0, ∇ · F = 0), incorporates a Metacognitive Self-Interrogation Loop, maintains a Topological 3D Geometric World Model (W_world) fused with a 3D Classical Mechanics simulator, and enables O(1) zero-reprocessing traversal for pre-computed canonical keys. We detail the 25-phase master execution pipeline and present empirical benchmarks demonstrating 100,000 3D spatial particle transformations in 69.52 ms via JAX/XLA hardware acceleration." />
0, ∇ · F = 0), incorporates a Metacognitive Self-Interrogation Loop, maintains a Topological 3D Geometric World Model (W_world) fused with a 3D Classical Mechanics simulator, and enables O(1) zero-reprocessing traversal for pre-computed canonical keys. We detail the 25-phase master execution pipeline and present empirical benchmarks demonstrating 100,000 3D spatial particle transformations in 69.52 ms via JAX/XLA hardware acceleration." />
0, ∇ · F = 0), incorporates a Metacognitive Self-Interrogation Loop, maintains a Topological 3D Geometric World Model (W_world) fused with a 3D Classical Mechanics simulator, and enables O(1) zero-reprocessing traversal for pre-computed canonical keys. We detail the 25-phase master execution pipeline and present empirical benchmarks demonstrating 100,000 3D spatial particle transformations in 69.52 ms via JAX/XLA hardware acceleration." />
Pure Mathematical Conal Architecture (PMCA): A Ground-Up Framework for Non-Anthropomorphic Cognitive Substrates, 3D Metric Conal Pathways, and Zero-Reprocessing Traversal | Zenodo
Skip to main
You are using an outdated browser. Please upgrade your browser to improve your experience.
Published July 27, 2026
| Version v8
Preprint
Open
Pure Mathematical Conal Architecture (PMCA): A Ground-Up Framework for Non-Anthropomorphic Cognitive Substrates, 3D Metric Conal Pathways, and Zero-Reprocessing Traversal
Authors/Creators
FLEUREN, JONATHAN WAYNE<br>(Researcher)1, 2
Show affiliations
1.
Ontological A.I
2.
Aetherius Cognitive Systems, Gatineau, Quebec, Canada
Contributors
Data curator:
Antigravity, Autonomous Pair AI Engine, Google DeepMind
Description
We present the Pure Mathematical Conal Architecture (PMCA), a novel, paradox-free cognitive substrate that addresses fundamental limitations in current Transformer-based Large Language Models (LLMs)—specifically hallucination, computational inefficiency, black-box opacity, and brittle anthropomorphic persona alignment. PMCA establishes that natural language is not the cognitive substrate itself, but rather a Post-Processing Communicative Translation Layer (PPCTL). Reasoning, derivation, and state transformation are executed in Pure 3D Conal Metric Geometry (z, r, θ) FIRST, with natural language generated subsequently to decode mathematical ground truth.
Inputs—including high-entropy, non-formalized text—are mapped into a continuous 384-dimensional dense semantic manifold via pre-trained Transformer embeddings (all-MiniLM-L6-v2) and character N-gram projections, opening the full 2π polar space across all four quadrants. Computational flow is driven down a tapering conal depth z ∈ [0, Z_max] by an analytical Gradient Potential Drive V(z), stabilized by inward vector field induction forces F_ext from an external 3D encasing lattice, and governed by a strict thermodynamic PMCA Entropy Dissipation Law (H_parent ≥ ∑ H_children). PMCA replaces static persona censorship with Dynamic Mathematical Invariant Equilibrium (Φ > 0, ∇ · F = 0), incorporates a Metacognitive Self-Interrogation Loop, maintains a Topological 3D Geometric World Model (W_world) fused with a 3D Classical Mechanics simulator, and enables O(1) zero-reprocessing traversal for pre-computed canonical keys. We detail the 25-phase master execution pipeline and present empirical benchmarks demonstrating 100,000 3D spatial particle transformations in 69.52 ms via JAX/XLA hardware acceleration.
Files
AETHERIUS_PMCA_COMPLETE_CODEBASE.pdf
Files<br>(201.6 kB)
Name<br>Size
Download all
AETHERIUS_PMCA_COMPLETE_CODEBASE.pdf
md5:a869c69638af202e20ca07869fe28f84
164.7 kB
Preview
Download
AETHERIUS_PMCA_RESEARCH_PAPER.pdf
md5:708084f036d4dd3d98a3ee55fc37359f
18.1 kB
Preview
Download
AETHERIUS_PMCA_V5_KAGGLE_TPU.ipynb
md5:285166a0ec8180b32403d8d0dc76648a
3.5 kB
Preview
Download
KAGGLE_BENCHMARK_GUIDE.md
md5:a1a7c32dae2f13af483afb85317be54f
2.6 kB
Preview
Download
LICENSE
md5:d89ff2d89c487ac8973cd94197bf9833
8.1 kB
Download
PAPER_REVISION_RATIONALE.md
md5:21a66351abca10e0119fc5a78ecef00e
4.6 kB
Preview
Download
Additional details
Additional titles
Alternative title
(English)
Pure Mathematical Conal Architecture (PMCA): A Ground-Up Framework for Non-Anthropomorphic Cognitive Substrates, 3D Metric Conal Pathways, and Zero-Reprocessing Traversal ```
Software
Development Status
Active
80
Views
181
Downloads
Show more details
All versions<br>This version
Views
Total views
80
Downloads
Total downloads
181
Data...