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This document aims to clarify the updates and findings of the Projective Dynamic Logo program, particularly regarding the coherence stress-energy tensor and associated theorems.

May 15, 2026Open Access

Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 21)

Key Points

This document aims to clarify the updates and findings of the Projective Dynamic Logo program, particularly regarding the coherence stress-energy tensor and associated theorems.
Systematic correction of the coherence stress-energy tensor (D48) with updates to formulas and dimensional checks.
Explicit computation of configurations for consistency with fundamental physical laws.
Review and update of auxiliary documents and tables to reflect theoretical advancements.
Correction of dimensional inconsistencies in formulas for C^(spin), C^(orb), and C^(leak).
Demonstrated that C^(spin) = 0 in the homogeneous ground state under specified conditions.
Established that the PDL Einstein equation is dimensionally consistent with the updates made.

Abstract

This document provides a systematic and self-contained guide to the Projective Dynamic Logo (PDL) programme, covering the complete corpus D01–D53 plus auxiliary documents (D10a, D16a, D16b, DN, DN-fr, D01F, D20F, DL01, DL02, DM). PDL is a foundational physics programme that derives fundamental physical constants and dynamical laws from four combinatorial axioms on finite signed graphs, without presupposing spacetime, particles, or fields. Version 21 incorporates a single but structurally significant update relative to v20: the correction and completion of D48 (coherence stress-energy tensor, now version 3). D48v3 resolves four dimensional errors present in v1/v2 and closes two open problems. Principal changes relative to v20: (1) D48v3 (doi: 10. 5281/zenodo. 20151380) replaces D48v1/v2. Four corrections: (C1) the geometric Chain 2 for VC was a tautology — VC is a theorem via Chain 1 alone; (C2) the formula for C^ (spin) was dimensionally incorrect and the magnitude 1e-12 was unverified — corrected to C^ (spin) = 0 in the homogeneous ground state; (C3) a factor mₚ was missing in the formula for C^ (orb) ; (C4) the formula for C^ (leak) had units m^-2, not J/m³, rendering the Einstein equation dimensionally inconsistent. (2) OP-spin is resolved as an unconditional theorem of C1–C4. Explicit computation over all 8 coherent configurations of K₄ and the 4 pulsation states Tᵏ|+> gives = 0 and = (1/4) deltaⁱj exactly. The Weyssenhoff–Raabe traceless part vanishes exactly. Combined with the London gauge theorem (D49), this gives C^ (spin) = 0 in the homogeneous ground state. (3) All four components of Ccoh are now unconditional theorems in uniform units J/m³. The PDL Einstein equation Ggₑff = kappaPDL (N) Ccoh is dimensionally consistent throughout. OP2-D35, OP1-D35, and OP-spin are fully resolved. (4) The entry for VC in the corpus table, the glossary, and the epistemic architecture table are updated to reflect that the double-forcing claim of D48v1/v2 is replaced bya single rigorous chain (D10a) with a geometric consistency remark (D23). All other content of DM v20 is unchanged. The causal chain C1–C4 → LambdaPDL, established in D51–D53 and synthesised in D53, is unaffected by the corrections to D48. Supersedes DM v20 (doi: 10. 5281/zenodo. 20054876).

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