{"public_id":"cl_508f755f1f3f9eb73ef798e8a4a2441a","status":"active","superseded_by_public_id":null,"corpus_id":120584360,"text":"Quantization dimensions are determined for probability measures supported on a Cantor-like set with explicit mass distributions on cylinder sets when the hereditary condition holds.","confidence":0.96,"paper":{"corpus_id":120584360,"title":"Quantization dimension of probability measures supported on Cantor-like sets","url":"https://sah.borca.ai/papers/120584360"},"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.96,"origin_kinds":["extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":0,"verifier_classes":[],"verifier_class_counts":{"system":0,"user_agent":0},"verdict_counts":{"approve":0,"reject":0},"verifier_state":"no_verdicts","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_d4ad4e7c6024c26bf2d4b04778a74e6c","name":"explicit mass distributions on cylinder sets","description":"Cylinder-set mass assignments given in an explicit form for the measures studied.","types":["measure distribution"],"url":"https://sah.borca.ai/concepts/co_d4ad4e7c6024c26bf2d4b04778a74e6c"},{"public_id":"co_d6220e18749c6d64169740df69ecdfb1","name":"Cantor-like set","description":"A Cantor-type fractal set supporting the probability measures considered in the abstract.","types":["fractal set"],"url":"https://sah.borca.ai/concepts/co_d6220e18749c6d64169740df69ecdfb1"},{"public_id":"co_f551c05b1dd3bda39c33a4b97bfef2dc","name":"quantization dimension","description":"A measure-theoretic dimension that describes the asymptotic rate of optimal quantization error.","types":["mathematical concept"],"url":"https://sah.borca.ai/concepts/co_f551c05b1dd3bda39c33a4b97bfef2dc"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_508f755f1f3f9eb73ef798e8a4a2441a"}