Unified Coherence–Projection Framework
Public-Safe Structural Formulation
Admissible Geometry, Structural Entropy, and Observer-Wave Propagation
Public-Safe Notice
This publication intentionally omits implementation-specific invariants, optimization operators, convergence conditions, scaling bounds, recursive search procedures, and high-capability reconstruction mechanisms.
The framework is presented as a public-safe structural formulation intended for academic discussion of admissible projection, coherence entropy, observer-limited reconstruction, and relational structure under finite bandwidth constraints.
The geometric representation layer introduced in this work is explicitly representational and conjectural. No claim is made that the proposed tetrahedral or Möbius constructions correspond directly to physical spacetime geometry or replace established physical theories.
Abstract
This paper presents a public-safe coherence-based framework in which observable structure emerges through admissible projection from a higher-order relational manifold.
Building on earlier work relating entropy to coherence deficit under projection, the present formulation introduces a constrained geometric representation layer based on triadic sphere systems, admissible tetrahedral decompositions, Gaussian occupancy fields, nonlinear projection coupling, and observer-relative coherence propagation.
The framework treats entropy not as intrinsic disorder but as coherence deficit induced by admissible projection. Structural time emerges from irreversible coherence reduction rather than existing as a primitive parameter. Finite observers are modeled as embedded coherence substructures capable of sensing more relational structure than can be fully metabolized through bounded projection.
A representation conjecture is proposed in which recursively expanding prime-triad sphere systems generate admissible tetrahedral projection families whose nonlinear overlap structures produce finite observer-accessible worlds. Observer continuity is interpreted through coherence propagation relative to dominant admissibility surfaces.
No claim is made that the geometric representation constitutes a literal physical ontology. Rather, the construction is proposed as a structural language for studying finite observers reconstructing hidden relational structure under bandwidth, locality, and admissibility constraints.
Keywords
coherence entropy; admissible projection; observer-limited reconstruction; structural entropy; nonlinear projection systems; relational coherence; embedded observers; finite bandwidth inference; geometric representation; coherence monotonicity; structural time
Overview
Unified Coherence–Projection Framework develops a public-safe structural language for describing how finite observers reconstruct hidden relational structure under admissible projection constraints.
The paper begins from relational coherence rather than primitive time, externally defined observers, or literal physical geometry. Entropy is interpreted as coherence deficit under admissible projection, while structural time is treated as the ordering induced by irreversible coherence reduction.
The geometric layer is introduced as a representation conjecture only. It provides a way to discuss finite observer accessibility, projection competition, nonlinear coupling, recursive admissibility expansion, and observer-relative coherence propagation without exposing operational reconstruction mechanisms.
A full PDF version of the paper is available through the PDF button in the upper-right corner of this page.
Official Links
CJCI Issue Page:
https://www.carlonoscopen.com/journal/v1i11
Reserved Zenodo DOI:
https://doi.org/10.5281/zenodo.20097285
Author ORCID:
https://orcid.org/0009-0005-2284-8891
Paper Details
- Title: Unified Coherence–Projection Framework
- Subtitle: Public-Safe Structural Formulation: Admissible Geometry, Structural Entropy, and Observer-Wave Propagation
- Author: Ivan Silva
- Publisher: Carlonoscopen, LLC
- Journal: Carlonoscopen Journal of Coherence Intelligence
- ISSN: 3069-874X
- Language: English
- Publication Date: May 9, 2026
- Format: Web publication and PDF paper
- Version: 1.3
- Reserved DOI: 10.5281/zenodo.20097285
Core Framework
The framework defines coherence as a relational structure measure and entropy as the coherence deficit induced by admissible projection.
Structural time is then interpreted as the ordering induced by irreversible coherence reduction, not as a primitive flow.
The observer is modeled as embedded within the relational structure being observed, rather than positioned outside it. This permits a distinction between sensing and metabolization: a finite observer may locally resonate with more relational structure than can be fully projected into bounded cognition.
Representation Conjecture
The paper introduces a constrained geometric representation layer based on triadic sphere systems, admissible tetrahedral decompositions, Gaussian occupancy fields, Möbius orientation continuity, and nonlinear observer projection.
This layer is conjectural and representational. It is not presented as experimentally verified spacetime geometry, and it is not asserted as a replacement for established physical theories.
Scope and Limits
This framework:
- does not claim experimental verification,
- does not replace established physical theories,
- does not define literal spacetime topology,
- does not provide operational reconstruction procedures,
- does not claim direct biological consciousness equivalence,
- and does not present a complete cosmology.
Applications and Research Directions
The work may have relevance for:
- observer-limited inference,
- latent-space reasoning,
- bounded AI systems,
- nonlinear projection reconstruction,
- memory-preserving architectures,
- coherence-aware representation learning.
Explicit Non-Claims
- This paper does not claim a replacement for quantum mechanics.
- This paper does not claim a replacement for relativity.
- This paper does not claim a complete cosmology.
- This paper does not claim a universal physical theory.
- This paper does not expose private operational invariants or implementation-level reconstruction mechanisms.
Suggested Citation
Silva, Ivan Pereira da. Unified Coherence–Projection Framework: Public-Safe Structural Formulation. Carlonoscopen Journal of Coherence Intelligence, 2026. Reserved DOI: 10.5281/zenodo.20097285.
References
- Silva, I. (2026). Entropy as a Structural Quantity: A Coherence-Based Reformulation Beyond Thermodynamic and Informational Limits. Carlonoscopen Journal of Coherence Intelligence (CJCI).
- Silva, I. (forthcoming). The Ledger of Irreversible Change: Entropy, Time, and the Structure of Commitment. Unpublished book manuscript. Planned Amazon KDP release.
- Silva, I. (2026). APIT Framework Papers and Related Coherence Publications. CJCI Research Archive.
- Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal.
- Boltzmann, L. (1896). Lectures on Gas Theory.
- von Neumann, J. (1932). Mathematical Foundations of Quantum Mechanics.
- Wheeler, J. A. (1990). Information, Physics, Quantum: The Search for Links.
Publication Note
This page is published as part of the Carlonoscopen Journal of Coherence Intelligence. The PDF linked from this page is the full public paper for offline reading, citation support, and archival use.
The DOI listed on this page was reserved before upload and will resolve after the Zenodo record is published.