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2026
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| Online Access: | https://doi.org/10.5281/zenodo.18270097 |
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| author | Washburn, Jonathan |
| author_facet | Washburn, Jonathan |
| contents | <p dir="auto">We prove a model-independent exclusivity theorem for Recognition Science (RS) on the quotient state space: states are identified when they are observationally indistinguishable (i.e., yield the same observable output). Working with an abstract “physics framework” consisting of a state space, an evolution operator, and an observable extraction map, we assume only structural constraints corresponding to the RS necessity stack: (i) zero adjustable parameters (algorithmic describability), (ii) self-similarity, (iii) the existence of a cost functional satisfying the Recognition Composition Law with normalization and calibration, and (iv) observables extracted from (and uniform under) the cost-minimizing structure. From these assumptions we derive, without importing any RS-specific connection data or outcome-matching hypotheses, that the preferred scale is forced to the golden ratio φ and the admissible cost functional is uniquely J_{cost}(x) = (1/2)(x + x^{-1})^{-1} on R_{>0}. Consequently, all states are observationally equivalent: the quotient state space collapses to a subsingleton (equivalently, StateQuotient(F) ≃ 1). This reframes RS as an inevitability theorem: any competing zero-parameter framework that derives observables must either introduce free parameters (violating the zero-parameter posture) or agree with RS at the level of observational content on the quotient. All core claims are machine-verified in Lean 4 in IndisputableMonolith.Verification.Exclusivity.ModelIndependent.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18270097 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Model-Independent Exclusivity on the Quotient State Space Recognition Science as an Inevitability Theorem for Zero-Parameter Frameworks Washburn, Jonathan <p dir="auto">We prove a model-independent exclusivity theorem for Recognition Science (RS) on the quotient state space: states are identified when they are observationally indistinguishable (i.e., yield the same observable output). Working with an abstract “physics framework” consisting of a state space, an evolution operator, and an observable extraction map, we assume only structural constraints corresponding to the RS necessity stack: (i) zero adjustable parameters (algorithmic describability), (ii) self-similarity, (iii) the existence of a cost functional satisfying the Recognition Composition Law with normalization and calibration, and (iv) observables extracted from (and uniform under) the cost-minimizing structure. From these assumptions we derive, without importing any RS-specific connection data or outcome-matching hypotheses, that the preferred scale is forced to the golden ratio φ and the admissible cost functional is uniquely J_{cost}(x) = (1/2)(x + x^{-1})^{-1} on R_{>0}. Consequently, all states are observationally equivalent: the quotient state space collapses to a subsingleton (equivalently, StateQuotient(F) ≃ 1). This reframes RS as an inevitability theorem: any competing zero-parameter framework that derives observables must either introduce free parameters (violating the zero-parameter posture) or agree with RS at the level of observational content on the quotient. All core claims are machine-verified in Lean 4 in IndisputableMonolith.Verification.Exclusivity.ModelIndependent.</p> |
| title | Model-Independent Exclusivity on the Quotient State Space Recognition Science as an Inevitability Theorem for Zero-Parameter Frameworks |
| url | https://doi.org/10.5281/zenodo.18270097 |