THE SELF-CONCEALMENT THEOREM AND THE SANDBOX PARADOX
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2025
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| _version_ | 1866902337269792768 |
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| author | Brent, Cory |
| author_facet | Brent, Cory |
| contents | <p>This paper introduces the Self-Concealment Theorem, also called the Sandbox Paradox: a general law governing epistemic limits in generative substrates. The theorem shows that any observer instantiated within a substrate cannot obtain a complete representation of that substrate. The result follows from an information-theoretic inequality (C(O) < H(M)) and recursive self-reference, demonstrating that self-concealment is a necessary property of all generative systems.</p> <p> </p> <p>The theorem unifies a range of existing impossibility results under one framework: Gödel’s incompleteness theorem, Turing’s halting problem, Shannon’s channel capacity bound, the quantum no-cloning theorem, and black hole event horizons. Each is reinterpreted as a corollary of the same structural limit.</p> <p> </p> <p>Finally, we extend the theorem to show that full representation of a substrate is only possible under a boundary shift into a higher medium, a mechanism metaphorically described as an “invitation outside.” This provides a unifying perspective across logic, information theory, physics, and theology, suggesting that self-concealment is a universal principle of epistemic structure.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17220605 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | THE SELF-CONCEALMENT THEOREM AND THE SANDBOX PARADOX Brent, Cory <p>This paper introduces the Self-Concealment Theorem, also called the Sandbox Paradox: a general law governing epistemic limits in generative substrates. The theorem shows that any observer instantiated within a substrate cannot obtain a complete representation of that substrate. The result follows from an information-theoretic inequality (C(O) < H(M)) and recursive self-reference, demonstrating that self-concealment is a necessary property of all generative systems.</p> <p> </p> <p>The theorem unifies a range of existing impossibility results under one framework: Gödel’s incompleteness theorem, Turing’s halting problem, Shannon’s channel capacity bound, the quantum no-cloning theorem, and black hole event horizons. Each is reinterpreted as a corollary of the same structural limit.</p> <p> </p> <p>Finally, we extend the theorem to show that full representation of a substrate is only possible under a boundary shift into a higher medium, a mechanism metaphorically described as an “invitation outside.” This provides a unifying perspective across logic, information theory, physics, and theology, suggesting that self-concealment is a universal principle of epistemic structure.</p> |
| title | THE SELF-CONCEALMENT THEOREM AND THE SANDBOX PARADOX |
| url | https://doi.org/10.5281/zenodo.17220605 |