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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19102201 |
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| _version_ | 1866901223122141184 |
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| author | Washburn, Jonathan |
| author_facet | Washburn, Jonathan |
| contents | <p>This paper rewrites the death-transition story in Recognition Science (RS) as a provenance-explicit program. The old claim set is retained, but each major statement is marked as forced now, defined now, hypothesized now, or open obligation. The presently forced core consists of three results formalized in Lean 4: the T7 forcing chain gives an abstract eight-slot basis; dissolution into light memory preserves the Z-pattern and does not increase maintenance cost; and any admissible diagonal retention mask cannot increase information. The current bridge layer then defines the semantic eight-channel basis, the 3 + 1 + 4 partition, the emotional threshold at k ≥ 3, the development gap gap(k), the transition index TI(k) = k - 5 (for k ≤ 8), the preservation budget φᵏ, and the σ-history correction. The φ-capacity recursion is now forced at the mathematical level: Lean proves that the reflexivity eigenvalue satisfies λ² = λ + 1, and that the recursion C(0) = 1, C(k+1) = φ·C(k) solves to C(k) = φᵏ (reflexivityEigenvalue_sq, informationCapacity_eq_pow). The present bridge layer then proves that any grounded embodied state satisfies the unconditional bound I_pres ≤ φᵏ (preservedInformation_le_budget_grounded). What remains explicit is the grounding step itself: the current theorem connecting R̂ dynamics to groundedness still uses an information-cost correspondence and a level-cost bound (r_hat_produces_grounded_state). The paper closes with a claim matrix and a Lean roadmap that identifies exactly which bridge theorems remain before the strongest death claims become unavoidable consequences of RS core theorems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19102201 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Death Transition in Recognition Science Washburn, Jonathan <p>This paper rewrites the death-transition story in Recognition Science (RS) as a provenance-explicit program. The old claim set is retained, but each major statement is marked as forced now, defined now, hypothesized now, or open obligation. The presently forced core consists of three results formalized in Lean 4: the T7 forcing chain gives an abstract eight-slot basis; dissolution into light memory preserves the Z-pattern and does not increase maintenance cost; and any admissible diagonal retention mask cannot increase information. The current bridge layer then defines the semantic eight-channel basis, the 3 + 1 + 4 partition, the emotional threshold at k ≥ 3, the development gap gap(k), the transition index TI(k) = k - 5 (for k ≤ 8), the preservation budget φᵏ, and the σ-history correction. The φ-capacity recursion is now forced at the mathematical level: Lean proves that the reflexivity eigenvalue satisfies λ² = λ + 1, and that the recursion C(0) = 1, C(k+1) = φ·C(k) solves to C(k) = φᵏ (reflexivityEigenvalue_sq, informationCapacity_eq_pow). The present bridge layer then proves that any grounded embodied state satisfies the unconditional bound I_pres ≤ φᵏ (preservedInformation_le_budget_grounded). What remains explicit is the grounding step itself: the current theorem connecting R̂ dynamics to groundedness still uses an information-cost correspondence and a level-cost bound (r_hat_produces_grounded_state). The paper closes with a claim matrix and a Lean roadmap that identifies exactly which bridge theorems remain before the strongest death claims become unavoidable consequences of RS core theorems.</p> |
| title | The Death Transition in Recognition Science |
| url | https://doi.org/10.5281/zenodo.19102201 |