{"id":"palindrome-instantiates-hash-then-stream","text":"Palindrome construction and permutation problems are specific instantiations of the hash-then-stream pipeline: Counter builds the frequency map in O(n) preprocessing, then a single-pass parity check over frequencies determines constructibility — the same two-phase structure that governs the broader pipeline taxonomy.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["palindrome-construction-reduces-to-frequency-parity","hash-preprocessing-universal-first-step"],"outlist":[],"label":"palindrome's Counter + parity-scan matches the canonical hash-then-stream decomposition"}],"dependents":["hash-pipeline-demonstrated-by-dual-exemplar-families","palindrome-is-canonical-counter-pipeline-exemplar"],"metadata":{"source_type":"derived","last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"palindrome-instantiates-hash-then-stream","truth_value":"IN","reason":"SL justification valid","antecedents":["palindrome-construction-reduces-to-frequency-parity","hash-preprocessing-universal-first-step"],"label":"palindrome's Counter + parity-scan matches the canonical hash-then-stream decomposition"},{"node":"palindrome-construction-reduces-to-frequency-parity","truth_value":"IN","reason":"SL justification valid","antecedents":["palindrome-perm-at-most-one-odd","palindrome-greedy-even-portions","palindrome-center-bonus-at-most-once","palindrome-perm-parity-reduction"],"label":"Depth-1 thematic grouping: four palindrome base beliefs share the same core insight that palindromicity is a parity property of frequencies"},{"node":"palindrome-perm-at-most-one-odd","truth_value":"IN","reason":"premise"},{"node":"palindrome-greedy-even-portions","truth_value":"IN","reason":"premise"},{"node":"palindrome-center-bonus-at-most-once","truth_value":"IN","reason":"premise"},{"node":"palindrome-perm-parity-reduction","truth_value":"IN","reason":"premise"},{"node":"hash-preprocessing-universal-first-step","truth_value":"IN","reason":"SL justification valid","antecedents":["counter-universal-frequency-primitive","set-for-o1-membership-universal"],"label":"Counter and set are complementary hash tools — Counter for \"how many\" and set for \"is present\" — and together cover the preprocessing needs of the majority of easy/medium problems"},{"node":"counter-universal-frequency-primitive","truth_value":"IN","reason":"SL justification valid","antecedents":["counter-dominant-frequency-tool","counter-pattern-dominates-frequency-problems","counter-missing-key-returns-zero","counter-subtraction-drops-nonpositive"],"label":"Counter's built-in semantics eliminate boilerplate that manual dicts would require"},{"node":"counter-dominant-frequency-tool","truth_value":"IN","reason":"premise"},{"node":"counter-pattern-dominates-frequency-problems","truth_value":"IN","reason":"premise"},{"node":"counter-missing-key-returns-zero","truth_value":"IN","reason":"premise"},{"node":"counter-subtraction-drops-nonpositive","truth_value":"IN","reason":"premise"},{"node":"set-for-o1-membership-universal","truth_value":"IN","reason":"SL justification valid","antecedents":["set-conversion-before-loop-for-o1-lookup","k-distant-uses-set-dedup","find-difference-set-minus-idiom","two-out-of-three-set-algebra"],"label":"Set algebra (intersection, difference, membership) replaces manual iteration wherever applicable"},{"node":"set-conversion-before-loop-for-o1-lookup","truth_value":"IN","reason":"premise"},{"node":"k-distant-uses-set-dedup","truth_value":"IN","reason":"premise"},{"node":"find-difference-set-minus-idiom","truth_value":"IN","reason":"premise"},{"node":"two-out-of-three-set-algebra","truth_value":"IN","reason":"premise"}]}}