{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KLYXJP2WA2Y325FHAMZNUUSSMR","short_pith_number":"pith:KLYXJP2W","canonical_record":{"source":{"id":"1807.10909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-28T08:10:50Z","cross_cats_sorted":[],"title_canon_sha256":"840bf1ceee7e175e13bb7951dc6db894e605c839007f154aef2fdd8f85545dd9","abstract_canon_sha256":"40a5c4632bf3d43693667e2e5083f8398bb63b2c40c1d572b15f3630f55d0cac"},"schema_version":"1.0"},"canonical_sha256":"52f174bf5606b1bd74a70332da52526472eba6f0665629eda0dd0af752068388","source":{"kind":"arxiv","id":"1807.10909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10909","created_at":"2026-05-18T00:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10909v1","created_at":"2026-05-18T00:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10909","created_at":"2026-05-18T00:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"KLYXJP2WA2Y3","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KLYXJP2WA2Y325FH","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KLYXJP2W","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KLYXJP2WA2Y325FHAMZNUUSSMR","target":"record","payload":{"canonical_record":{"source":{"id":"1807.10909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-28T08:10:50Z","cross_cats_sorted":[],"title_canon_sha256":"840bf1ceee7e175e13bb7951dc6db894e605c839007f154aef2fdd8f85545dd9","abstract_canon_sha256":"40a5c4632bf3d43693667e2e5083f8398bb63b2c40c1d572b15f3630f55d0cac"},"schema_version":"1.0"},"canonical_sha256":"52f174bf5606b1bd74a70332da52526472eba6f0665629eda0dd0af752068388","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:35.045475Z","signature_b64":"tP4XObuCNjVe6fpMmL0rHMJ7LY2yHn9lIkOiqut8bei5FQto43a5O1nLlQBdpAjaa3VUMuFnmA4tnJKLK9WoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52f174bf5606b1bd74a70332da52526472eba6f0665629eda0dd0af752068388","last_reissued_at":"2026-05-18T00:09:35.044863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:35.044863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.10909","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":"2026-05-18T00:09:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vl85xRM9E7/ZX/1xTS0OYg+SVPl2XHvM3j36qw+O7dvu47alTW1V65B8Hbk/UkSugi5gfq1GdngiETJTbxYjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:36:14.978234Z"},"content_sha256":"dabb6a92c940b9de9e32353d8f8e1feb57dc90eaf2fdd5e76b547cedf241bbf7","schema_version":"1.0","event_id":"sha256:dabb6a92c940b9de9e32353d8f8e1feb57dc90eaf2fdd5e76b547cedf241bbf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KLYXJP2WA2Y325FHAMZNUUSSMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal H\\\"older-Zygmund exponent of semi-regular refinable functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alberto Viscardi, Costanza Conti, Joachim St\\\"ockler, Lucia Romani, Maria Charina","submitted_at":"2018-07-28T08:10:50Z","abstract_excerpt":"The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting is crucial for these approaches. We propose an efficient method based on wavelet tight frame decomposition techniques for estimating H\\\"older-Zygmund regularity of univariate semi-regular refinable functions generated, e.g., by subdivision schemes defined on semi-regular meshes $\\mathbf{t}\\;=\\;-h_\\ell\\mathbb{N}\\cup\\{0\\}\\cup h_r\\mathbb{N}$, $h_\\ell,h_r \\in ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10909","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiSavE/P6v75yN6z7QhnDizAq+3uqr8EPTOAmAcnLMIezwsXRBAh5zClpyQSFfmXuFhIpCrwNR1YCjDdbbaQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:36:14.978590Z"},"content_sha256":"0320b3ee55d4f4e81abcecdde85bcf997c7a0c6534b61ae001aacce5f436daa3","schema_version":"1.0","event_id":"sha256:0320b3ee55d4f4e81abcecdde85bcf997c7a0c6534b61ae001aacce5f436daa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLYXJP2WA2Y325FHAMZNUUSSMR/bundle.json","state_url":"https://pith.science/pith/KLYXJP2WA2Y325FHAMZNUUSSMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLYXJP2WA2Y325FHAMZNUUSSMR/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":"2026-06-26T11:36:14Z","links":{"resolver":"https://pith.science/pith/KLYXJP2WA2Y325FHAMZNUUSSMR","bundle":"https://pith.science/pith/KLYXJP2WA2Y325FHAMZNUUSSMR/bundle.json","state":"https://pith.science/pith/KLYXJP2WA2Y325FHAMZNUUSSMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLYXJP2WA2Y325FHAMZNUUSSMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KLYXJP2WA2Y325FHAMZNUUSSMR","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":"40a5c4632bf3d43693667e2e5083f8398bb63b2c40c1d572b15f3630f55d0cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-28T08:10:50Z","title_canon_sha256":"840bf1ceee7e175e13bb7951dc6db894e605c839007f154aef2fdd8f85545dd9"},"schema_version":"1.0","source":{"id":"1807.10909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10909","created_at":"2026-05-18T00:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10909v1","created_at":"2026-05-18T00:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10909","created_at":"2026-05-18T00:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"KLYXJP2WA2Y3","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KLYXJP2WA2Y325FH","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KLYXJP2W","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:0320b3ee55d4f4e81abcecdde85bcf997c7a0c6534b61ae001aacce5f436daa3","target":"graph","created_at":"2026-05-18T00:09:35Z","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":"The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting is crucial for these approaches. We propose an efficient method based on wavelet tight frame decomposition techniques for estimating H\\\"older-Zygmund regularity of univariate semi-regular refinable functions generated, e.g., by subdivision schemes defined on semi-regular meshes $\\mathbf{t}\\;=\\;-h_\\ell\\mathbb{N}\\cup\\{0\\}\\cup h_r\\mathbb{N}$, $h_\\ell,h_r \\in (","authors_text":"Alberto Viscardi, Costanza Conti, Joachim St\\\"ockler, Lucia Romani, Maria Charina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-28T08:10:50Z","title":"Optimal H\\\"older-Zygmund exponent of semi-regular refinable functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10909","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:dabb6a92c940b9de9e32353d8f8e1feb57dc90eaf2fdd5e76b547cedf241bbf7","target":"record","created_at":"2026-05-18T00:09:35Z","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":"40a5c4632bf3d43693667e2e5083f8398bb63b2c40c1d572b15f3630f55d0cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-28T08:10:50Z","title_canon_sha256":"840bf1ceee7e175e13bb7951dc6db894e605c839007f154aef2fdd8f85545dd9"},"schema_version":"1.0","source":{"id":"1807.10909","kind":"arxiv","version":1}},"canonical_sha256":"52f174bf5606b1bd74a70332da52526472eba6f0665629eda0dd0af752068388","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52f174bf5606b1bd74a70332da52526472eba6f0665629eda0dd0af752068388","first_computed_at":"2026-05-18T00:09:35.044863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:35.044863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tP4XObuCNjVe6fpMmL0rHMJ7LY2yHn9lIkOiqut8bei5FQto43a5O1nLlQBdpAjaa3VUMuFnmA4tnJKLK9WoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:35.045475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dabb6a92c940b9de9e32353d8f8e1feb57dc90eaf2fdd5e76b547cedf241bbf7","sha256:0320b3ee55d4f4e81abcecdde85bcf997c7a0c6534b61ae001aacce5f436daa3"],"state_sha256":"f634673fcbe90d0bad5f003640c16f4feb45b121f19e14d3e841f6f231d4daf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sqVheys0lH8usQ+GUibAG8wi62jmzDhRVw5YvEQM+p5nxIagXFfMlv6HQu06YOQGcXlBFHXE3WDWiqvI+SxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:36:14.980482Z","bundle_sha256":"bb9ee4592115973dfd1d54ec6c5c8a8c6f25cd33d091522dd1b170940f23ec72"}}