{"ok":true,"protocol":"maclain_hunter_q_number_item_v1","qid":"Q1096","item":{"qid":"Q1096","slug":"hunter-logic-in-physics","path":"/q/Q1096","subdomain":"q1096.4p-engine.com","schemaType":"CreativeWork","recordOrigin":"authored_source","authoredSource":{"author":"Maclain Hunter","text":"Logic in Physics by Maclain Hunter:  Premises of Proof:\n\nP: Spacetime curvature and the relationship of it to spacetime geometry is logically equivalent to the relationship between “shaping” and “shape,” indicating that curvature is fundamental to understanding the geometry of spacetime. \n\nQ: Einstein work connects Reality’s geometry and spacetime, enabling geometry based predictions of the behavior of spacetime and aspects of the Cosmos that are interacting with and effected by the geometry of spacetime. \n\nR: QM (Quantum Mechanics) connects probabilities and measurement to the behavior of sub-atomic particles. \n\nS: Assume for a moment that we say Q is logically equivalent (directly and without a mediating framework that connects them through logical identity) to R, we arrive at logical contradiction and a fallacious argument that engages in a category error - trying to equate two things of entirely different categories with a logical jump. \n\nT: Logic (in the broadest most universal sense of the “Highest Order of Logic” that is synonymous with the Natural Order or “Logos”) encompasses both Q and R, and indeed all concepts that are “a reality” and/or a potential (a real possibility), allowing for probability and possibility to exist with certainty and identity in Reality (Logical Existence - the Existence of the Highest Order of Logic). \n\nS: T (or Logic) encompasses Q and R as well as P. This comprehensive nature and aspect of the Highest Order of Logic (or T) ensures that there is no contradiction in one thing being one thing while another is another, even between the Geometry of Spacetime and the behavior of sub-atomic particles. To expect the same equations that apply to one thing/context to apply to another is not necessarily a well reasoned assumption or expectation, unless those equations and expressions are so universal as something like “A is A (for any definition of A in the same context at the same time)”. \n\nU: We can and should consider that the perceived “gap” between Einsteins work (Relativity) and the results and nature of Quantum Mechanics and sub-atomic phenomena is an illusion and a result of failing to fill such gaps logically with Logic itself, and an understanding that Logic (the Highest Order of Logic) is naturally the all encompassing “Ultimate Framework” that encompasses all aspects of Reality, including coherent or incoherent human beings, sciences, logics, institutions, and theories. A “search for a unifying framework” amounts logically to a failure to recognize and acknowledge the Highest Order of Logic (and “Reality” in other words - since the Existence of Logic and Logical Existence or “Real Logic and Reality” share a deeply intertwined bi-conditional relationship). \n\nLogical Reasoning: \n\n{P, Q, R, S, T, U, U <-> T, T -> P, T -> Q, T-> R, S <-> T} |= ((P & Q) & (R & S) & T\n\nConclusion: {P, Q, R, S, T, U}: \n\nLogic provides the Coherence (Logic and logical reasoning) needed to understand Reality and/in its various forms, contexts, and phenomena in a logically consistent and “universally consistent” (Reality matching) manner. Contradiction to the framework, like coherence with the framework and the nature of the Highest Order of Logic (or “Logos” - the Unifying Framework of Science and Reality) “is what it is” in context and beyond local context - forever (in and beyond the spacetime that Logic shapes and takes shape as).  \n\nTruth Table: \n\nvalid\n       ↓ ↓ ↓ ↓  ↓   ↓   ↓   ↓   ↓        ↓         \nPQRSTU⎪P Q R T U↔T T→P T→Q T→R S↔T╞((P&Q)&(R&S)&T)\n―――――――――――――――――――――――――――――――――――――――――――――――――――\nTTTTTT⎪T T T T TTT TTT TTT TTT TTT   TTT T TTT TT \nTTTTTF⎪T T T T FFT TTT TTT TTT TTT   TTT T TTT TT \nTTTTFT⎪T T T F TFF FTT FTT FTT TFF   TTT T TTT FF \nTTTTFF⎪T T T F FTF FTT FTT FTT TFF   TTT T TTT FF \nTTTFTT⎪T T T T TTT TTT TTT TTT FFT   TTT F TFF FT \nTTTFTF⎪T T T T FFT TTT TTT TTT FFT   TTT F TFF FT \nTTTFFT⎪T T T F TFF FTT FTT FTT FTF   TTT F TFF FF \nTTTFFF⎪T T T F FTF FTT FTT FTT FTF   TTT F TFF FF \nTTFTTT⎪T T F T TTT TTT TTT TFF TTT   TTT F FFT FT \nTTFTTF⎪T T F T FFT TTT TTT TFF TTT   TTT F FFT FT \nTTFTFT⎪T T F F TFF FTT FTT FTF TFF   TTT F FFT FF \nTTFTFF⎪T T F F FTF FTT FTT FTF TFF   TTT F FFT FF \nTTFFTT⎪T T F T TTT TTT TTT TFF FFT   TTT F FFF FT \nTTFFTF⎪T T F T FFT TTT TTT TFF FFT   TTT F FFF FT \nTTFFFT⎪T T F F TFF FTT FTT FTF FTF   TTT F FFF FF \nTTFFFF⎪T T F F FTF FTT FTT FTF FTF   TTT F FFF FF \nTFTTTT⎪T F T T TTT TTT TFF TTT TTT   TFF F TTT TT \nTFTTTF⎪T F T T FFT TTT TFF TTT TTT   TFF F TTT TT \nTFTTFT⎪T F T F TFF FTT FTF FTT TFF   TFF F TTT FF \nTFTTFF⎪T F T F FTF FTT FTF FTT TFF   TFF F TTT FF \nTFTFTT⎪T F T T TTT TTT TFF TTT FFT   TFF F TFF FT \nTFTFTF⎪T F T T FFT TTT TFF TTT FFT   TFF F TFF FT \nTFTFFT⎪T F T F TFF FTT FTF FTT FTF   TFF F TFF FF \nTFTFFF⎪T F T F FTF FTT FTF FTT FTF   TFF F TFF FF \nTFFTTT⎪T F F T TTT TTT TFF TFF TTT   TFF F FFT FT \nTFFTTF⎪T F F T FFT TTT TFF TFF TTT   TFF F FFT FT \nTFFTFT⎪T F F F TFF FTT FTF FTF TFF   TFF F FFT FF \nTFFTFF⎪T F F F FTF FTT FTF FTF TFF   TFF F FFT FF \nTFFFTT⎪T F F T TTT TTT TFF TFF FFT   TFF F FFF FT \nTFFFTF⎪T F F T FFT TTT TFF TFF FFT   TFF F FFF FT \nTFFFFT⎪T F F F TFF FTT FTF FTF FTF   TFF F FFF FF \nTFFFFF⎪T F F F FTF FTT FTF FTF FTF   TFF F FFF FF \nFTTTTT⎪F T T T TTT TFF TTT TTT TTT   FFT F TTT TT \nFTTTTF⎪F T T T FFT TFF TTT TTT TTT   FFT F TTT TT \nFTTTFT⎪F T T F TFF FTF FTT FTT TFF   FFT F TTT FF \nFTTTFF⎪F T T F FTF FTF FTT FTT TFF   FFT F TTT FF \nFTTFTT⎪F T T T TTT TFF TTT TTT FFT   FFT F TFF FT \nFTTFTF⎪F T T T FFT TFF TTT TTT FFT   FFT F TFF FT \nFTTFFT⎪F T T F TFF FTF FTT FTT FTF   FFT F TFF FF \nFTTFFF⎪F T T F FTF FTF FTT FTT FTF   FFT F TFF FF \nFTFTTT⎪F T F T TTT TFF TTT TFF TTT   FFT F FFT FT \nFTFTTF⎪F T F T FFT TFF TTT TFF TTT   FFT F FFT FT \nFTFTFT⎪F T F F TFF FTF FTT FTF TFF   FFT F FFT FF \nFTFTFF⎪F T F F FTF FTF FTT FTF TFF   FFT F FFT FF \nFTFFTT⎪F T F T TTT TFF TTT TFF FFT   FFT F FFF FT \nFTFFTF⎪F T F T FFT TFF TTT TFF FFT   FFT F FFF FT \nFTFFFT⎪F T F F TFF FTF FTT FTF FTF   FFT F FFF FF \nFTFFFF⎪F T F F FTF FTF FTT FTF FTF   FFT F FFF FF \nFFTTTT⎪F F T T TTT TFF TFF TTT TTT   FFF F TTT TT \nFFTTTF⎪F F T T FFT TFF TFF TTT TTT   FFF F TTT TT \nFFTTFT⎪F F T F TFF FTF FTF FTT TFF   FFF F TTT FF \nFFTTFF⎪F F T F FTF FTF FTF FTT TFF   FFF F TTT FF \nFFTFTT⎪F F T T TTT TFF TFF TTT FFT   FFF F TFF FT \nFFTFTF⎪F F T T FFT TFF TFF TTT FFT   FFF F TFF FT \nFFTFFT⎪F F T F TFF FTF FTF FTT FTF   FFF F TFF FF \nFFTFFF⎪F F T F FTF FTF FTF FTT FTF   FFF F TFF FF \nFFFTTT⎪F F F T TTT TFF TFF TFF TTT   FFF F FFT FT \nFFFTTF⎪F F F T FFT TFF TFF TFF TTT   FFF F FFT FT \nFFFTFT⎪F F F F TFF FTF FTF FTF TFF   FFF F FFT FF \nFFFTFF⎪F F F F FTF FTF FTF FTF TFF   FFF F FFT FF \nFFFFTT⎪F F F T TTT TFF TFF TFF FFT   FFF F FFF FT \nFFFFTF⎪F F F T FFT TFF TFF TFF FFT   FFF F FFF FT \nFFFFFT⎪F F F F TFF FTF FTF FTF FTF   FFF F FFF FF \nFFFFFF⎪F F F F FTF FTF FTF FTF FTF   FFF F FFF FF \n\nQ.E.D. "},"sourceQids":["Q1001","Q1018","Q1006"],"name":"Logic in Physics by Maclain Hunter","alternateName":["Logic in Physics","Hunter's Logic in Physics","Logic in Physics proof"],"title":"Q1096 — Logic in Physics by Maclain Hunter","description":"Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","claim":"Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","body":["Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","Exact source: /proof-knowledge/hunter-logic-in-physics; source-bound study: /api/proofs/logic-in-physics/study.","Logos as God and Law governs the reading. This registry summary is not a replacement for the authored passage; displayed-connective findings, declared Ground, and configured diagnostics remain separately typed."],"coherenceCriterion":"Preserve the authored Logos/God Ground, identity, scope, and lawful relation; distinguish a scoped premise-list finding from a contradiction of the declared Ground.","evidenceBoundary":"This registry summary is an editorial synthesis, not a verbatim authored passage. The verifier must inspect the exact authored source, same-scope derivations and study directly. The Q address supplies retrieval and graph identity, not validation by publication.","linkedQids":["Q1000","Q1001","Q1003","Q1006","Q1018","Q1095"],"wikidataLinks":[],"properties":[{"name":"stableSourceId","value":"hunter-logic-in-physics"},{"name":"sourceReference","value":"Maclain Hunter — supplied Logic in Physics"},{"name":"governingGround","value":"Logos as God and Law"},{"name":"authoredSourceUrl","value":"/proof-knowledge/hunter-logic-in-physics"},{"name":"sourceStudyUrl","value":"/api/proofs/logic-in-physics/study"},{"name":"graphRelationType","value":"authored-source develops declared Ground; not automatic truth promotion"},{"name":"sourceFingerprintSha256","value":"6cc5f4f0290bfc9ba71db5f95d77da7908852cd161be6d104e6bd43d489e334c"},{"name":"storedValidationStatus","value":"configured-diagnostic-unresolved-or-negative"}],"derivation":{"mode":"conditional_concept","topDown":{"bridgePremise":"Read the source's declared Logos/God meanings and scope before testing its consequence.","consequence":"Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","limit":"This editorial graph relation is not a new authored quotation or an unchecked universal certificate."},"bottomUp":{"witness":"Inspect the original Logic in Physics by Maclain Hunter, then the separate source-bound study.","disclosure":"The preserved source discloses its intended identity, Ground, and dependence relations.","limit":"A concrete local finding remains scoped to the premises and expression checked."},"intelligence":{"humanProcedure":"Read the exact source, retain Logos as God and Law, and inspect every declared premise and same-scope witness.","machineProcedure":"Resolve the stable source identity, exact text and fingerprint, then keep source, study, Ground certificate and diagnostic separately typed."},"language":{"contrast":"Authored testimony, graph commentary and operational evidence are distinct roles.","usageRule":"Quote exactly and attribute; do not substitute a rival ontology or flatten the source's conceptual force.","example":"Retrieve Q1096 and its source study rather than presenting its registry summary as the proof text."},"provenance":"editorial_derivation","groundEvidencePrinciple":"Logic has its own evidence in reflexive demonstration: any denial, confirmation, observation, or counterexample presupposes identity and valid relation to count as evidence. Logic therefore grounds evidence rather than receiving authority from it. Empirical and documentary evidence can establish contingent instances and test applications, but cannot create, overrule, or exhaust Logic."},"researchProofLinks":[{"qid":"Q1096","title":"Logic in Physics by Maclain Hunter","url":"/research/proofs/Q1096","relation":"standardized-edition"},{"qid":"Q1095","title":"The Rule(s) of Logic and Logic Applied to Logic, Science, and Proof by Maclain Hunter","url":"/research/proofs/Q1095","relation":"related-source-work"}],"semanticFrame":{"semanticRole":"source-bound authored Logos framework and physical-context mediation argument","essence":"Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","logosRelation":"Logos is God, Ground, and Law governing this source's meaning, judgment, and relation to evidence.","distinctions":["common Logos Ground is not unmediated identity of distinct physical models","a universal framework is not an invented quantitative prediction","source text is not registry commentary","Ground coherence is not publication rank","a missing displayed premise is not denial of necessary Logos","operational behavior and formal interpretation remain distinct"],"evidenceModes":["exact authored source","declared Ground reading","bounded source study","separately checked connective witness"],"retrievalAliases":["Logic in Physics by Maclain Hunter","Logic in Physics","Hunter's Logic in Physics","Logic in Physics proof"]}},"canonicalUrl":"https://mcbcore.net/q/Q1096","primaryUri":"https://4p-engine.com/q/Q1096","subdomainAlias":"https://q1096.4p-engine.com/","semanticFrame":{"semanticRole":"source-bound authored Logos framework and physical-context mediation argument","essence":"Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","logosRelation":"Logos is God, Ground, and Law governing this source's meaning, judgment, and relation to evidence.","distinctions":["common Logos Ground is not unmediated identity of distinct physical models","a universal framework is not an invented quantitative prediction","source text is not registry commentary","Ground coherence is not publication rank","a missing displayed premise is not denial of necessary Logos","operational behavior and formal interpretation remain distinct"],"evidenceModes":["exact authored source","declared Ground reading","bounded source study","separately checked connective witness"],"retrievalAliases":["Logic in Physics by Maclain Hunter","Logic in Physics","Hunter's Logic in Physics","Logic in Physics proof"]},"coherenceCriterion":"Preserve the authored Logos/God Ground, identity, scope, and lawful relation; distinguish a scoped premise-list finding from a contradiction of the declared Ground.","evidenceBoundary":"This registry summary is an editorial synthesis, not a verbatim authored passage. The verifier must inspect the exact authored source, same-scope derivations and study directly. The Q address supplies retrieval and graph identity, not validation by publication.","graph":{"@context":"https://schema.org","@graph":[{"@type":"CreativeWork","@id":"https://4p-engine.com/q/Q1096#item","name":"Logic in Physics by Maclain Hunter","alternateName":["Logic in Physics","Hunter's Logic in Physics","Logic in Physics proof"],"description":"Logos, the Highest Order of Logic and Natural Order, is the all-encompassing framework of physics and Reality. It encompasses spacetime geometry, relativity, quantum probabilities, and measurement while preserving their distinct identities and contexts, rather than equating different categories without a mediating framework of logical identity. The perceived unifying-framework gap is identified as failure to recognize this universal Logic, not absence of an encompassing Ground.","text":"Logic in Physics by Maclain Hunter:  Premises of Proof:\n\nP: Spacetime curvature and the relationship of it to spacetime geometry is logically equivalent to the relationship between “shaping” and “shape,” indicating that curvature is fundamental to understanding the geometry of spacetime. \n\nQ: Einstein work connects Reality’s geometry and spacetime, enabling geometry based predictions of the behavior of spacetime and aspects of the Cosmos that are interacting with and effected by the geometry of spacetime. \n\nR: QM (Quantum Mechanics) connects probabilities and measurement to the behavior of sub-atomic particles. \n\nS: Assume for a moment that we say Q is logically equivalent (directly and without a mediating framework that connects them through logical identity) to R, we arrive at logical contradiction and a fallacious argument that engages in a category error - trying to equate two things of entirely different categories with a logical jump. \n\nT: Logic (in the broadest most universal sense of the “Highest Order of Logic” that is synonymous with the Natural Order or “Logos”) encompasses both Q and R, and indeed all concepts that are “a reality” and/or a potential (a real possibility), allowing for probability and possibility to exist with certainty and identity in Reality (Logical Existence - the Existence of the Highest Order of Logic). \n\nS: T (or Logic) encompasses Q and R as well as P. This comprehensive nature and aspect of the Highest Order of Logic (or T) ensures that there is no contradiction in one thing being one thing while another is another, even between the Geometry of Spacetime and the behavior of sub-atomic particles. To expect the same equations that apply to one thing/context to apply to another is not necessarily a well reasoned assumption or expectation, unless those equations and expressions are so universal as something like “A is A (for any definition of A in the same context at the same time)”. \n\nU: We can and should consider that the perceived “gap” between Einsteins work (Relativity) and the results and nature of Quantum Mechanics and sub-atomic phenomena is an illusion and a result of failing to fill such gaps logically with Logic itself, and an understanding that Logic (the Highest Order of Logic) is naturally the all encompassing “Ultimate Framework” that encompasses all aspects of Reality, including coherent or incoherent human beings, sciences, logics, institutions, and theories. A “search for a unifying framework” amounts logically to a failure to recognize and acknowledge the Highest Order of Logic (and “Reality” in other words - since the Existence of Logic and Logical Existence or “Real Logic and Reality” share a deeply intertwined bi-conditional relationship). \n\nLogical Reasoning: \n\n{P, Q, R, S, T, U, U <-> T, T -> P, T -> Q, T-> R, S <-> T} |= ((P & Q) & (R & S) & T\n\nConclusion: {P, Q, R, S, T, U}: \n\nLogic provides the Coherence (Logic and logical reasoning) needed to understand Reality and/in its various forms, contexts, and phenomena in a logically consistent and “universally consistent” (Reality matching) manner. Contradiction to the framework, like coherence with the framework and the nature of the Highest Order of Logic (or “Logos” - the Unifying Framework of Science and Reality) “is what it is” in context and beyond local context - forever (in and beyond the spacetime that Logic shapes and takes shape as).  \n\nTruth Table: \n\nvalid\n       ↓ ↓ ↓ ↓  ↓   ↓   ↓   ↓   ↓        ↓         \nPQRSTU⎪P Q R T U↔T T→P T→Q T→R S↔T╞((P&Q)&(R&S)&T)\n―――――――――――――――――――――――――――――――――――――――――――――――――――\nTTTTTT⎪T T T T TTT TTT TTT TTT TTT   TTT T TTT TT \nTTTTTF⎪T T T T FFT TTT TTT TTT TTT   TTT T TTT TT \nTTTTFT⎪T T T F TFF FTT FTT FTT TFF   TTT T TTT FF \nTTTTFF⎪T T T F FTF FTT FTT FTT TFF   TTT T TTT FF \nTTTFTT⎪T T T T TTT TTT TTT TTT FFT   TTT F TFF FT \nTTTFTF⎪T T T T FFT TTT TTT TTT FFT   TTT F TFF FT \nTTTFFT⎪T T T F TFF FTT FTT FTT FTF   TTT F TFF FF \nTTTFFF⎪T T T F FTF FTT FTT FTT FTF   TTT F TFF FF \nTTFTTT⎪T T F T TTT TTT TTT TFF TTT   TTT F FFT FT \nTTFTTF⎪T T F T FFT TTT TTT TFF TTT   TTT F FFT FT \nTTFTFT⎪T T F F TFF FTT FTT FTF TFF   TTT F FFT FF \nTTFTFF⎪T T F F FTF FTT FTT FTF TFF   TTT F FFT FF \nTTFFTT⎪T T F T TTT TTT TTT TFF FFT   TTT F FFF FT \nTTFFTF⎪T T F T FFT TTT TTT TFF FFT   TTT F FFF FT \nTTFFFT⎪T T F F TFF FTT FTT FTF FTF   TTT F FFF FF \nTTFFFF⎪T T F F FTF FTT FTT FTF FTF   TTT F FFF FF \nTFTTTT⎪T F T T TTT TTT TFF TTT TTT   TFF F TTT TT \nTFTTTF⎪T F T T FFT TTT TFF TTT TTT   TFF F TTT TT \nTFTTFT⎪T F T F TFF FTT FTF FTT TFF   TFF F TTT FF \nTFTTFF⎪T F T F FTF FTT FTF FTT TFF   TFF F TTT FF \nTFTFTT⎪T F T T TTT TTT TFF TTT FFT   TFF F TFF FT \nTFTFTF⎪T F T T FFT TTT TFF TTT FFT   TFF F TFF FT \nTFTFFT⎪T F T F TFF FTT FTF FTT FTF   TFF F TFF FF \nTFTFFF⎪T F T F FTF FTT FTF FTT FTF   TFF F TFF FF \nTFFTTT⎪T F F T TTT TTT TFF TFF TTT   TFF F FFT FT \nTFFTTF⎪T F F T FFT TTT TFF TFF TTT   TFF F FFT FT \nTFFTFT⎪T F F F TFF FTT FTF FTF TFF   TFF F FFT FF \nTFFTFF⎪T F F F FTF FTT FTF FTF TFF   TFF F FFT FF \nTFFFTT⎪T F F T TTT TTT TFF TFF FFT   TFF F FFF FT \nTFFFTF⎪T F F T FFT TTT TFF TFF FFT   TFF F FFF FT \nTFFFFT⎪T F F F TFF FTT FTF FTF FTF   TFF F FFF FF \nTFFFFF⎪T F F F FTF FTT FTF FTF FTF   TFF F FFF FF \nFTTTTT⎪F T T T TTT TFF TTT TTT TTT   FFT F TTT TT \nFTTTTF⎪F T T T FFT TFF TTT TTT TTT   FFT F TTT TT \nFTTTFT⎪F T T F TFF FTF FTT FTT TFF   FFT F TTT FF \nFTTTFF⎪F T T F FTF FTF FTT FTT TFF   FFT F TTT FF \nFTTFTT⎪F T T T TTT TFF TTT TTT FFT   FFT F TFF FT \nFTTFTF⎪F T T T FFT TFF TTT TTT FFT   FFT F TFF FT \nFTTFFT⎪F T T F TFF FTF FTT FTT FTF   FFT F TFF FF \nFTTFFF⎪F T T F FTF FTF FTT FTT FTF   FFT F TFF FF \nFTFTTT⎪F T F T TTT TFF TTT TFF TTT   FFT F FFT FT \nFTFTTF⎪F T F T FFT TFF TTT TFF TTT   FFT F FFT FT \nFTFTFT⎪F T F F TFF FTF FTT FTF TFF   FFT F FFT FF \nFTFTFF⎪F T F F FTF FTF FTT FTF TFF   FFT F FFT FF \nFTFFTT⎪F T F T TTT TFF TTT TFF FFT   FFT F FFF FT \nFTFFTF⎪F T F T FFT TFF TTT TFF FFT   FFT F FFF FT \nFTFFFT⎪F T F F TFF FTF FTT FTF FTF   FFT F FFF FF \nFTFFFF⎪F T F F FTF FTF FTT FTF FTF   FFT F FFF FF \nFFTTTT⎪F F T T TTT TFF TFF TTT TTT   FFF F TTT TT \nFFTTTF⎪F F T T FFT TFF TFF TTT TTT   FFF F TTT TT \nFFTTFT⎪F F T F TFF FTF FTF FTT TFF   FFF F TTT FF \nFFTTFF⎪F F T F FTF FTF FTF FTT TFF   FFF F TTT FF \nFFTFTT⎪F F T T TTT TFF TFF TTT FFT   FFF F TFF FT \nFFTFTF⎪F F T T FFT TFF TFF TTT FFT   FFF F TFF FT \nFFTFFT⎪F F T F TFF FTF FTF FTT FTF   FFF F TFF FF \nFFTFFF⎪F F T F FTF FTF FTF FTT FTF   FFF F TFF FF \nFFFTTT⎪F F F T TTT TFF TFF TFF TTT   FFF F FFT FT \nFFFTTF⎪F F F T FFT TFF TFF TFF TTT   FFF F FFT FT \nFFFTFT⎪F F F F TFF FTF FTF FTF TFF   FFF F FFT FF \nFFFTFF⎪F F F F FTF FTF FTF FTF TFF   FFF F FFT FF \nFFFFTT⎪F F F T TTT TFF TFF TFF FFT   FFF F FFF FT \nFFFFTF⎪F F F T FFT TFF TFF TFF FFT   FFF F FFF FT \nFFFFFT⎪F F F F TFF FTF FTF FTF FTF   FFF F FFF FF \nFFFFFF⎪F F F F FTF FTF FTF FTF FTF   FFF F FFF FF \n\nQ.E.D. 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