Fundamental Equation of Open Systems (Aleph Equation)
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2026
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| _version_ | 1866901682603950080 |
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| author | Bresciano, Claudio |
| author_facet | Bresciano, Claudio |
| contents | <p>This paper introduces a unified structural framework for the realization limits of open systems, centered on the <strong>Aleph Equation</strong> and the <strong>Oniric Value Theorem</strong>. We propose that the operational openness of a system is not a function of instantaneous state, but a result of the historical accumulation of unrealized surplus. Formally, we define the <strong>Aleph Principle</strong>: a system remains operationally closed only as long as its cumulative surplus—the integral of generative capacity (<span>G</span>) minus control capacity (<span>Psi</span>)—does not exceed its maximum internal absorptive capacity (<span>\aleph_{\max}</span>).</p> <p>When this threshold is breached, the system undergoes a topological transition where closure becomes structurally impossible, forcing externalization through leakage, bifurcation, or emergence. Parallelly, we formalize the <strong>Oniric Value Theorem</strong> as the diagnostic criterion for this regime. It identifies "oniric value" as declared assets or capabilities that remain stable only while deferred; their attempted exercise triggers systemic degradation because the cumulative surplus has already reached the absorptive limit.</p> <p>By applying this dual framework to censorship regimes, cloud computing, and AI alignment, we demonstrate that systemic stability is often a consequence of non-exercise rather than genuine capacity. This synthesis provides a non-moral, measurable, and domain-independent diagnostic tool for distinguishing operational value from narrative value before irreversible structural commitment occurs.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18174402 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Fundamental Equation of Open Systems (Aleph Equation) Bresciano, Claudio Aleph Equation, Oniric Value Theorem, Open-System Realization, Cumulative Surplus Dynamics, Absorptive Capacity (\aleph_{\max}), Narrative vs. Operational ValueStructural ClosureAI Alignment ArchitectureCensorship RealizabilityThroughput Optimization (Psi) <p>This paper introduces a unified structural framework for the realization limits of open systems, centered on the <strong>Aleph Equation</strong> and the <strong>Oniric Value Theorem</strong>. We propose that the operational openness of a system is not a function of instantaneous state, but a result of the historical accumulation of unrealized surplus. Formally, we define the <strong>Aleph Principle</strong>: a system remains operationally closed only as long as its cumulative surplus—the integral of generative capacity (<span>G</span>) minus control capacity (<span>Psi</span>)—does not exceed its maximum internal absorptive capacity (<span>\aleph_{\max}</span>).</p> <p>When this threshold is breached, the system undergoes a topological transition where closure becomes structurally impossible, forcing externalization through leakage, bifurcation, or emergence. Parallelly, we formalize the <strong>Oniric Value Theorem</strong> as the diagnostic criterion for this regime. It identifies "oniric value" as declared assets or capabilities that remain stable only while deferred; their attempted exercise triggers systemic degradation because the cumulative surplus has already reached the absorptive limit.</p> <p>By applying this dual framework to censorship regimes, cloud computing, and AI alignment, we demonstrate that systemic stability is often a consequence of non-exercise rather than genuine capacity. This synthesis provides a non-moral, measurable, and domain-independent diagnostic tool for distinguishing operational value from narrative value before irreversible structural commitment occurs.</p> |
| title | Fundamental Equation of Open Systems (Aleph Equation) |
| topic | Aleph Equation, Oniric Value Theorem, Open-System Realization, Cumulative Surplus Dynamics, Absorptive Capacity (\aleph_{\max}), Narrative vs. Operational ValueStructural ClosureAI Alignment ArchitectureCensorship RealizabilityThroughput Optimization (Psi) |
| url | https://doi.org/10.5281/zenodo.18174402 |