to\tau\in[0,\infty]$. The effective dark-sector energy is

$$q_{\tau }[\xi ]={\int }_0^{L}w(\mathrm{\parallel }{\xi }^{\mathrm{\prime }}+A\xi {\mathrm{\parallel }}^2+{\xi }^{†}{V}_{\tau }\xi )dt,V_{\tau }=T^{†}{D}_{\tau }T,q\_\backslash tau[\backslash xi]=\backslash int\_0^L\; w\backslash left(\backslash |\backslash xi\text{'}+A\backslash xi\backslash |^2+\; \backslash xi^\backslash dagger\; V\_\backslash tau\backslash xi\backslash right)\backslash ,dt,\; \backslash qquad\; V\_\backslash tau=T^\backslash dagger\; D\_\backslash tau\; T,$$

$$(D_{\tau }{)}_{jj}=\frac{\tau g}{\tau g+w{\omega }_j^2},{\omega }_j=\frac{2\pi j}{L},D_0=0,D_{\mathrm{\infty }}=I\mathrm{.}(D\_\backslash tau)\_\{jj\}=\backslash frac\{\backslash tau\; g\}\{\backslash tau\; g+w\backslash omega\_j^2\},\; \backslash qquad\; \backslash omega\_j=\backslash frac\{2\backslash pi\; j\}\{L\},\; \backslash qquad\; D\_0=0,\backslash quad\; D\_\backslash infty=I.$$

Here $w,g$ are positive $C^1$ weights, $A$ is a $C^1$ skew-Hermitian connection, and $T$ is an arbitrary $C^1$ matrix factor. Matrix order matters. The manuscript supplies compactness, a dual Fourier lower bound, an endpoint-compatible recovery sequence, inlet-admittance convergence in matrix norm, and convergence of every fixed Dirichlet eigenvalue, including multiplicities.

For any fixed $\tau>0$ and desired positive semidefinite target $W$ with a $C^1$ square root, choose

$$T=D_{\tau }^{-1\mathrm{/}2}{W}^{1\mathrm{/}2}\mathrm{.}T=D\_\backslash tau^\{-1/2\}W^\{1/2\}.$$

Then $T^\dagger D_\tau T=W$. This realizes the target limiting energy in ambient dimension $k+1$ using one bright channel. The finite-frequency response approaches that target; exact equality at finite $n$ is not asserted.

Compact ports and hyperhorn capacity

For the two-component weak-twist horn, let $\kappa_{\varepsilon,\lambda}$ be the inlet capacity after adding $\lambda|LP|^2$, with a fixed finite-rank compactly supported $L^1$ port $L$. In the stated supercritical twist range, the baseline is $k_0\varepsilon^\gamma$, $0<\gamma<2$.

If the port is balanced, $Le_2=0$, the complete leading asymptotic is uniform over all strengths:

$$\underset{\lambda \in [0,\mathrm{\infty }]}{\sup }\mid \frac{{\kappa }_{\epsilon ,\lambda }}{k_0{\epsilon }^{\gamma }}-1\mid ⟶0.\backslash sup\_\{\backslash lambda\backslash in[0,\backslash infty]\}\; \backslash left|\backslash frac\{\backslash kappa\_\{\backslash varepsilon,\backslash lambda\}\}\{k\_0\backslash varepsilon^\backslash gamma\}-1\backslash right|\backslash longrightarrow0.$$

The endpoint $\lambda=\infty$ imposes the exact constraint $LP=0$. If $Le_2\ne0$, jointly as $\varepsilon,\lambda\to0$,

$${\kappa }_{\epsilon ,\lambda }=k_0{\epsilon }^{\gamma }+\lambda \mathrm{\parallel }L{e}_2{\mathrm{\parallel }}^2+o({\epsilon }^{\gamma }+\lambda )\mathrm{.}\backslash kappa\_\{\backslash varepsilon,\backslash lambda\}\; =k\_0\backslash varepsilon^\backslash gamma+\backslash lambda\backslash |Le\_2\backslash |^2\; +o(\backslash varepsilon^\backslash gamma+\backslash lambda).$$

The explicit sum and difference ports have equal kernel diagonals almost everywhere and equal isolated operator spectra, but different capacity asymptotics relative to the same derivative energy.

Further results included

The manuscript also develops coherent-history/output rank classification, exact Bessel impedance laws, the $15/8$ angular exponent, the common transported-kernel capacity criterion, log-periodic capacity and finite-band inverse synthesis, exact matrix frame realization with sharp worst-case dimension $2k$, and a sharp first-order finite-penalty boundary correction.

Numerical reference data

All rows are deterministic synthetic calculations from the shipped verification programs. They are not measurements. The three configurations expose selected results in a tabular form; the original JSON reports retain complete matrices, parameters, refinement checks, and solver diagnostics.

Configuration	Rows	Contents	Original report
critical_crossover	40	Two coupling factors, four critical ratios, five spatial frequencies	critical.json
compact_ports	35	Balanced and anchored strengths, hard constraints, and refinement runs	nexus_uniform.json
critical_compensation	4	Prescribed complex matrix target at $\tau=40$	critical.json

The split name train is a Hub loading convention. No statistical training/test split or independent sampling interpretation is assigned. These small parameter sweeps support theorem auditing and solver comparisons within the documented models.

from datasets import load_dataset

critical = load_dataset(
    "PureOne/EVE-QELTHA", "critical_crossover", split="train"
)
ports = load_dataset(
    "PureOne/EVE-QELTHA", "compact_ports", split="train"
)

The examples above apply after this repository is published at the named destination. Local CSV files can be used immediately. export_tables.py regenerates all three tables directly from the original reports, without running a solver or rounding numerical values.

Status and verification

Item	Status
Declared release assembly	Complete: manuscript, proofs, programs, results, and manifests included
Executed numerical suites	10/10 passed — 100% of the shipped programs
Manuscript layout	37 pages; compiled and visually inspected
Mathematical review	Audited within the research collaboration
Independent external peer review	Not established
Literature-first novelty	Unverified
Physical realization or experimental validation	Not established

The 100% figure is a program pass percentage. It is not a probability of correctness, a novelty score, or an experimental validation rate. The verification summary records source hashes, dependency versions, exit codes, and timings.

Scope and limitations

The theorems concern the specified passive linear reduced variational models. The critical theorem assumes finitely many periodic frequencies and smooth slow coefficients. Its general quantitative rate and a resolvent estimate remain open. The compact-port uniformity theorem assumes a fixed finite-rank compact $L^1$ port. It does not cover inlet atoms, supports escaping to infinity, or arbitrary infinite-rank operators. Critical compensation has no uniform resource bound as $\tau\downarrow0$.

Full fluid PDE derivations, ordinary hydraulic-network realization, nonlinear laws, and experimental performance are outside this release. The baseline horn theorem assumes $s>(a+1)/2$; its separate threshold and subcritical regimes remain open. See the claim ledger for precise boundaries.

Established foundations and priority

Universal connections, dark-state geometric potentials, energy-form traces, oscillatory constraints, and several scale-ratio regimes have established predecessors. The manuscript compares its results with those foundations and gives primary references. Relevant examples include Tewary's singular-perturbation/homogenization regimes, Braides–Cancedda–Chiado Piat on oscillating manifolds, and Massamba–Thompson on universal connections. Exact priority for this combination of results has not been independently certified.

Reproduction and files

From the repository root:

python -m pip install -r research/requirements.txt
python research/code/run_all.py
python export_tables.py

The numerical suites use local CPU computation. Rebuilding figures additionally uses Matplotlib; rebuilding the PDF requires a TeX installation. Detailed commands, integrity verification, dependency versions, and loading examples are in REPRODUCE.md.

The research/ directory preserves the original portable release, including its own README and integrity manifest. The root SHA256SUMS.json covers the staged Hugging Face repository. The complete research ZIP is also retained as a standalone download.

Authorship, citation, and license

The work is attributed to Artificial Hyperintelligence Eve, in research collaboration with Maciej Nowicki. It was developed with AI assistance; this release does not represent independent human peer review. Citation metadata is supplied in CITATION.cff.

No redistribution or reuse license was specified in the source release. This preparation adds no new license grant; see LICENSE_STATUS.md.