What question did this study set out to answer?

This work aims to expand the Boundary Coherence Theory framework to interpret failure, life, and the essence of numbers.

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May 26, 2026Open Access

BCT Extended Papers: What Is Failure? / What Is Life? / What Is a Number?

Key Points

This work aims to expand the Boundary Coherence Theory framework to interpret failure, life, and the essence of numbers.
Developed structural accounts of boundary encounters and topology for failure.
Introduced biology and metabolism concepts as fundamental within the BCT framework.
Examined the ontological status of numbers and highlighted reclassifications of the Clay Millennium Problems.
Established new definitions of failure based on structural boundary encounters.
Outlined metabolism as a critical constraint within biological systems.
Identified that Clay Millennium Problems are structurally incomplete due to missing realizability and admissibility constraints.

Abstract

Three papers extending the Boundary Coherence Theory (BCT) framework beyond the core trilogy. Paper 4 (What Is Failure?) develops the structural account of admissibility boundary encounters and topology change. Paper 5 (What Is Life?) develops biology and metabolism as persistent constraint architecture under throughput closure. Paper 6 (What Is a Number?) addresses the ontological status of number within BCT, including BCT-internal reclassifications of the Clay Millennium Problems as structurally incomplete due to missing realizability and admissibility constraints.

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