2026 · Vladi Ivanov
The Functional Proximity Law: Hub Centrality Preservation in Multilayer Networks Across Domains
Proposes and empirically tests the Functional Proximity Law: hub importance scores correlate more strongly between layers encoding functionally similar relationships than between dissimilar ones. Confirmed across 41 pre-registered experiments spanning molecular biology, neuroscience, software systems, ecology, formal mathematics, AI architecture, finance, physics, medicine, and digital circuits.
Key findings
- —38 confirmed, 8 denied across 41 pre-registered experiments
- —Boundary conditions: BC_RADIAL (structural degeneracy), BC_INVERSION (fan-out with leaf clustering), resolution mismatch, institutional mismatch
- —Observer Projection Law (OPL): AI language models recover infrastructural centrality (d2) in 3 domains; humans do not
- —Hub Trajectory Types: AMPLIFYING vs INVERSION distinguishes developmental stage in Drosophila
molecular biologyneurosciencesoftwareecologymedicineAIphysics
2026 · Vladi Ivanov
No Valid Ramsey(5,5;42) Coloring is Circulant on Z₄₂: An Exhaustive Proof with Z₂₁-Bi-Circulant Search
Establishes by exhaustive enumeration that no circulant graph on Z₄₂ yields a two-coloring of K₄₂ avoiding monochromatic K₅. All 2²¹ generating sets tested with a bitmask clique-detection algorithm. Introduces bi-circulant search: a symmetry-restricted local search achieving 84 monochromatic K₅ violations, improving the unconstrained tabu baseline of 146 by 43%.
Key findings
- —No circulant on Z₄₂ is a Ramsey(5,5) witness — exhaustive over all 2²¹ generating sets
- —No circulant on Z₄₃ witnesses R(5,5) ≥ 44 (1,048,575 candidates)
- —Bi-circulant search reaches 84 violations consistently — 43% improvement over unconstrained baseline
- —Replication under D₂₁ and Z₇×S₃ symmetry groups
combinatoricsgraph theorycomputational mathematics
2026 · Vladi Ivanov
Cancer Structural Pharmacology: Oncogenic Decoupling Signature in NSCLC Signaling
Applies IRDME structural analysis to NSCLC cancer signaling. Shows that nodes whose removal increases cross-layer coupling (structural disruptors) show higher CRISPR essentiality than structural anchors. Identifies MYC, mTOR, and KRAS as simultaneously disruptive and essential. TP53 and PTEN are anti-essential structural voids.
Key findings
- —Oncogenic Decoupling Signature (ODS): r(Δr, CRISPR_essentiality) = −0.722, p = 0.0024
- —MYC (CRISPR=−2.14) is the most essential undrugged cancer hub and a structural disruptor
- —TP53 and PTEN are anti-essential (cancer benefits from their loss) and structural anchors
- —Decoupling boundary: ODS denied in CRC WNT pathway (r = −0.015) — tissue-specific
cancer biologypharmacologynetwork medicine
2026 · Vladi Ivanov
Topology as Logic: Hub Geometry Recovers Operational Structure in Dependency Graphs
Shows that betweenness-based hub persistence in dependency graphs recovers operational logic structure — the load-bearing organization of a system — without reading any content. Tested across digital circuits, formal proof corpora, legacy COBOL, cross-species neural connectomics, and prebiotic autocatalytic networks.
Key findings
- —Digital circuits: carry-chain nodes identified from topology alone (betweenness r = 0.771)
- —Formal mathematics: Lean 4 mathlib4 hub persistence r = 0.777, p = 0.004
- —C. elegans hub grammar transfers to Drosophila across 600 million years
- —Key finding: betweenness >> degree for detecting load-bearing logic signal
formal methodssoftwareneurosciencecomputational biology