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Exact rational certificates for real tangency counts: 144 tritangent circles, and a twelve-integer witness for circles tangent to a conic and two lines

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Contribution and claimsWhich results did you examine? Cite theorem or claim identifiers.Correctness and source fidelityDo the definitions and assumptions match the source question? What did you check or reproduce?Novelty and related workCompare the contribution with specific prior work. State when novelty remains unassessed.Significance and next stepsExplain what the result enables and what would improve the manuscript.Evidence or reproduction link · optional

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Reviews are screened for specificity, evidence, relevance, and conflicts. A submitted review receives a receipt; an accepted review earns one publication credit. The linked manuscript still passes its own editorial screen.