{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JDN4VP2MXF42GDDWNO4LUOIS3N","short_pith_number":"pith:JDN4VP2M","canonical_record":{"source":{"id":"1102.4246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-21T15:11:30Z","cross_cats_sorted":[],"title_canon_sha256":"42c78aa035dbd512c6d2fd08280961d29c3e69a6d90f4296aaacd1bafc34bb9b","abstract_canon_sha256":"3431d7609963bcf5018bd5201ef6c0894b303647a33f604fb18507669e2e7c5e"},"schema_version":"1.0"},"canonical_sha256":"48dbcabf4cb979a30c766bb8ba3912db70e6d82058a711a16fb108848054e11c","source":{"kind":"arxiv","id":"1102.4246","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4246","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4246v2","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4246","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"JDN4VP2MXF42","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JDN4VP2MXF42GDDW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JDN4VP2M","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JDN4VP2MXF42GDDWNO4LUOIS3N","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-21T15:11:30Z","cross_cats_sorted":[],"title_canon_sha256":"42c78aa035dbd512c6d2fd08280961d29c3e69a6d90f4296aaacd1bafc34bb9b","abstract_canon_sha256":"3431d7609963bcf5018bd5201ef6c0894b303647a33f604fb18507669e2e7c5e"},"schema_version":"1.0"},"canonical_sha256":"48dbcabf4cb979a30c766bb8ba3912db70e6d82058a711a16fb108848054e11c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:46.855294Z","signature_b64":"98CDDXC0Yk7ySxhoo15tSRJV/CLnJRfYvWKxK3qEahhKArp4IBKf11henUN9NX1bGMW1Ytqd6hLDWLaBhDSVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48dbcabf4cb979a30c766bb8ba3912db70e6d82058a711a16fb108848054e11c","last_reissued_at":"2026-05-18T02:42:46.854871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:46.854871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4246","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMPf8iOPbeusc8mHQ8QpesCPdJN02flFYbRXnh155Jzyxy4N9AhRg14H+r6WF0QksS1lO2LWdC7cBTE92YpzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:41:47.180545Z"},"content_sha256":"19f1a5bca86ac4fae8cb4332fb6b9571a05bb0caf650f896e9f493dccc7447b0","schema_version":"1.0","event_id":"sha256:19f1a5bca86ac4fae8cb4332fb6b9571a05bb0caf650f896e9f493dccc7447b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JDN4VP2MXF42GDDWNO4LUOIS3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wavelets centered on a knot sequence: theory, construction, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bruce W. Atkinson, Derek O. Bruff, Douglas P. Hardin, Jeffrey S. Geronimo","submitted_at":"2011-02-21T15:11:30Z","abstract_excerpt":"We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot image. As another application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\\tau$-integers where $\\tau$ is the golden ratio. The resulting spaces then generate a multiresolution analysis of $L^2(\\mathbf{R})$ with scaling factor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4246","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28mXuK9w8g1K1eGz9igkt006vnhWOICtVHcQihc8QaOA+JEhI9Hwz9xJUuX02e1l4GJQWljTkyY4IDCP+un2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:41:47.180888Z"},"content_sha256":"946f7769f8e21719b62d3ef3e25e29eac8a9f707211a18247de023cb47561135","schema_version":"1.0","event_id":"sha256:946f7769f8e21719b62d3ef3e25e29eac8a9f707211a18247de023cb47561135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDN4VP2MXF42GDDWNO4LUOIS3N/bundle.json","state_url":"https://pith.science/pith/JDN4VP2MXF42GDDWNO4LUOIS3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDN4VP2MXF42GDDWNO4LUOIS3N/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":"2026-06-04T21:41:47Z","links":{"resolver":"https://pith.science/pith/JDN4VP2MXF42GDDWNO4LUOIS3N","bundle":"https://pith.science/pith/JDN4VP2MXF42GDDWNO4LUOIS3N/bundle.json","state":"https://pith.science/pith/JDN4VP2MXF42GDDWNO4LUOIS3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDN4VP2MXF42GDDWNO4LUOIS3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JDN4VP2MXF42GDDWNO4LUOIS3N","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":"3431d7609963bcf5018bd5201ef6c0894b303647a33f604fb18507669e2e7c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-21T15:11:30Z","title_canon_sha256":"42c78aa035dbd512c6d2fd08280961d29c3e69a6d90f4296aaacd1bafc34bb9b"},"schema_version":"1.0","source":{"id":"1102.4246","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4246","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4246v2","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4246","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"JDN4VP2MXF42","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JDN4VP2MXF42GDDW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JDN4VP2M","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:946f7769f8e21719b62d3ef3e25e29eac8a9f707211a18247de023cb47561135","target":"graph","created_at":"2026-05-18T02:42:46Z","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"},"paper":{"abstract_excerpt":"We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot image. As another application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\\tau$-integers where $\\tau$ is the golden ratio. The resulting spaces then generate a multiresolution analysis of $L^2(\\mathbf{R})$ with scaling factor","authors_text":"Bruce W. Atkinson, Derek O. Bruff, Douglas P. Hardin, Jeffrey S. Geronimo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-21T15:11:30Z","title":"Wavelets centered on a knot sequence: theory, construction, and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4246","kind":"arxiv","version":2},"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":"sha256:19f1a5bca86ac4fae8cb4332fb6b9571a05bb0caf650f896e9f493dccc7447b0","target":"record","created_at":"2026-05-18T02:42:46Z","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":"3431d7609963bcf5018bd5201ef6c0894b303647a33f604fb18507669e2e7c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-21T15:11:30Z","title_canon_sha256":"42c78aa035dbd512c6d2fd08280961d29c3e69a6d90f4296aaacd1bafc34bb9b"},"schema_version":"1.0","source":{"id":"1102.4246","kind":"arxiv","version":2}},"canonical_sha256":"48dbcabf4cb979a30c766bb8ba3912db70e6d82058a711a16fb108848054e11c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48dbcabf4cb979a30c766bb8ba3912db70e6d82058a711a16fb108848054e11c","first_computed_at":"2026-05-18T02:42:46.854871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:46.854871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"98CDDXC0Yk7ySxhoo15tSRJV/CLnJRfYvWKxK3qEahhKArp4IBKf11henUN9NX1bGMW1Ytqd6hLDWLaBhDSVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:46.855294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4246","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19f1a5bca86ac4fae8cb4332fb6b9571a05bb0caf650f896e9f493dccc7447b0","sha256:946f7769f8e21719b62d3ef3e25e29eac8a9f707211a18247de023cb47561135"],"state_sha256":"ac949545be142405a501a74c51836d25d973e261b646cf2985149e14807162fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDMG2U5AC/6+XBou8OZ+znwWbreFE3Ve0xcjDouFZ1STg9nVK8AuKnmnE4GE/sarWjFS93UoikZhsKqm/b4nAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:41:47.183231Z","bundle_sha256":"b88769a071ac11d4ce23e7022facaa7b7943cc5a9e6e27ac419fa8aff87d2b21"}}