{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TQTXVLI4C2DUVPGME3AB6PDNES","short_pith_number":"pith:TQTXVLI4","schema_version":"1.0","canonical_sha256":"9c277aad1c16874abccc26c01f3c6d24b964e9ab8ea517d39ce481f5c917fa03","source":{"kind":"arxiv","id":"1112.1403","version":1},"attestation_state":"computed","paper":{"title":"Consistency of Variational Continuous-Domain Quantization via Kinetic Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Steidl, Jan Haskovec, Massimo Fornasier","submitted_at":"2011-12-05T21:24:36Z","abstract_excerpt":"We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we provide a rigorous derivation of the mean-field kinetic equation. Moreover, we study the energy of the system, show that it is a Lyapunov functional and prove that in the long time limit the solution tends to an equilibrium given by a local minimum of the energy. In a special case we prove that the equilibrium is unique and is identical to the prescribed image "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.1403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-05T21:24:36Z","cross_cats_sorted":[],"title_canon_sha256":"0435348961324fe7dc1b215b6a3baa4f46763dee237aea04feb0486ad42435a8","abstract_canon_sha256":"48cf56a1c8a772069cff0dd1ff50b8f8ba3ec685a213aebd5ad1eb68956b4c3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:54.579731Z","signature_b64":"62rqD5ZX3HCPUlnYNlRzyL7r08RnJfREs6qVZuFjMTQRALayzYWwAfsP8Bdw31qT1rMpikmCogxRqMeycdKgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c277aad1c16874abccc26c01f3c6d24b964e9ab8ea517d39ce481f5c917fa03","last_reissued_at":"2026-05-18T04:06:54.579264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:54.579264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consistency of Variational Continuous-Domain Quantization via Kinetic Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Steidl, Jan Haskovec, Massimo Fornasier","submitted_at":"2011-12-05T21:24:36Z","abstract_excerpt":"We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we provide a rigorous derivation of the mean-field kinetic equation. Moreover, we study the energy of the system, show that it is a Lyapunov functional and prove that in the long time limit the solution tends to an equilibrium given by a local minimum of the energy. In a special case we prove that the equilibrium is unique and is identical to the prescribed image "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1403","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.1403","created_at":"2026-05-18T04:06:54.579342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1403v1","created_at":"2026-05-18T04:06:54.579342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1403","created_at":"2026-05-18T04:06:54.579342+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQTXVLI4C2DU","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQTXVLI4C2DUVPGM","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQTXVLI4","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES","json":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES.json","graph_json":"https://pith.science/api/pith-number/TQTXVLI4C2DUVPGME3AB6PDNES/graph.json","events_json":"https://pith.science/api/pith-number/TQTXVLI4C2DUVPGME3AB6PDNES/events.json","paper":"https://pith.science/paper/TQTXVLI4"},"agent_actions":{"view_html":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES","download_json":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES.json","view_paper":"https://pith.science/paper/TQTXVLI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1403&json=true","fetch_graph":"https://pith.science/api/pith-number/TQTXVLI4C2DUVPGME3AB6PDNES/graph.json","fetch_events":"https://pith.science/api/pith-number/TQTXVLI4C2DUVPGME3AB6PDNES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES/action/storage_attestation","attest_author":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES/action/author_attestation","sign_citation":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES/action/citation_signature","submit_replication":"https://pith.science/pith/TQTXVLI4C2DUVPGME3AB6PDNES/action/replication_record"}},"created_at":"2026-05-18T04:06:54.579342+00:00","updated_at":"2026-05-18T04:06:54.579342+00:00"}