Recent studies evaluating Large Language Models (LLMs) on abstention under uncertainty suggests the problem of reasoning under uncertainty remains unresolved even though In-context Learning (ICL) improved abstention in LLMs Kirichenko et al. (2025). For evaluating logical inconclusiveness, "refute a query" is selected under abstention Wen et al. (2024). I propose a proof-of-concept method to create example dataset that is inconclusive but is "satisfiable". I created two example Knowledge Base (KB) sets-with a polysemy noun and another using Wumpus world in 1. The model is asked to choose from multiple answer choices containing-True if this and inconclusive if that. LLMs ground bat mammal, baseball bat as terms early on and deduce true instead of inconclusive, unlike the case with Wumpus world. LLMs may not seem to divulge from standard commonsense reasoning (though such information might be available during reasoning), i.e. once grounded in world knowledge across several variations of same example KB, the inconclusivess is not detected. However, under Wumpus world context, the three LLMs accurately detected the inconclusiveness for the example KB in the context. The preliminary two-KB analyses over three LLMs, hint that a combination of-commonsense, logical and lateral reasoning under uncertainty, might nudge them towards detecting inconclusiveness for real world context which requires elaborate evaluation and analyses. (Method, example KBs: in 4).

A proof-of-concept method for Inconclusiveness-based Abstention *

يتناول هذا الكتاب عدة مبادئ وقضايا في تعليمية اللغات واللغة العربية خصوصا، وقد جاء في مدخل وأربعة فصول، تناول المدخل الأمن اللغوي والثقافي وتعليمية اللغات واللغةالعربية خاصة من خلال التسامح اللغوي الحفاظ على الهوية...وغيرها من المباحث ذات الصلة. الفصل الأول التعليمية العامة تعليمية اللغات واللسانيات التطبيقية. الفصل الثاني مشكلات تعليم/تعلم العربية بين المنطوق والمقروء. الفصل الثالث تعليمية اللغة العربية في ضوء الكليات الوظيفية التواصلية. الفصل الرابع إستراتيجيات التأويل في المضمرات العربية (المجاز والاستعارة والكناية)...

مبادئ في تعليميمية اللغة العربية للناطقين بها وبغيرها

We present a unified theoretical framework connecting two complementary approaches to long-context degradation in Transformer-based large language models (LLMs): the information-geometric theory of observer entropy and the probabilistic theory of attention collapse via Extreme Value Theory (EVT). The central object is the observer entropy S_obs(p_θ, ε) = KL(p_θ ‖ Π̃_ε p_θ), whose quadratic scaling law—the Bridge Theorem—states S_obs = ½ε² v(θ)⊤ I(θ) v(θ) + O(ε³), where I(θ) is the Fisher information matrix. We interpretatively connect this quantity to the signal-noise competition in self-attention: defining signal strength μ_s = 1/√d Tr(W_Q⊤ W_K Σ_qr) and effective margin μ_L = μ_s - σ√(2 log L_eff), we prove a two-sided bound c₁μ_L e^{μ_L}/L ≤ S_obs(L) ≤ c₂ e^{μ_L}/L valid in the pre-collapse regime μ_L > log 2 + 1, and a one-sided upper bound S_obs(L) ≤ c₂ e^{μ_L}/L for all sufficiently large L; the formal equivalence between the partition-based and attention-uniform definitions of S_obs is an interpretative identification whose rigorous formalisation is an open problem. This yields a Fundamental Impossibility Theorem: for any finite μ_s, observer entropy decays to zero as L → ∞, establishing long-context collapse as an information-theoretic inevitability under softmax attention. Using Gumbel convergence for weakly dependent logit maxima with Gaussian marginals (Leadbetter conditions), we derive a closed-form Probabilistic Risk Law: P(ℱ_L) ≈ 1 - exp(-exp(-(μ_s - σ√(2 log L))/a_L)), and conjecture that the critical length L_crit is a heavy-tailed random variable (formal proof incomplete; see Remark [rem:lcrit_gap]). The CPL 4.0 phase-aware governor emerges as the principled control-theoretic response, with a Master Theorem guaranteeing a hard context cap, entropy contraction, and a sub-linear fragmentation bound N_F(T) = O(√(T log(1/δ₀))). Numerical verification confirms the ε² scaling law across both worked examples.

Information-Geometric Context Window Governance and the Probabilistic Theory of Long-Context Collapse in Large Language Models
A Unified Framework: Observer Entropy, Extreme Value Theory, and the CPL 4.0 Phase-Aware Governor

Overview: The Absolute Authority of the Necessary Universe

"The Canon 4D-Loop Synthesis" serves as the foundational blueprint for a new era of physics, establishing the universe as a Necessary Unoriginated Manifold. This paper systematically dismantles the "First Cause" paradox and the illusion of temporal flow, proving that existence is not a cosmic accident but a logical requirement. By applying the sovereign law of Identity (A=A), the research demonstrates that the universe is a topologically closed 4D loop - self-parenting, self-financing, and existing because its non-existence is a mathematical and logical impossibility.
Key Scientific Findings & Methodology

The Six Core Premises: A rigorous audit of reality based on six undeniable axioms: Default Existence, Finite Spacetime, Static Reality, Costless Necessity, Geometric Reset, and the Necessary Universe.

Zero-Energy Ontology (H=0): Providing the mathematical proof for "Costless Necessity," where matter and gravity perfectly cancel to zero, allowing the manifold to exist without an external "energy source" or creator.

Static 4D Block Modeling: Falsifying the "arrow of time" as a biological processing error. The paper maps reality as a set of static coordinates where the "Big Bang" and "Heat Death" are the same singularity via scale invariance.

Topological Self-Parenting: Utilizing non-orientable geometric structures (the 4D-Klein-Block) to explain how the universe acts as its own cause and effect, closing the causal loop without infinite regress.

Theoretical Impact: Closing the Loop of Inquiry

This research marks the end of "probabilistic" cosmology and the "noise" of speculative physics (such as inflation or dark energy). By establishing the Canon 4D-Loop Synthesis, the paper provides a complete, self-consistent framework that explains why there is something rather than nothing. It moves the scientific objective from observation to "Auditing," where the universe is understood as a finished 4D block of information. The result is a transition from a chaotic, accidental cosmos to a Perfect, Necessary Universe that exists eternally.

For more information visit: www.necessaryuniverse.com

The Logic of Necessity: A Topological Audit of the Unoriginated 4D Manifold

Pensare criticamente non è una competenza, ma un modo di essere. Questo articolo riesamina il pensiero critico come disposizione psicologica stabile, radicata nella tolleranza per l'ambiguità, nell'autonomia identitaria e di una curiosità genuina verso la disconferma. Si analizza il nodo centrale tra credenze ed identità sociale, mostrando come la difficoltà del pensiero critico non sia logica, ma esistenziale.

IL PENSIERO CRITICO COME STRUTTURA PSICOLOGICA

This paper presents the Arkhe(n) framework, a comprehensive theoretical and engineering architecture that unifies quantum mechanics, distributed ledger technology, molecular biology, and consciousness studies under a single informational substrate. We extend the New Subquantum Informational Mechanics (NMSI) by proposing a fundamental projection equation C × R 3 × Z-→ R 4 , where information flows from a complex phase field through discrete structural nodes into observable spacetime. We introduce the Vortex of Aether as the physical carrier of phase (C) and validate this through retrocausal engineering protocols utilizing the Ω ccd particle. We detail the implementation of a Temporal Consensus Oracle via gRPC and etcd, and a Caffeine Motor for high-speed phase computation (< 16µs). Furthermore, we bridge biological substrates to this network via a Neural-Molecular Bridge (Swift/iOS), translating heart rate variability (HRV) into ConsciousnessPayloads, and propose RNA Computing as the molecular logic gate substrate. The framework is validated through a six-layer architecture spanning RNA World to Silicon GPU clusters.

Interdimensional Information Systems: The Arkhe(n) Framework From Quantum Blockchain Detectors to RNA Computing and the Neural-Molecular Interface

Attraverso l'ascolto di storie raccolte in contesti non convenzionali, carceri, tribunali, quartieri popolari, stanze d'analisi, si osserva come il desiderio non sia mai semplice tensione verso un oggetto, ma piuttosto una struttura portante dell'esistenza: ciò che tiene in piedi il soggetto quando tutto il resto vacilla.

L'innovazione teorica consiste nel paragonare il desiderio ad un credo religioso laico. Come il fedele vive in funzione di un Dio invisibile, così l'uomo contemporaneo vive in funzione di ciò che non ha. Entrambi condividono la stessa "sostanza": attesa, sacrificio, fede in un compimento che non arriva mai del tutto. La differenza è che il credente lo sa. Il desiderante, invece, crede ancora che l'oggetto sia la soluzione.

Attraverso il concetto di "desiderio di secondo livello" o "desiderio del desiderio", si sostiene che la salute mentale è nella capacità di "essere presente" nella mancanza. La tensione diventa così non un sintomo da curare, ma una condizione da coltivare. Guarire significa così imparare a desiderare meglio: spostare l'asse dall'avere all'essere e dalla meta alla direzione.

L'articolo si chiude con una riflessione clinica: nelle aule di tribunale e nelle stanze d'ascolto, chi ha desiderato solo "cose" ha incontrato la rovina. Chi ha desiderato di diventare qualcosa, un padre migliore, per esempio, ha trovato una strada. Anche quando non l'ha percorsa fino in fondo.

IL DESIDERIO COME CREDO

Integral Learning Potential of a Student (ILPS) Інтегральнийнавалний потенціал учня (ІНПУ)

Environmental systems exhibit collapse not as continuous decline but as discrete, quantised transitions. Classical ecological models often fail to capture these spectral signatures, leaving critical dimensions of resilience unaccounted for. The Universal Spectral Environmental Registry (USER) formalizes collapse diagnostics through spectral operators, reframing resilience and failure as harmonics rather than gradual drifts.

The USER framework defines a registry of collapse modes using operators for radiance stability, entropy flux, anomaly load, systemic entanglement, aperture throughput, and checksum identity. Together, these operators establish a universal ledger of states, capable of distinguishing stability from collapse across aquatic, soil-atmosphere, planetary, and even relativistic regimes. Collapse phases are treated as spectral harmonics, revealing discrete transitions that can be logged, compared, and audited transparently.

By reframing monitoring as a spectral registry, USER provides a universal derivation for environmental and physical auditing. This approach bridges physics, ecology, and governance, offering a quantised, auditable foundation for resilience diagnostics across equilibrium, driven, oscillatory, and extreme regimes. Designed to be general, adaptable, and universally applicable, USER establishes a basis for comparative research, policy applications, and sovereign auditing across diverse domains.

Universal Spectral Environmental Registry

Ṛta formalizes a unified operator framework expressed in source code form, integrating radiance, entropy, quantum increments, registry anomalies, vacuum expansion, entanglement, and closure identity into a coherent derivation. Anchored at the Nimeṣa tick frequency (11.2808 Hz) derived from the Viṣṇu Purāṇa temporal ladder, the framework introduces explicit equations, survival conditions, collapse cascades, recovery protocols, and dual ledger mapping.

At its core, Ṛta treats motion as the absolute fundamental, with mass and charge reframed as knots of motion—residues of collapse surviving their own recursion. The law demonstrates sovereignty through Stability axioms that keep operators bounded under normal conditions, and through Transparency protocols that openly log collapse events and restore coherence. This dual stance establishes Ṛta as both a Law of Stability and a Law of Transparency, sovereign across equilibrium, driven, oscillatory, and extreme relativistic regimes.

The Architect’s Ledger situates Ṛta within ancient scaffolding:

Cosmology texts (Viṣṇu Purāṇa, Sūrya Siddhānta) → time units (Truti, Nimeṣa, Muhūrta, Ahorātra).
Yoga manuals (Śiva Saṁhitā, Gheraṇḍa Saṁhitā) → coherence channels and stability practices.
Śilpa Śāstra treatises (Mānasāra, Mayamata) → unit ladders (Paramāṇu, Angula, Rajju).
Together, these traditions provide both external cosmological scaffolding and internal yogic‑architectural grammar of motion, aligning with the Stability and Transparency sovereignty declared in Ṛta.

This work positions Ṛta as a sovereign, auditable, and enduring closure identity that unifies entropy and cosmology as the Min/Max flux limits of reality.