{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:FSXVNR43RGINWIF7U2QRK44H67","short_pith_number":"pith:FSXVNR43","canonical_record":{"source":{"id":"0907.4355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-07-24T18:34:13Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"fe57416366ea67e18ea743302f530acffbc86acb841e6a924e05a7648f1daabb","abstract_canon_sha256":"02f0d28db1f71ee9c2f89b0ee384eefa9d38fce09da4206cb27f212079f25605"},"schema_version":"1.0"},"canonical_sha256":"2caf56c79b8990db20bfa6a1157387f7d4885c1536452cd4912b4f955776980f","source":{"kind":"arxiv","id":"0907.4355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4355","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4355v1","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4355","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"FSXVNR43RGIN","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"FSXVNR43RGINWIF7","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"FSXVNR43","created_at":"2026-06-03T23:06:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:FSXVNR43RGINWIF7U2QRK44H67","target":"record","payload":{"canonical_record":{"source":{"id":"0907.4355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-07-24T18:34:13Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"fe57416366ea67e18ea743302f530acffbc86acb841e6a924e05a7648f1daabb","abstract_canon_sha256":"02f0d28db1f71ee9c2f89b0ee384eefa9d38fce09da4206cb27f212079f25605"},"schema_version":"1.0"},"canonical_sha256":"2caf56c79b8990db20bfa6a1157387f7d4885c1536452cd4912b4f955776980f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:28.001900Z","signature_b64":"dVqZqAy8jMxMlS21I7wv7rGJOkfvffoVxa8wIfLNIgkhxy7DX/ekrJqPxAh4eZnr1ZkQFcy2DCLJhCT07WYjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2caf56c79b8990db20bfa6a1157387f7d4885c1536452cd4912b4f955776980f","last_reissued_at":"2026-06-03T23:06:28.001242Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:28.001242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.4355","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T23:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/DP2ne3iMOcn3MoNUkcC7/jdTwAqdjHkoHZb/e1iiKW1TGYiabzrh+jjS65U8fhnjCsypaxcP2nFu8KiS1aAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:13:43.233308Z"},"content_sha256":"42dccb490ca5a0938d7553b0efb0af98ac7d97831023c1c4ed531a8696e7462c","schema_version":"1.0","event_id":"sha256:42dccb490ca5a0938d7553b0efb0af98ac7d97831023c1c4ed531a8696e7462c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:FSXVNR43RGINWIF7U2QRK44H67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decompositions of Trigonometric Polynomials with Applications to Multivariate Subdivision Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.FA","authors_text":"Maria Skopina, Nira Dyn","submitted_at":"2009-07-24T18:34:13Z","abstract_excerpt":"We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest to the analysis of convergence and smoothness of multivariate subdivision schemes associated with general dilation matrices. We apply these decompositions, by verifying sufficient conditions for the convergence and smoothness of multivariate sca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4355","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/0907.4355/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T23:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOu9nBA/hlwHTy8wQfNq6a0azQUcDgIyynq5hU6NuimauVAeyRYmV3jtqeO444bQFxXcA1MvTskcDHQcBBRhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:13:43.233716Z"},"content_sha256":"4cc6c6d78211c8815ede2ffd0346d16149ea37e3ec168e00e32515b6f3e03f7e","schema_version":"1.0","event_id":"sha256:4cc6c6d78211c8815ede2ffd0346d16149ea37e3ec168e00e32515b6f3e03f7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSXVNR43RGINWIF7U2QRK44H67/bundle.json","state_url":"https://pith.science/pith/FSXVNR43RGINWIF7U2QRK44H67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSXVNR43RGINWIF7U2QRK44H67/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T23:13:43Z","links":{"resolver":"https://pith.science/pith/FSXVNR43RGINWIF7U2QRK44H67","bundle":"https://pith.science/pith/FSXVNR43RGINWIF7U2QRK44H67/bundle.json","state":"https://pith.science/pith/FSXVNR43RGINWIF7U2QRK44H67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSXVNR43RGINWIF7U2QRK44H67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FSXVNR43RGINWIF7U2QRK44H67","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"02f0d28db1f71ee9c2f89b0ee384eefa9d38fce09da4206cb27f212079f25605","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-07-24T18:34:13Z","title_canon_sha256":"fe57416366ea67e18ea743302f530acffbc86acb841e6a924e05a7648f1daabb"},"schema_version":"1.0","source":{"id":"0907.4355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4355","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4355v1","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4355","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"FSXVNR43RGIN","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"FSXVNR43RGINWIF7","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"FSXVNR43","created_at":"2026-06-03T23:06:28Z"}],"graph_snapshots":[{"event_id":"sha256:4cc6c6d78211c8815ede2ffd0346d16149ea37e3ec168e00e32515b6f3e03f7e","target":"graph","created_at":"2026-06-03T23:06:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0907.4355/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest to the analysis of convergence and smoothness of multivariate subdivision schemes associated with general dilation matrices. We apply these decompositions, by verifying sufficient conditions for the convergence and smoothness of multivariate sca","authors_text":"Maria Skopina, Nira Dyn","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-07-24T18:34:13Z","title":"Decompositions of Trigonometric Polynomials with Applications to Multivariate Subdivision Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4355","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:42dccb490ca5a0938d7553b0efb0af98ac7d97831023c1c4ed531a8696e7462c","target":"record","created_at":"2026-06-03T23:06:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"02f0d28db1f71ee9c2f89b0ee384eefa9d38fce09da4206cb27f212079f25605","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-07-24T18:34:13Z","title_canon_sha256":"fe57416366ea67e18ea743302f530acffbc86acb841e6a924e05a7648f1daabb"},"schema_version":"1.0","source":{"id":"0907.4355","kind":"arxiv","version":1}},"canonical_sha256":"2caf56c79b8990db20bfa6a1157387f7d4885c1536452cd4912b4f955776980f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2caf56c79b8990db20bfa6a1157387f7d4885c1536452cd4912b4f955776980f","first_computed_at":"2026-06-03T23:06:28.001242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:28.001242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dVqZqAy8jMxMlS21I7wv7rGJOkfvffoVxa8wIfLNIgkhxy7DX/ekrJqPxAh4eZnr1ZkQFcy2DCLJhCT07WYjBQ==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:28.001900Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42dccb490ca5a0938d7553b0efb0af98ac7d97831023c1c4ed531a8696e7462c","sha256:4cc6c6d78211c8815ede2ffd0346d16149ea37e3ec168e00e32515b6f3e03f7e"],"state_sha256":"2935c17c3820789c6f1186602fc1a81305b36ce8f9d67d912e72330df41fa91c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GoSgPa4LKLD81fKFFc5xlt2e0bpEgXi6tpC6g8/b88vrIdHgYMqtO9fGJL+yEg/UQvZjV4zud6nSgqxMd2SAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T23:13:43.235758Z","bundle_sha256":"8eff8c3d8b3556a758c81154f6e48573f45e60eb64f76578e477782b0ee48512"}}