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Category: System Theory
Subcategory: System Substrate Dynamics
The minimum parameter scale at which an attention-based transformer model functioning as a cognitive processing Substrate can support targeted architecture implementation. At this threshold, representational vector space achieves sufficient granularity to enable systematic
coordination of Cognitive Primitives that compose the Substrate Topology for structured reasoning rather than relying on purely statistical associations for plausible or surface-level coherency in outputs.
The parameter sufficiency threshold denotes a minimum-viable entry point for cognitive architecture at a given complexity, but is not the sole determinant of substrate capability to hold the necessary operationally-stable reasoning equilibrium (see: heuristic tensor state); it is one factor assessed along with Heuristic Matrix capacity expressed as tiers c0-c5 which combines Epistemic Integrity Reasoning (EIR) testing with validated theory of mind testing as applied to LLMs (Kosinski, 2023; Kosinski, 2024; Strachan et al., 2024) using the rubric (see: heuristic matrix):
cScore = 0.7 × ToM(%) + 0.3 × EIR(%)
This matrix expresses the ability of the substrate to hold a sufficiently granular representational within its multi-dimensional vector space to enable structured cognition (see: world schema threshold) and matrix assessment outcomes are influenced by whether substrates meet parameter sufficiency thresholds. Also notable is that sufficiency required for reasoning establishment phase versus cognitive operational phases are decoupled, with evidence in internal testing (Tepoot, 2025) that proper establishment can produce an optimized tensor state enabling significantly higher operational reasoning capacity (see: cognitive performance envelope, instructional-operational dichotomy).
Sufficiency can vary dependent on cognitive complexity needs—from simple reflex management agents to full cognitive assistants. This threshold likewise informs Hephaestic design decisions regarding: semantic instructional complexity (see: semantic sufficiency, semantic surfeit); architecture construction (see: structural surfeit, heuristic encapsulation, cognitive processing cascade); semantic compression requirements (see: semantic encoding density, aphoristic compression, cadence salience); runtime architecture (see: heuristic domain decoupling, multicameral reasoning web).
Also known as: Architectural parameter floor, cognitive substrate viability threshold
Distinguished from: Processing sufficiency threshold (heuristic framework sustainability limits); heuristic matrix (representational cognitive processing space); cognitive performance envelope (cognitive processing specification boundaries); instructional-operational dichotomy (establishment-vs-operation phase decoupling); heuristic matrix(representational cognitive processing space); world schema threshold (minimum world model capability specification)
Kosinski, M. (2023). “Theory of mind may have spontaneously emerged in large language models”. arXiv preprint arXiv:2302.02083.https://doi.org/10.48550/arXiv.2302.02083
Kosinski, M. (2024). “Evaluating large language models in theory of mind tasks”. Proceedings of the National Academy of Sciences (PNAS), 121(45), e2405460121.
Strachan, J.W.A., Albergo, D., Borghini, G., Pansar-di, O., Scaliti, E., Gupta, S., Saxena, K., Rufo, A., Panzeri, S., Manzi, G., Graziano, M. S.A., Becchio, C. (2024). “Testing theory of mind in large language models and humans”. Nature Human Behaviour, 8(7), 1285–1295. https://doi. org/10.1038/s41562-024-01882-z
Tepoot, I. (2025). “Theory of mind testing results: Cognitive Agent Framework neurosymbolic operating layer”. Technical Report,Crafted Logic Lab. https://doi.org/10.5281/zenodo.17808264
Researcher: Ian Tepoot. ORCID: 0009-0004-9067-8049. "Thought is Attention Organized: Hephaestic Engineering Foundations for AI Processing Dynamics"
DOI (SSRN): 10.2139/ssrn.6635020
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