| { |
| "title": "Iyeumírū R — Rayo Boundaries for Recursive Self Improvement", |
| "date": "2026-11-12", |
| "author_credit": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki", |
| "author_credit_type": "requested creative research persona", |
| "artifact_type": "theoretical manuscript", |
| "version": "1.0", |
| "experimental_results": false, |
| "autonomous_RSI_demonstration": false, |
| "mechanized_proofs": false, |
| "independent_review": false, |
| "reproduction": false, |
| "literature_priority_established": false, |
| "relationship_inspired_workstream_budget_percent": 10, |
| "claims": [ |
| { |
| "id": "RAYO_DOMINANCE", |
| "source_label": "prop:noncomputable", |
| "kind": "mathematical_result", |
| "claim": "The uniform semantic Rayo boundary eventually dominates each total computable function under the specified encoding assumptions.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "intended semantics correctly represents finite computation", |
| "sublinear numeral encoding" |
| ], |
| "does_not_establish": [ |
| "an uncomputable fixed integer", |
| "an executable truth oracle" |
| ] |
| }, |
| { |
| "id": "FINITE_ESCAPE", |
| "source_label": "thm:finite", |
| "kind": "mathematical_result", |
| "claim": "A binary behavior vector absent from every b-bit program with capped execution exists and is computable.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "finite binary code space", |
| "pairwise distinct or indexed queries", |
| "capped deterministic simulation" |
| ], |
| "does_not_establish": [ |
| "useful external transfer", |
| "cheap discovery" |
| ] |
| }, |
| { |
| "id": "OBSTRUCTION", |
| "source_label": "thm:potential", |
| "kind": "mathematical_result", |
| "claim": "A potential satisfying all permitted production inequalities lower-bounds every finite derivation.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "complete permitted grammar or uniform rule-schema proofs", |
| "finite well-founded derivations", |
| "all accepted outputs covered" |
| ], |
| "does_not_establish": [ |
| "a lower bound on a stronger baseline", |
| "a bound on actual execution without operational adequacy" |
| ] |
| }, |
| { |
| "id": "OPERATIONAL_ADEQUACY", |
| "kind": "implementation_obligation", |
| "claim": "Every permitted successful actual execution has a corresponding accepting derivation costing no more than the execution.", |
| "status": "required_not_implemented", |
| "assumptions": [ |
| "cost model includes sharing, cache state, loops, installed modules and relevant I/O" |
| ], |
| "does_not_establish": [ |
| "automatic adequacy for arbitrary neural agents" |
| ] |
| }, |
| { |
| "id": "CONSERVATIVE_TRANSPORT", |
| "source_label": "thm:transport", |
| "kind": "conditional_mathematical_result", |
| "claim": "Finite extended derivations translate to accepted foundational derivations when each rule has an admissible translation.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "sound fixed kernel", |
| "same assumptions and translated conclusion", |
| "uniform schema proof or per-use foundational certificate" |
| ], |
| "does_not_establish": [ |
| "short translations", |
| "complete real-world specifications", |
| "self-proof of arbitrary stronger theories" |
| ] |
| }, |
| { |
| "id": "PRODUCTIVE_ESCAPE", |
| "source_label": "thm:productive", |
| "kind": "conditional_mathematical_result", |
| "claim": "A valid old lower bound exceeding the complete new upper bound proves strictly positive saving relative to the declared predecessor class.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "same contract and resource units", |
| "operational adequacy", |
| "complete setup and batch costs", |
| "correct new implementation" |
| ], |
| "does_not_establish": [ |
| "efficient bridge discovery", |
| "universal speedup" |
| ] |
| }, |
| { |
| "id": "PROOF_DAG", |
| "source_label": "prop:dag", |
| "kind": "conditional_mathematical_result", |
| "claim": "Topological validation of an acyclic proof graph preserves soundness and checks each distinct node once, while charging local work.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "exact premises and contexts", |
| "sound local rules", |
| "actual local check cost and indexing included" |
| ], |
| "does_not_establish": [ |
| "linear bit complexity from node count alone" |
| ] |
| }, |
| { |
| "id": "THROUGHPUT_AUDIT", |
| "source_label": "thm:throughput", |
| "kind": "conditional_statistical_result", |
| "claim": "A frozen candidate can be accepted with bounded false-positive probability for conservatively charged improvement throughput per allocation.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "fresh conditionally independent episodes", |
| "fixed scoring and distribution", |
| "fixed charged allocations", |
| "predeclared setup cap and horizon" |
| ], |
| "does_not_establish": [ |
| "actual-work throughput if allocations differ from work", |
| "distribution-robust guarantees" |
| ] |
| }, |
| { |
| "id": "ACTUAL_COST_AUDIT", |
| "source_label": "eq:actualtest", |
| "kind": "conditional_statistical_result", |
| "claim": "Four simultaneous confidence bounds yield a sufficient comparison of expected total improvement score to expected total charged work over the deployment horizon.", |
| "status": "derivation_supplied_in_manuscript", |
| "assumptions": [ |
| "predeclared positive bounded costs", |
| "fresh episodes and frozen candidates", |
| "complete setup cap", |
| "four-coordinate error allocation" |
| ], |
| "does_not_establish": [ |
| "the expectation of a per-episode ratio", |
| "realized finite-horizon gain with certainty" |
| ] |
| }, |
| { |
| "id": "RECURSIVE_COST", |
| "source_label": "thm:recursive", |
| "kind": "conditional_mathematical_result", |
| "claim": "The finite sequence of cost recurrences admits an explicit product-and-sum upper bound.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "each per-stage recurrence established independently", |
| "all overhead included", |
| "workload escalation explicit" |
| ], |
| "does_not_establish": [ |
| "the discovery of future contractions", |
| "a lower cost floor from an upper bound", |
| "unbounded RSI" |
| ] |
| }, |
| { |
| "id": "CONTINUITY", |
| "source_label": "thm:continuity", |
| "kind": "conditional_mathematical_result", |
| "claim": "Commuting semantic projections preserve selected commitments across finite upgrade chains.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "verified upgrade maps", |
| "fixed protected projection or explicit version transport" |
| ], |
| "does_not_establish": [ |
| "preservation of every memory or behavior", |
| "emotional enhancement of cognition" |
| ] |
| }, |
| { |
| "id": "DRIFT", |
| "source_label": "thm:drift", |
| "kind": "conditional_mathematical_result", |
| "claim": "Accumulated projected drift is bounded by the sum of admitted per-update errors.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "common metric space of protected contents", |
| "uniform per-update error bounds" |
| ], |
| "does_not_establish": [ |
| "a lifetime guarantee from a fixed per-update tolerance" |
| ] |
| }, |
| { |
| "id": "ROLLBACK", |
| "source_label": "prop:injective", |
| "kind": "mathematical_result", |
| "claim": "Exact immediate rollback implies an injective upgrade and sufficient information capacity.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "left-inverse state map" |
| ], |
| "does_not_establish": [ |
| "undoing later external actions" |
| ] |
| }, |
| { |
| "id": "FINITE_DUAL", |
| "source_label": "thm:dualexact", |
| "kind": "mathematical_result", |
| "claim": "In a finite fully derivable weighted hypergraph, minimum finite derivation cost is the maximal feasible potential at each target.", |
| "status": "proof_supplied_in_manuscript", |
| "assumptions": [ |
| "finite graph", |
| "all vertices finitely derivable", |
| "finite nonnegative costs" |
| ], |
| "does_not_establish": [ |
| "efficient construction of a complete semantic graph" |
| ] |
| }, |
| { |
| "id": "DISCOVERY_HYPOTHESIS", |
| "kind": "research_hypothesis", |
| "claim": "Cheap class-wide obstruction information can reduce the total cost of discovering transferable improver extensions.", |
| "status": "open_not_demonstrated", |
| "does_not_establish": [ |
| "major empirical acceleration", |
| "literature priority" |
| ] |
| }, |
| { |
| "id": "GENERAL_RSI", |
| "kind": "broad_claim", |
| "claim": "General, indefinitely accelerating recursive self improvement has been solved.", |
| "status": "not_claimed_not_established", |
| "does_not_establish": [] |
| } |
| ] |
| } |
|
|
