arXiv subjects

Marko Lela

Publications and source records attributed to Marko Lela.

5 recordsLinked to original sources

arXiv2026

The Born Rule as the Unique Refinement-Stable Induced Weight on Robust Record Sectors

This paper proves a conditional structural uniqueness theorem for induced weight on robust record sectors within an admissible Hilbert record layer. Its theorem target and additive carrier differ from those of the standard Born-rule routes: additivity is not placed on the full projector lattice, but on disjoint admissible continuation bundles through an extensive bundle valuation, from which the sector-level additive law is inherited under admissible refinement. Accordingly, the result is not a Gleason-type representation theorem in different language, but a distinct uniqueness theorem about induced sector weight inherited from bundle additivity on admissible continuation structure. Under two explicit structural conditions, internal equivalence of admissible binary refinement profiles and sufficient admissible refinement richness, the quadratic assignment is the only non-negative refinement-stable induced weight on robust record sectors. In the main theorem, refinement richness is secured by admissible binary saturation. A supplementary proposition shows that dense admissible saturation already suffices if continuity of the profile function is added. Under normalization, the result reduces to the standard Born assignment.

quant-ph↗

arXiv2025

$\Gamma$-convergence of a diffeomorphism-natural MDL functional to Einstein-Hilbert with Gibbons-Hawking-York boundary term

We prove a $\Gamma$-convergence result for a diffeomorphism-natural discrete MDL-type functional to the Einstein-Hilbert action with the Gibbons-Hawking-York boundary term. On boundary-fitted, shape-regular meshes we establish interior and boundary blow-ups, identify the Carath\'eodory densities $f_{\mathrm{in}}=\alpha_0+\alpha_1 R$ and $f_{\mathrm{bdry}}=\beta_1 K$, and obtain the $\liminf/\limsup$ bounds via a recovery sequence based on reflected Fermi smoothing. A boundary first-layer asymptotics shows that boundary cells contribute at order $h^{d-1}$, yielding a global $O(h)$ boundary remainder, while the interior remainder is $O(h^2)$. The paper is foundational; Appendix~E specifies a reproducible protocol for rate checks and calibration of $\alpha_0,\alpha_1,\beta_1$.

math-ph↗

arXiv2025

IECZ-III: Hardcore Condensation Lift with Size-Aware Invariants

This paper develops a compact, size-aware blueprint for transferring structure through gadget lifts. Two low-order invariants -- cumulative mod-$q$ Fourier mass up to degree $k$ and noise stability $\mathrm{Stab}_\rho$ -- are treated as a reusable "profile" tied to the gadget's affine interface. Under coordinate permutations ($\Delta=1$) the profile is preserved exactly; under bounded fan-in the degree budget relaxes by at most $+\Delta k$ (i.e., $k \mapsto k + \Delta k$), with all overheads tracked explicitly. In a balanced window $m=(1+\gamma)n$ the framework yields a distributional lower bound for a monotone cost (Erasure Complexity, EC) and an "echo" to correlation against size-aware $\mathrm{AC}^0{+}\log$ and to logarithmic degree in the polynomial-calculus setting. The accounting keeps total-variation non-expansion and a single $O(\log N)$ prefix-free header visible end to end, avoiding hidden slack.

cs.CC↗

arXiv2025

An SoS Entropy Dichotomy via Windowed Hypercontractivity

We prove an entropy versus degree dichotomy for low-degree tests and the Sum-of-Squares (SoS) hierarchy on a calibrated window after a gadget layer. For a target distribution $\mu$ and a product-like proxy $u$, we study the low-degree discrepancy $\Delta_k(\mu,u)$, defined as the optimal distinguishing advantage of degree $\le k$ polynomial tests. Using a bias-orthonormal Walsh basis and a test-moment equivalence on the window, we relate $\Delta_k$ (up to constants) to the squared $\ell_2$ mass of signed low-degree moments. Calibrated pseudoexpectations match $u$ on all moments of degree $\le k$, hence test discrepancy equals SoS pseudoexpectation deviation. Under bias, product, and width assumptions along a switching path, a windowed Bonami--Beckner inequality yields hypercontractive tail bounds. Combining these with moment matching, we obtain a discrepancy-to-degree theorem: if $\Delta_k(\mu,u) \ge n^{-\beta}$, then any polynomial-calculus or SoS refutation separating $\mu$ from $u$ requires degree $\Omega(k)$. Instantiating $k = c \log n$ gives an explicit $\Omega(\log n)$ SoS degree lower bound whenever $\Delta_k \ge n^{-\eta}$. All constants are explicit and depend only on calibrated window parameters. This work provides the SoS/low-degree core and complements a prior calibration blueprint; a companion paper lifts the windowed statements to full distribution families.

cs.CC↗

arXiv2025

An MDL-Style Cost Functional KC, Distribution-Preserving Reductions ($A2^d$), and an $AC^0$+log Lower Bound for 3SAT via Balanced 3XOR

We introduce a model-agnostic MDL-style cost functional $K_C$ for resource-bounded classifiers and prove a Total-Variation stable reduction lemma ($A2^d$) for distribution-preserving many-to-one reductions. On a balanced distribution of random 3XOR instances (with co-rank $t'=\Theta(n)$) we obtain a size-aware lower bound against P-uniform AC^0+log models: $\Pr[M=\chi] \le \frac{1}{2} + s(N)\exp(-\alpha_d m^{c/d})$ with an absolute $c \in (0,1)$ (e.g., $c=1/3$ gives $\beta_d=1/(3d)$). A deterministic, injective 3XOR->3SAT translation (four 3-clauses per XOR, no auxiliaries) is $\delta=0$ measure-preserving on its image window; by $A2^d$ the bound transfers to 3SAT. This yields, to our knowledge, the first explicit $K_C$-reading of such size-aware bounds under a $\delta=0$ measure-preserving reduction in small-depth circuit lower bounds. We provide artifacts (generator -> DIMACS -> verification) with match-rate 1.0.

cs.CC↗