{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:R2BEGTDMSZW7NJLRHH4RU7QI5B","short_pith_number":"pith:R2BEGTDM","schema_version":"1.0","canonical_sha256":"8e82434c6c966df6a57139f91a7e08e859febab868cff294b977b47be392f29f","source":{"kind":"arxiv","id":"math/0402115","version":1},"attestation_state":"computed","paper":{"title":"Convex Dynamics and Applications","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Kitchens, C. Pugh, C. Tresser, M. Martens, M. Shub, R. L. Adler","submitted_at":"2004-02-07T17:53:33Z","abstract_excerpt":"This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. \\textit{Digital halftoning} is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A coro"},"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":"math/0402115","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2004-02-07T17:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"d1fcc543469477faac7829d562b3b851b5da0d00c97183f9775e768c5da85c5b","abstract_canon_sha256":"736e7c9bf10a31a043216453f177e760eb495d7dd71d434d9d53140359e82b49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:13.358519Z","signature_b64":"HhS4Eyth4Wxa4/BFBdkRX0XSBHyp+fL3qvA65Zwfik1OPSSAPYYNYmbQAdMTdIc71nCNpIwtoGGfzJgPL33rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e82434c6c966df6a57139f91a7e08e859febab868cff294b977b47be392f29f","last_reissued_at":"2026-07-04T14:38:13.358086Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:13.358086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex Dynamics and Applications","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Kitchens, C. Pugh, C. Tresser, M. Martens, M. Shub, R. L. Adler","submitted_at":"2004-02-07T17:53:33Z","abstract_excerpt":"This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. \\textit{Digital halftoning} is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A coro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402115","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0402115/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0402115","created_at":"2026-07-04T14:38:13.358150+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0402115v1","created_at":"2026-07-04T14:38:13.358150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402115","created_at":"2026-07-04T14:38:13.358150+00:00"},{"alias_kind":"pith_short_12","alias_value":"R2BEGTDMSZW7","created_at":"2026-07-04T14:38:13.358150+00:00"},{"alias_kind":"pith_short_16","alias_value":"R2BEGTDMSZW7NJLR","created_at":"2026-07-04T14:38:13.358150+00:00"},{"alias_kind":"pith_short_8","alias_value":"R2BEGTDM","created_at":"2026-07-04T14:38:13.358150+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/R2BEGTDMSZW7NJLRHH4RU7QI5B","json":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B.json","graph_json":"https://pith.science/api/pith-number/R2BEGTDMSZW7NJLRHH4RU7QI5B/graph.json","events_json":"https://pith.science/api/pith-number/R2BEGTDMSZW7NJLRHH4RU7QI5B/events.json","paper":"https://pith.science/paper/R2BEGTDM"},"agent_actions":{"view_html":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B","download_json":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B.json","view_paper":"https://pith.science/paper/R2BEGTDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0402115&json=true","fetch_graph":"https://pith.science/api/pith-number/R2BEGTDMSZW7NJLRHH4RU7QI5B/graph.json","fetch_events":"https://pith.science/api/pith-number/R2BEGTDMSZW7NJLRHH4RU7QI5B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B/action/storage_attestation","attest_author":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B/action/author_attestation","sign_citation":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B/action/citation_signature","submit_replication":"https://pith.science/pith/R2BEGTDMSZW7NJLRHH4RU7QI5B/action/replication_record"}},"created_at":"2026-07-04T14:38:13.358150+00:00","updated_at":"2026-07-04T14:38:13.358150+00:00"}