The Pyramid of Truth: A Geometric Epistemology of Subjective Reality

This record deposits the full academic paper *“The Pyramid of Truth: A Geometric Theory of Subjective Reality”*, a formal exploration of perspectival truth grounded in geometric projection theory. The work demonstrates that truth is inherently subjective at the level of perception and objective at the level of structure, using a pyramid as the canonical “truth object.” Each observer perceives a valid but incomplete projection of a multidimensional polyhedral reality, and the paper formalizes this through mathematical definitions, projection operators, theorems, corollaries, and ASCII geometric diagrams. The core mathematical framework defines the truth object as a convex polyhedron: \[P \subset \mathbb{R}^3\] with observer-dependent truth projections: \[T_i = \Pi_i(P)\] where each projection operator \(\Pi_i : \mathbb{R}^3 \rightarrow \mathbb{R}^2\) reduces dimensionality and guarantees: \[T_i \neq P.\] The paper proves six formal theorems, including: **Theorem 1 — Incompleteness of Perspective Truth** \[T_i \not\cong P\] Dimensional reduction ensures no observer can perceive the full truth object. **Theorem 2 — Validity of Contradictory Truths** \[T_a = \Pi_a(P), \quad T_b = \Pi_b(P)\] Contradictory truths arise naturally from incompatible observer frames. **Theorem 3 — Non‑Observability of Total Truth** \[T_{\text{total}} = \bigcup_i T_i\] Total truth exists but is epistemically inaccessible. **Theorem 4 — Necessity of Subjective Truth** \[O_a \neq O_b \Rightarrow \Pi_a \neq \Pi_b\] **Theorem 5 — Polyhedral Nature of Truth**Truth is structurally polyhedral, not planar. **Theorem 6 — Paradox of Simultaneity** \[P = \text{square} \land P = \text{triangle} \land P = \text{diamond} \land P \neq \text{any single one}\] The paper concludes that truth is:- subjective in perception,- objective in structure,- geometric in nature,- epistemically fractured,- ontologically whole. ASCII diagrams illustrate how different observers perceive square, triangular, or diamond projections of the same pyramid, demonstrating the perspectival fragmentation of truth. This record also includes four photographs of the acrylic Pyramid of Truth object used in the original paper. The first image shows the pyramid resting in my hand for scale and reference; the remaining three display the object from different angles to illustrate its geometric facets and internal structure. The pyramid itself was cast in acrylic two years ago after I had a tooth extracted during a particularly bad toothache. I decided to embed the tooth inside the pyramid simply because I enjoy preserving and examining physical objects—there’s no symbolic or medical reason behind it. The translucent material refracts light and reveals the embedded form differently from each angle, making it a perfect physical analogue for the theory’s central idea: that truth changes with perspective. Together, these four images provide a tactile, visual complement to the Pyramid of Truth paper, showing the object that inspired the geometric model in real space. KEYWORDS:Truth; Epistemology; Geometry; Projection Theory; Polyhedral Reality; Subjective Truth; Objective Structure; Carlo Canon; Pyramid Model; Perspectival Philosophy; Mathematical Metaphysics; Cognitive Frames; Dimensional Reduction; Contradiction Theory; Ontology. SUBJECTS:Philosophy of Mind; Epistemology; Metaphysics; Mathematical Philosophy; Cognitive Science; Geometry and Topology; Theoretical Models of Truth; Interdisciplinary Metaphysics; Computational Epistemology. Contact: For enquiries or research questions related to this work, email [email protected]