{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YM7H3FUN3LX7R2ZE5JMBWXRYZX","short_pith_number":"pith:YM7H3FUN","canonical_record":{"source":{"id":"1306.0685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-04T07:36:37Z","cross_cats_sorted":[],"title_canon_sha256":"35ef46fb95ef8e81f1f72be0cdd107849eba85ed3567e23e732431d6d6efbb81","abstract_canon_sha256":"cf3669640e81e0a37f7820279f6686f24156c80d6ebe17ba186189031a70d99b"},"schema_version":"1.0"},"canonical_sha256":"c33e7d968ddaeff8eb24ea581b5e38cdc811d02496bd3facb0da04e34b42d03f","source":{"kind":"arxiv","id":"1306.0685","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0685","created_at":"2026-05-18T02:27:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0685v2","created_at":"2026-05-18T02:27:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0685","created_at":"2026-05-18T02:27:32Z"},{"alias_kind":"pith_short_12","alias_value":"YM7H3FUN3LX7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YM7H3FUN3LX7R2ZE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YM7H3FUN","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YM7H3FUN3LX7R2ZE5JMBWXRYZX","target":"record","payload":{"canonical_record":{"source":{"id":"1306.0685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-04T07:36:37Z","cross_cats_sorted":[],"title_canon_sha256":"35ef46fb95ef8e81f1f72be0cdd107849eba85ed3567e23e732431d6d6efbb81","abstract_canon_sha256":"cf3669640e81e0a37f7820279f6686f24156c80d6ebe17ba186189031a70d99b"},"schema_version":"1.0"},"canonical_sha256":"c33e7d968ddaeff8eb24ea581b5e38cdc811d02496bd3facb0da04e34b42d03f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:32.929154Z","signature_b64":"csdip2AS2nrUJrLRMBYG45fVDbbYBmw/EyHXKqvU6tmmFC5lOEbY8NWpzNgppRZ0gvcF+za3FSR+dIXgcka0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c33e7d968ddaeff8eb24ea581b5e38cdc811d02496bd3facb0da04e34b42d03f","last_reissued_at":"2026-05-18T02:27:32.928353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:32.928353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.0685","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":"2026-05-18T02:27:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHBbwTS3i2rbubwNPSztsQ7fxVmL01VtPvYwb8kdaMlGd+DZbo4a9X0F9Jil9gsHjat271PUg/YLiTAt2b3SCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:50:36.822156Z"},"content_sha256":"31fe0873e14646462bcfff88465eefc94657fab68c45f116928761fb25b93b4d","schema_version":"1.0","event_id":"sha256:31fe0873e14646462bcfff88465eefc94657fab68c45f116928761fb25b93b4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YM7H3FUN3LX7R2ZE5JMBWXRYZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subdivision schemes, network flows and linear optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Geir Dahl, Maria Charina","submitted_at":"2013-06-04T07:36:37Z","abstract_excerpt":"We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal difference masks that posses crucial properties unifying the regularity analysis of univariate and multivariate subdivision schemes. We also provide efficient optimization algorithms for construction of such optimal masks. Integrality of the corresponding optimal values leads to purely analytic proofs of $C^k-$regularity of subdivision."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0685","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":"2026-05-18T02:27:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsqiMBNEGbQGhphCVVloA0f+PXM2rXsl/cjAUeEflIhZ/r6qNOJfODe8CGScwxNX1Np+LimYAq+K0IE4aJTaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:50:36.822516Z"},"content_sha256":"e2d911eebf7b22ff9e14277942eac8b4f58513fab6c19cbebeae278933bd9794","schema_version":"1.0","event_id":"sha256:e2d911eebf7b22ff9e14277942eac8b4f58513fab6c19cbebeae278933bd9794"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX/bundle.json","state_url":"https://pith.science/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX/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":"2026-06-23T16:50:36Z","links":{"resolver":"https://pith.science/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX","bundle":"https://pith.science/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX/bundle.json","state":"https://pith.science/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YM7H3FUN3LX7R2ZE5JMBWXRYZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YM7H3FUN3LX7R2ZE5JMBWXRYZX","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":"cf3669640e81e0a37f7820279f6686f24156c80d6ebe17ba186189031a70d99b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-04T07:36:37Z","title_canon_sha256":"35ef46fb95ef8e81f1f72be0cdd107849eba85ed3567e23e732431d6d6efbb81"},"schema_version":"1.0","source":{"id":"1306.0685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0685","created_at":"2026-05-18T02:27:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0685v2","created_at":"2026-05-18T02:27:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0685","created_at":"2026-05-18T02:27:32Z"},{"alias_kind":"pith_short_12","alias_value":"YM7H3FUN3LX7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YM7H3FUN3LX7R2ZE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YM7H3FUN","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:e2d911eebf7b22ff9e14277942eac8b4f58513fab6c19cbebeae278933bd9794","target":"graph","created_at":"2026-05-18T02:27:32Z","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 link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal difference masks that posses crucial properties unifying the regularity analysis of univariate and multivariate subdivision schemes. We also provide efficient optimization algorithms for construction of such optimal masks. Integrality of the corresponding optimal values leads to purely analytic proofs of $C^k-$regularity of subdivision.","authors_text":"Geir Dahl, Maria Charina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-04T07:36:37Z","title":"Subdivision schemes, network flows and linear optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0685","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":"sha256:31fe0873e14646462bcfff88465eefc94657fab68c45f116928761fb25b93b4d","target":"record","created_at":"2026-05-18T02:27:32Z","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":"cf3669640e81e0a37f7820279f6686f24156c80d6ebe17ba186189031a70d99b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-04T07:36:37Z","title_canon_sha256":"35ef46fb95ef8e81f1f72be0cdd107849eba85ed3567e23e732431d6d6efbb81"},"schema_version":"1.0","source":{"id":"1306.0685","kind":"arxiv","version":2}},"canonical_sha256":"c33e7d968ddaeff8eb24ea581b5e38cdc811d02496bd3facb0da04e34b42d03f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c33e7d968ddaeff8eb24ea581b5e38cdc811d02496bd3facb0da04e34b42d03f","first_computed_at":"2026-05-18T02:27:32.928353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:32.928353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csdip2AS2nrUJrLRMBYG45fVDbbYBmw/EyHXKqvU6tmmFC5lOEbY8NWpzNgppRZ0gvcF+za3FSR+dIXgcka0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:32.929154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31fe0873e14646462bcfff88465eefc94657fab68c45f116928761fb25b93b4d","sha256:e2d911eebf7b22ff9e14277942eac8b4f58513fab6c19cbebeae278933bd9794"],"state_sha256":"923f56306666c4ad58c0b05c4a498292ee34458ef8f6870c9e8a332c8e33a950"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KmspoGZaEdu+H2qzQ3R1SjbQ6eh2kUZquVQV7/8WM8EeJw4ZzYRtM3wlRCDN+fuEDBKi3KEdgSCyBPdrZI6TAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:50:36.824586Z","bundle_sha256":"71d02bdefe30f3e4719b246a1a8877baef68ed341451abdc8c634682c93a0871"}}