Maxdi Inc.
ORCID: https://orcid.org/0000-0002-5438-8923
January 4, 2026
Mahdi Haghzadeh, PhD
Maxdi Inc
Cognitave Inc
Keywords: Quantum Computing, Simulations and Modeling, Integrated Systems, Analysis and Applied Mathematics, MXD-COGN, mixed-domain cognition, mixed-depth cognition, deformed-control inference, order parameter, coherence functional, inferential closure, non-commutativity, inference operator, operator norm, commutator, closure error, EDFS, Emergent Deformed Field Structure, Emergent Deformed Field Structure, gradient, curvature, phase transition,.
Complex systems fail in ways that are neither random nor well explained by existing theories of control, learning, or cognition. Advanced artificial systems, large organizations, and socio-technical infrastructures often exhibit prolonged periods of apparent stability followed by abrupt, irreversible collapse. These failures are typically attributed post hoc to insufficient data, incorrect objectives, or implementation errors. Such explanations are incomplete. This textbook introduces a fundamentally new theoretical framework—MXD-COGN—that explains these phenomena as structural consequences of cognition and control operating across mismatched domains. The central claim of this work is that instability, misalignment, and catastrophic failure are not anomalies of intelligent systems but predictable outcomes of mixed-domain, mixed-depth inference. When inference operators do not commute, when representations are heterogeneous, and when control is mediated through layered abstractions, classical assumptions of global state consistency break down. Failure, in this setting, takes the form of a phase transition rather than gradual degradation.
MXD-COGN (Mixed-Domain Cognition) provides: an algebraic formalism for non-commuting inference operators, a macroscopic coherence order parameter governing control, a geometric field structure encoding stability and irreversibility, and a phase-theoretic account of failure, alignment, and safety.
MXD-Cogn does not promise perfect control. It explains when control is possible—and when it is not.
Copyright Notice © 2026 Maxdi Inc.. All rights reserved. No part of this publication may be reproduced, stored, or transmitted in any form or by any means without prior written permission of the copyright holder
Access related on-demand EE courses at: https://www.cognitave.com/
Maxdi Inc.
ORCID: https://orcid.org/0000-0002-5438-8923
January 4, 2026
Mahdi Haghzadeh, PhD
Maxdi Inc
Cognitave Inc
Keywords: Quantum Computing, Simulations and Modeling, Integrated Systems, Analysis and Applied Mathematics, MXD-COGN, mixed-domain cognition, mixed-depth cognition, deformed-control inference, order parameter, coherence functional, inferential closure, non-commutativity, inference operator, operator norm, commutator, closure error, EDFS, Emergent Deformed Field Structure, Emergent Deformed Field Structure, gradient, curvature, phase transition,.
Complex systems fail in ways that are neither random nor well explained by existing theories of control, learning, or cognition. Advanced artificial systems, large organizations, and socio-technical infrastructures often exhibit prolonged periods of apparent stability followed by abrupt, irreversible collapse. These failures are typically attributed post hoc to insufficient data, incorrect objectives, or implementation errors. Such explanations are incomplete. This textbook introduces a fundamentally new theoretical framework—MXD-COGN—that explains these phenomena as structural consequences of cognition and control operating across mismatched domains. The central claim of this work is that instability, misalignment, and catastrophic failure are not anomalies of intelligent systems but predictable outcomes of mixed-domain, mixed-depth inference. When inference operators do not commute, when representations are heterogeneous, and when control is mediated through layered abstractions, classical assumptions of global state consistency break down. Failure, in this setting, takes the form of a phase transition rather than gradual degradation.
MXD-COGN (Mixed-Domain Cognition) provides: an algebraic formalism for non-commuting inference operators, a macroscopic coherence order parameter governing control, a geometric field structure encoding stability and irreversibility, and a phase-theoretic account of failure, alignment, and safety.
MXD-Cogn does not promise perfect control. It explains when control is possible—and when it is not.
Copyright Notice © 2026 Maxdi Inc.. All rights reserved. No part of this publication may be reproduced, stored, or transmitted in any form or by any means without prior written permission of the copyright holder
Access related on-demand EE courses at: https://www.cognitave.com/
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