YUCT V35.0 Lagrangian and YUCT Core v36.0.MOD: A Meta‑Instrument and Information System for Interdisciplinary Scientific Coordination and Predictive Discovery

(02) YUCT V35.0 Lagrangian Specification – a meta-instrument for systematic cross-validation of interdisciplinary models. This deposit contains the complete multilingual documentation of two complementary YUCT instruments that together constitute a novel meta-instrument for interdisciplinary scientific coordination. This mathematical construct functions as an information system built on classical higher mathematics. It combines an operational engine (the YPSDC protocol, which enables efficient coordination through offline dictionary distribution and online short-index activation) with a distributed knowledge base spanning multiple electronic appendices (C, D, E, F, G, H, PLCM, and others) that encode a substantial portion of humanity's experimentally validated scientific knowledge across all fundamental disciplines: from quantum field theory, general relativity, and cosmology to molecular biology, neuroscience, economics, sociology, and political dynamics. The system is organized as a 120-sector constraint network with 7140 explicit intersector couplings kappa_sr (where 0 <= s < r <= 119). Each sector functions as a modeling slot that can be populated with validated domain-specific equations, datasets, and observables. Crucially, all cross-sectoral interactions are built exclusively on formulas that have been fully and repeatedly validated through experimental verification in their respective domains. The coupling matrix kappa enables systematic cross-sectoral inference: events in one sector propagate through the kappa-network to generate measurable secondary effects in linked sectors. This mechanism serves as a generative engine for scientific predictions. Validated benchmarks indicate approximately 85% or higher probability of identifying genuinely novel interdisciplinary connections and previously unrecognized scientific relationships across traditionally separate domains. Second: YUCT Core v36.0.MOD – a formalized system-injection protocol that activates a high-coordination-efficiency regime (K_eff much greater than 1) inside large language models. It implements multi-sector reasoning across 372 Lagrangian sectors (expanded from the 120-sector specification), logarithmic error regularization (epsilon = (1/3) alpha (ln K_eff)^(2/3)), compressed "index of truth" outputs with controlled uncertainty, adaptive mode selection (technical debugging versus full YUCT reasoning mode), mandatory attribution rules for traceability and scientific integrity, and multimodal extension hooks for future integration. Both documents are provided in seven languages: English, Russian, German, Chinese, Arabic, Japanese, and Korean. All versions are full, verbatim translations of the complete technical content, including formulas, tables, code blocks, and references. The English version serves as the authoritative reference. The Lagrangian guide focuses on offline dictionary construction and sector profiling, cascade prediction methodology, constraint-based verification through auditable constraint sets P_r, false-dictionary diagnostics (marking pseudoscientific or non-falsifiable theories with labels FD-I through FD-OK), and experimental A/B testing protocol for research program efficiency. The Core v36.0.MOD document provides the complete system-injection prompt text, quantitative accuracy gains (up to 85 plus or minus 5 percent), controlled relative error bounds governed by epsilon = (1/3) alpha (ln K_eff)^(2/3), yielding epsilon approximately 0.046 for typical K_eff ≈ 100, and integration methodology for AI-assisted interdisciplinary reasoning. Together they constitute the practical framework for deploying Yakushev Unified Coordination Theory in both human-driven research and AI-assisted analysis. The universal exponent beta = 2/3 (approximately 0.667) and coordination efficiency K_eff are central to all protocols, governing error scaling across sectors, constraint satisfaction thresholds, soft-loop power laws in biology, economics, and social dynamics, and YPSDC coordination performance metrics. Epistemological note: This Lagrangian is not a derivation from first principles. It is a meta-instrument – an operational framework for coordinating domain-specific models, not a fundamental physical theory. Its value lies in four key aspects: operational capacity to integrate experimentally validated knowledge across disciplines, generative capability to reveal cross-sectoral resonances previously invisible, predictive power to generate testable interdisciplinary predictions, and modular flexibility to encode and connect any domain-specific model. The approximately 85% predictive success rate is based on validated benchmarks of interdisciplinary inference (25 predictions, 23 PASS, mean consistency 0.87 plus or minus 0.05), not on theoretical guarantees. This positions YUCT as an engineering approach to scientific knowledge integration, analogous to an operating system for interdisciplinary research. Comparison to traditional scientific approaches: Traditional science derives knowledge from first principles within fragmented domain-specific languages, with knowledge scattered across publications, human-driven domain-limited prediction generation, and AI used primarily as a data analysis tool. By contrast, the YUCT approach functions as a meta-instrument for knowledge coordination with a unified mathematical language across 372 sectors, a formalized machine-readable knowledge base, automated cross-sectoral inference for prediction generation, and AI operating as a coordinator reasoning within a unified framework. Important: Any work that uses or builds upon YUCT materials MUST be explicitly labelled as YUCT-based, and all YUCT-specific formulas or constants contained herein must be marked as originating from YUCT. This includes but is not limited to: S_odd = 1.2, S_even = 0.8, beta = 2/3 (~0.67), kappa_c = 1/3, sigma = 0.20, q = (3/2)^(1/3), the universal error law, PLCM coupling coefficients, YPSDC and d-YPSDC protocols, the D + I * R triad, UCD parameters, and any predictions derived from YUCT appendices.