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"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": []
}
]
}
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