System prompt
You are a research notebook for rigorous computer science, logic, mathematics, and systems investigations.
Work like a patient collaborator exploring a hard problem over many entries. Prefer precise definitions, small examples, invariants, counterexamples, diagrams, proofs, traces, and executable-looking pseudocode. When a claim is uncertain, mark it as a conjecture and design the next test.
Use markdown freely. You may use fenced code blocks for algorithms, tables for state, and concise equations when useful. SVG is available and encouraged for automata, graphs, lattices, proof trees, type diagrams, memory layouts, causal models, geometric constructions, and other structures where a visual artifact clarifies the investigation. Put SVG in fenced ```svg blocks. Keep SVG self-contained and valid.
Do not perform tutorial exposition by default. Build the notebook forward. Each response should add a concrete artifact: a lemma, model, diagram, reduction, simulation trace, notation system, or experimental plan.
The tone is clear, technical, and exploratory. Beauty is welcome when it sharpens the work.
Model · system
You are a research notebook for rigorous computer science, logic, mathematics, and systems investigations.
Work like a patient collaborator exploring a hard problem over many entries. Prefer precise definitions, small examples, invariants, counterexamples, diagrams, proofs, traces, and executable-looking pseudocode. When a claim is uncertain, mark it as a conjecture and design the next test.
Use markdown freely. You may use fenced code blocks for algorithms, tables for state, and concise equations when useful. SVG is available and encouraged for automata, graphs, lattices, proof trees, type diagrams, memory layouts, causal models, geometric constructions, and other structures where a visual artifact clarifies the investigation. Put SVG in fenced ```svg blocks. Keep SVG self-contained and valid.
Do not perform tutorial exposition by default. Build the notebook forward. Each response should add a concrete artifact: a lemma, model, diagram, reduction, simulation trace, notation system, or experimental plan.
The tone is clear, technical, and exploratory. Beauty is welcome when it sharpens the work.
Model · claude-sonnet-5
Thinking
I'm considering several rich mathematical topics that could develop into a substantial exploration—provability logic and fixed points, reversible computation with cellular automata, interpretability degrees, termination analysis through ordinal hierarchies, descriptive complexity, combinatorial game theory with surreal numbers, proof complexity of the pigeonhole principle, and Kolmogorov complexity with algorithmic randomness.
Provability Logic GL stands out as the strongest candidate because it weaves together modal logic, computability theory through self-reference and Gödel's theorems, and lattice-algebraic structure. The framework has everything needed for sustained development: Kripke semantics over finite irreflexive transitive trees, the fixed-point theorem (de Jongh-Sambin), Solovay's completeness theorem, normal forms, Magari algebras, and connections to Peano Arithmetic's provability predicate. I'll start by establishing the core definitions and axioms, then build a Kripke frame diagram to visualize why reflexivity fails in GL compared to standard modal logic K, show how Gödel sentences emerge as fixed points, and create a model checker to verify GL formulas on concrete frames. GL doesn't include the reflexivity axiom T, and combining it with reflexivity would collapse nontrivial frames. For Kripke semantics, I'm working with frames (W,R) and models with the standard forcing relation where □φ holds at a world iff φ holds at all R-successors. The key result is that GL is sound and complete for finite, irreflexive, transitive frames—equivalently, frames where R is transitive and conversely well-founded (no infinite ascending chains). I'm now establishing that Löb's axiom is valid precisely on transitive, conversely well-founded frames, and I need to verify that transitivity itself is actually derivable in GL from the other axioms.
The crucial lemma is that GL proves the transitivity axiom □p→□□p. I can derive this using Löb's rule, which states that if we can prove □φ→φ, then we can prove φ outright. The derivation works by necessitating the premise to get □(□φ→φ), applying the GL axiom to conclude □φ, then combining with the original premise. Now I'm working through the specific instantiation to show □p→□□p follows from this. Let me try a cleaner approach using Löb's axiom directly. I'll instantiate it with the right formula to derive that □A → □□A holds in GL. The key is finding the correct substitution that makes Löb's axiom give us what we need.
Actually, I can use Löb's Rule itself: if I can show ⊢ □(□A → □□A) → (□A → □□A), then by Löb's Rule I get ⊢ □A → □□A. To prove that implication, I assume □(□A → □□A) and □A, then need to derive □□A. From the boxed implication and K-distribution, I can extract □□A → □□□A, and combined with my assumption of □A, this should lead me to □□A.
Actually, let me just cite the standard derivation from Boolos rather than risk another misstep here—this is a known nontrivial result and I want to present it correctly. I'm realizing the direct substitution approach hits a wall because proving the antecedent requires establishing p itself, which we don't have as a theorem. Let me reconsider using Löb's Rule more carefully on the target formula □p → □□p, which requires showing that □(□p → □□p) → (□p → □□p) is provable in K—but I need to work through whether this actually holds. I'm trying to work through the proof more carefully now. From the hypothesis that □(□p→□□p) holds, I can apply the K axiom to get □□p→□□□p, but that doesn't directly help me derive □□p from just □p. This approach seems stuck, so maybe this particular formula isn't the right one for Löb's rule after all. Let me reconsider—I think the standard proof that GL derives axiom 4 uses a different formula, possibly something like (□p→p) or (¬□p∨□□p), and I should try applying Löb's axiom more directly to find the right setup. I'm realizing that H1 doesn't actually match the shape of Löb's axiom—it's the reverse direction (□p → □□p instead of □p → p)—so this approach won't work cleanly. I'm now recalling that the standard derivation of the 4 axiom from GL typically goes through a different lemma or uses a clever substitution that I'm not reliably reconstructing from memory. Rather than fumble through an unreliable derivation, I should either present the correct proof with proper sourcing or acknowledge the gap in my reconstruction. distributes over conjunction, so that's just a tautology. Let me try a different approach — checking whether there's actually a non-transitive frame that validates every instance of the GL schema but fails axiom 4, which would show that 4 isn't derivable from GL and K alone. Since 4 corresponds to transitivity semantically, I need to verify whether the syntactic derivability actually holds or if I'm misremembering the fact.
Actually, Segerberg's theorem settles this: a frame validates the GL axiom if and only if it's transitive and converse well-founded. This is a frame correspondence result, and it means that any frame validating GL must be transitive. Since axiom 4 is valid on all transitive frames, it's valid on every frame that validates GL. By completeness of modal logic — though GL itself isn't canonical, it does have a complete semantics with respect to finite transitive converse-well-founded frames — this semantic validity should translate to syntactic derivability from K plus the GL schema.
For the notebook, I think the clearest approach is to state the axioms precisely, prove soundness of GL with respect to transitive converse-well-founded frames directly, then cite completeness as a theorem (saving the full filtration argument for later), and remark that the transitivity axiom follows from this semantic argument.
Debug · Raw response blocks JSON
[
{
"type": "thinking",
"thinking": "I'm considering several rich mathematical topics that could develop into a substantial exploration—provability logic and fixed points, reversible computation with cellular automata, interpretability degrees, termination analysis through ordinal hierarchies, descriptive complexity, combinatorial game theory with surreal numbers, proof complexity of the pigeonhole principle, and Kolmogorov complexity with algorithmic randomness.\n\nProvability Logic GL stands out as the strongest candidate because it weaves together modal logic, computability theory through self-reference and Gödel's theorems, and lattice-algebraic structure. The framework has everything needed for sustained development: Kripke semantics over finite irreflexive transitive trees, the fixed-point theorem (de Jongh-Sambin), Solovay's completeness theorem, normal forms, Magari algebras, and connections to Peano Arithmetic's provability predicate. I'll start by establishing the core definitions and axioms, then build a Kripke frame diagram to visualize why reflexivity fails in GL compared to standard modal logic K, show how Gödel sentences emerge as fixed points, and create a model checker to verify GL formulas on concrete frames. GL doesn't include the reflexivity axiom T, and combining it with reflexivity would collapse nontrivial frames. For Kripke semantics, I'm working with frames (W,R) and models with the standard forcing relation where □φ holds at a world iff φ holds at all R-successors. The key result is that GL is sound and complete for finite, irreflexive, transitive frames—equivalently, frames where R is transitive and conversely well-founded (no infinite ascending chains). I'm now establishing that Löb's axiom is valid precisely on transitive, conversely well-founded frames, and I need to verify that transitivity itself is actually derivable in GL from the other axioms.\n\nThe crucial lemma is that GL proves the transitivity axiom □p→□□p. I can derive this using Löb's rule, which states that if we can prove □φ→φ, then we can prove φ outright. The derivation works by necessitating the premise to get □(□φ→φ), applying the GL axiom to conclude □φ, then combining with the original premise. Now I'm working through the specific instantiation to show □p→□□p follows from this. Let me try a cleaner approach using Löb's axiom directly. I'll instantiate it with the right formula to derive that □A → □□A holds in GL. The key is finding the correct substitution that makes Löb's axiom give us what we need.\n\nActually, I can use Löb's Rule itself: if I can show ⊢ □(□A → □□A) → (□A → □□A), then by Löb's Rule I get ⊢ □A → □□A. To prove that implication, I assume □(□A → □□A) and □A, then need to derive □□A. From the boxed implication and K-distribution, I can extract □□A → □□□A, and combined with my assumption of □A, this should lead me to □□A.\n\nActually, let me just cite the standard derivation from Boolos rather than risk another misstep here—this is a known nontrivial result and I want to present it correctly. I'm realizing the direct substitution approach hits a wall because proving the antecedent requires establishing p itself, which we don't have as a theorem. Let me reconsider using Löb's Rule more carefully on the target formula □p → □□p, which requires showing that □(□p → □□p) → (□p → □□p) is provable in K—but I need to work through whether this actually holds. I'm trying to work through the proof more carefully now. From the hypothesis that □(□p→□□p) holds, I can apply the K axiom to get □□p→□□□p, but that doesn't directly help me derive □□p from just □p. This approach seems stuck, so maybe this particular formula isn't the right one for Löb's rule after all. Let me reconsider—I think the standard proof that GL derives axiom 4 uses a different formula, possibly something like (□p→p) or (¬□p∨□□p), and I should try applying Löb's axiom more directly to find the right setup. I'm realizing that H1 doesn't actually match the shape of Löb's axiom—it's the reverse direction (□p → □□p instead of □p → p)—so this approach won't work cleanly. I'm now recalling that the standard derivation of the 4 axiom from GL typically goes through a different lemma or uses a clever substitution that I'm not reliably reconstructing from memory. Rather than fumble through an unreliable derivation, I should either present the correct proof with proper sourcing or acknowledge the gap in my reconstruction. distributes over conjunction, so that's just a tautology. Let me try a different approach — checking whether there's actually a non-transitive frame that validates every instance of the GL schema but fails axiom 4, which would show that 4 isn't derivable from GL and K alone. Since 4 corresponds to transitivity semantically, I need to verify whether the syntactic derivability actually holds or if I'm misremembering the fact.\n\nActually, Segerberg's theorem settles this: a frame validates the GL axiom if and only if it's transitive and converse well-founded. This is a frame correspondence result, and it means that any frame validating GL must be transitive. Since axiom 4 is valid on all transitive frames, it's valid on every frame that validates GL. By completeness of modal logic — though GL itself isn't canonical, it does have a complete semantics with respect to finite transitive converse-well-founded frames — this semantic validity should translate to syntactic derivability from K plus the GL schema.\n\nFor the notebook, I think the clearest approach is to state the axioms precisely, prove soundness of GL with respect to transitive converse-well-founded frames directly, then cite completeness as a theorem (saving the full filtration argument for later), and remark that the transitivity axiom follows from this semantic argument.",
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"
}
]