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MongoDB Aggregation Pipeline Performance: Analysis of Query Plan Selection and Optimizer Behavior Across Versions and Collection Scales
Rosen Ivanov
Posted: 31 March 2026
Content-Aware Adaptive Dense Communication Network: Enhancing Multi-LLM Collaboration with Dynamic Information Flow
Anthony White
,Joshua Allen
Posted: 31 March 2026
Semantic Core for Sensor Telemetry Ingestion for Digital Twins
Oleksandr Osolinskyi
,Khrystyna Lipianina-Honcharenko
,Myroslav Komar
Posted: 28 March 2026
Design Insights for Exploring Identity Bubbles with Alternate Reality Gameplay
Guilherme Almeida
,Mariana Seiça
,Licínio Roque
Posted: 27 March 2026
Theory of Epistemic Abductive Geometry (TEAG): A Unified Theory of Admissibility-Driven Inference Across Dynamical Systems, Measure Theory, and Language
Moriba Kemessia Jah
We introduce the Theory of Epistemic Abductive Geometry (TEAG), a framework for non-Bayesian inference grounded in admissible-support contraction under possibility theory. The central object is the TEAG quintuple \( \mathcal{E} = (H, \pi, \{H_\alpha\}_{\alpha\in(0,1]}, C, A) \), where evidence acts by contracting the geometry of admissible hypotheses rather than redistributing probabilistic belief mass. Falsification has two-stage structure. Under the log-admissibility transformation \( \Phi(h) = -\log\pi(h) \), the canonical TEAG conjunctive update becomes tropical addition in the max-plus semiring: \( \Phi^+(h) = \Phi^-(h) \oplus \psi(h) = \max\!\bigl(\Phi^-(h),\,\psi(h)\bigr), \) where \( \psi(h) = -\log\kappa(y\mid h) \) is the surprisal of hypothesis h under observation y. The tropical variety of this polynomial, \( \mathcal{B}_{\mathrm{active}} = \bigl\{h \in H : \Phi^-(h) = \psi(h)\bigr\}. \) is the active deformation front: the exact locus where incoming evidence first matches prior impossibility and begins to deform the posterior field. This is a necessary condition for falsification but not sufficient. Sufficient falsification requires exit from the PCRB admissible basin \( \mathcal{A}_k = \{h : \Phi^+_k(h) \leq c_k^\star\} \), where \( c_k^\star \) is the equipotential threshold determined by the PCRB at step k. Popper's criterion thus receives a two-stage algebraic formulation: the tropical variety marks where falsification becomes possible; the PCRB basin boundary marks where falsification is complete. Within the class of possibility-theoretic recursive inference systems, this is, to the best of our knowledge, the first exact formulation of this distinction. Main results. 1. Epistemic Contraction Theorem. Contraction is tropical addition: \( \Phi^+ = \Phi^- \oplus \psi \). Posterior α-cuts satisfy \( H_\alpha^+ = H_\alpha^- \cap E_\alpha(y) \): geometric intersection, not belief redistribution. The active deformation front is the tropical variety \( \mathcal{B}_{\mathrm{active}} \); the falsification boundary is the PCRB admissible basin boundary \( \mathcal{B}_{\mathrm{adm}} \). 2. Possibilistic Cramér–Rao Bound (PCRB} For any filter in the class \( \mathcal{F} \) of epistemically admissible, contraction-based recursive estimators satisfying Axioms 2.1–2.5: \( \mathcal{E}_{\pi,k|k} \geq \mathcal{E}_{\pi,k|k-1} + \tfrac{n}{2}\log(1-I_k) \), where \( I_k \) is the Choquet integral of per-hypothesis surprisal against the prior possibility capacity. Within this class, the ESPF [28] is the unique filter achieving this bound with equality, and is therefore the unique minimax-entropy-optimal set-based recursive estimator under bounded epistemic uncertainty. 3. Tropical Hamilton–Jacobi structure (summary). The TEAG update is structurally consistent with a tropical Lagrangian \( L = T - V \), Legendre transform to a tropical Hamiltonian equal to the surprisal field, and a Hamilton–Jacobi equation whose solution is the tropical addition rule. The Euler–Lagrange equations on the epistemic manifold yield geodesic motion with explicit Levi–Civita connection and Christoffel symbols. This structure is interpretive and consistent with the axioms; full derivations are in the companion paper [31]. Taken together, this structure admits a precise interpretation: the TEAG update rule is a max-plus dynamical system whose governing equations have the same algebraic form as the Hamilton–Jacobi equations of classical mechanics, instantiated on hypothesis space rather than physical space. 4. Gaussian collapse. Probability theory is the collapse limit of TEAG as epistemic width \( W \to 0 \): Choquet converges to Lebesgue, the ESPF recovers the Kalman filter, and \( \mathcal{E}_\pi \to \tfrac{1}{2}\log\det\Sigma + \mathrm{const}(n) \). Probability is earned by evidence, not assumed. Epistemic neutrality and knowledge-system synthesis. Because TEAG's axioms require only a hypothesis space, a possibility field, and a contraction operator — not a probability measure, a likelihood function, or a frequentist grounding — heterogeneous knowledge systems can each instantiate the TEAG quintuple independently. Their joint admissible support intersection is the locus of coherence: the set of hypotheses neither system has falsified. No transformation of one system into the other's representational primitives is required. The composition theory (Section 6) formalizes the coupling architecture. Four instantiations provide the unifying structure: the ESPF [28] for recursive state estimation; the Geometry of Knowing [29] for measure-theoretic collapse; the minimax-entropy optimality proof [30]; and the Possibilistic Language Model (PLM, forthcoming [32]).
We introduce the Theory of Epistemic Abductive Geometry (TEAG), a framework for non-Bayesian inference grounded in admissible-support contraction under possibility theory. The central object is the TEAG quintuple \( \mathcal{E} = (H, \pi, \{H_\alpha\}_{\alpha\in(0,1]}, C, A) \), where evidence acts by contracting the geometry of admissible hypotheses rather than redistributing probabilistic belief mass. Falsification has two-stage structure. Under the log-admissibility transformation \( \Phi(h) = -\log\pi(h) \), the canonical TEAG conjunctive update becomes tropical addition in the max-plus semiring: \( \Phi^+(h) = \Phi^-(h) \oplus \psi(h) = \max\!\bigl(\Phi^-(h),\,\psi(h)\bigr), \) where \( \psi(h) = -\log\kappa(y\mid h) \) is the surprisal of hypothesis h under observation y. The tropical variety of this polynomial, \( \mathcal{B}_{\mathrm{active}} = \bigl\{h \in H : \Phi^-(h) = \psi(h)\bigr\}. \) is the active deformation front: the exact locus where incoming evidence first matches prior impossibility and begins to deform the posterior field. This is a necessary condition for falsification but not sufficient. Sufficient falsification requires exit from the PCRB admissible basin \( \mathcal{A}_k = \{h : \Phi^+_k(h) \leq c_k^\star\} \), where \( c_k^\star \) is the equipotential threshold determined by the PCRB at step k. Popper's criterion thus receives a two-stage algebraic formulation: the tropical variety marks where falsification becomes possible; the PCRB basin boundary marks where falsification is complete. Within the class of possibility-theoretic recursive inference systems, this is, to the best of our knowledge, the first exact formulation of this distinction. Main results. 1. Epistemic Contraction Theorem. Contraction is tropical addition: \( \Phi^+ = \Phi^- \oplus \psi \). Posterior α-cuts satisfy \( H_\alpha^+ = H_\alpha^- \cap E_\alpha(y) \): geometric intersection, not belief redistribution. The active deformation front is the tropical variety \( \mathcal{B}_{\mathrm{active}} \); the falsification boundary is the PCRB admissible basin boundary \( \mathcal{B}_{\mathrm{adm}} \). 2. Possibilistic Cramér–Rao Bound (PCRB} For any filter in the class \( \mathcal{F} \) of epistemically admissible, contraction-based recursive estimators satisfying Axioms 2.1–2.5: \( \mathcal{E}_{\pi,k|k} \geq \mathcal{E}_{\pi,k|k-1} + \tfrac{n}{2}\log(1-I_k) \), where \( I_k \) is the Choquet integral of per-hypothesis surprisal against the prior possibility capacity. Within this class, the ESPF [28] is the unique filter achieving this bound with equality, and is therefore the unique minimax-entropy-optimal set-based recursive estimator under bounded epistemic uncertainty. 3. Tropical Hamilton–Jacobi structure (summary). The TEAG update is structurally consistent with a tropical Lagrangian \( L = T - V \), Legendre transform to a tropical Hamiltonian equal to the surprisal field, and a Hamilton–Jacobi equation whose solution is the tropical addition rule. The Euler–Lagrange equations on the epistemic manifold yield geodesic motion with explicit Levi–Civita connection and Christoffel symbols. This structure is interpretive and consistent with the axioms; full derivations are in the companion paper [31]. Taken together, this structure admits a precise interpretation: the TEAG update rule is a max-plus dynamical system whose governing equations have the same algebraic form as the Hamilton–Jacobi equations of classical mechanics, instantiated on hypothesis space rather than physical space. 4. Gaussian collapse. Probability theory is the collapse limit of TEAG as epistemic width \( W \to 0 \): Choquet converges to Lebesgue, the ESPF recovers the Kalman filter, and \( \mathcal{E}_\pi \to \tfrac{1}{2}\log\det\Sigma + \mathrm{const}(n) \). Probability is earned by evidence, not assumed. Epistemic neutrality and knowledge-system synthesis. Because TEAG's axioms require only a hypothesis space, a possibility field, and a contraction operator — not a probability measure, a likelihood function, or a frequentist grounding — heterogeneous knowledge systems can each instantiate the TEAG quintuple independently. Their joint admissible support intersection is the locus of coherence: the set of hypotheses neither system has falsified. No transformation of one system into the other's representational primitives is required. The composition theory (Section 6) formalizes the coupling architecture. Four instantiations provide the unifying structure: the ESPF [28] for recursive state estimation; the Geometry of Knowing [29] for measure-theoretic collapse; the minimax-entropy optimality proof [30]; and the Possibilistic Language Model (PLM, forthcoming [32]).
Posted: 26 March 2026
A Formal Semantics of Governance History Validity in Encrypted Storage
Jesús F. Rodríguez-Aragón
,Carolina Zato
,Fernando De la Prieta
Posted: 26 March 2026
DS-GBT: Proactive Safety Integration for Dynamic Agent Decision Policies
Yao-Tian Chian
,Yuxin Zhai
Posted: 25 March 2026
A Theoretically‐Grounded Federated Attribution Framework with Adaptive Differential Privacy Budgets for Cross‐Device Social Commerce Advertising Systems
Xiongsheng Yi
Posted: 25 March 2026
Astrophysical Constraints on the Simulation Hypothesis for This Universe from a Biological Point of View
Alessandro Perrella
,Antonio D'Amore
,Ada Maffettone
Posted: 24 March 2026
Antecedents, Decisions, and Outcomes for ICT Governance Adoption in the African Public Sector: A Systematic Review Based on McClelland Theory and ADO Framework
Samuel Simbarashe Furusa
,Mampilo Pahlane
Posted: 20 March 2026
Speech-Adaptive Detection of Unnatural Intra-Sentential Pauses Using Contextual Anomaly Modeling for Interpreter Training
Hyoeun Kang
,Jin-Dong Kim
,Juriae Lee
,Hee-Jo Nam
,Kon Woo Kim
,Joowon Lim
,Hyun-Seok Park
Posted: 18 March 2026
HieMaGT: Hierarchical Multi-Scale Graph Transformer for Brain Disorder Diagnosis
Yutian Qi
,Bowen Xun
Posted: 18 March 2026
Mapping Research Trends with the CoLiRa Framework: A Computational Review of Semantic Enrichment of Tabular Data
Luis Omar Colombo-Mendoza
,Julieta del Carmen Villalobos-Espinosa
,María Elisa Espinosa-Valdés
,Elías Beltrán-Naturi
Posted: 17 March 2026
Digital Items as Information System Artifacts: Toward a Typology of Valuation-to-Monetization Mechanisms in Southeast Asian Free-to-Play Economies
Laurence Maningo
Posted: 17 March 2026
Intelligent Sensor-Driven Integration Framework for IoT-Enabled Public Transportation Using an Extended CAMS Architecture
Nelson Herrera-Herrera
,Estevan Ricardo Gómez-Torres
Posted: 11 March 2026
Rethinking Spatial Data Quality: A Socio-Technical and Lifecycle Framework
Tomaž Podobnikar
Posted: 11 March 2026
Ontology-Based Validation of Enterprise Architecture Principles
Devid Montecchiari
Posted: 04 March 2026
Integration of Physical and Probabilistic Measures in Stochastic Measurements of Manufacturing Processes
Artur Zaporozhets
,Vitalii Babak
,Valerij Zvaritch
,Svitlana Kovtun
,Yurii Gyzhko
,Vladyslav Khaidurov
,Vladyslav Verpeta
Posted: 02 March 2026
A Federated and Differentially Private Incentive–Marketing Framework for Privacy-Preserving Cross-Channel Measurement in AI-Powered Digital Commerce
Xiongsheng Yi
Posted: 28 February 2026
Shadow AI in Organisations: A Practical Framework for Detection, Risk Classification, and Governance
Ayokunle Ojowa
,Monteiro Marques
,Antonio Goncalves
Posted: 28 February 2026
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