{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FPEK56OIDGJ75ALG53SE25NZIK","short_pith_number":"pith:FPEK56OI","canonical_record":{"source":{"id":"1412.1975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-12-05T12:08:48Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0e15fa8bc56b237be5276021e9c86c881e7e9088279bd9cb104cb46f05ea4420","abstract_canon_sha256":"b90a7623a303c89ae38a1775555954a048ac07103e42b2278489242b52f26689"},"schema_version":"1.0"},"canonical_sha256":"2bc8aef9c81993fe8166eee44d75b942b037711206cad9d576f4c79ee6055c96","source":{"kind":"arxiv","id":"1412.1975","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1975","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1975v1","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1975","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"FPEK56OIDGJ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FPEK56OIDGJ75ALG","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FPEK56OI","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FPEK56OIDGJ75ALG53SE25NZIK","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-12-05T12:08:48Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0e15fa8bc56b237be5276021e9c86c881e7e9088279bd9cb104cb46f05ea4420","abstract_canon_sha256":"b90a7623a303c89ae38a1775555954a048ac07103e42b2278489242b52f26689"},"schema_version":"1.0"},"canonical_sha256":"2bc8aef9c81993fe8166eee44d75b942b037711206cad9d576f4c79ee6055c96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:05.675529Z","signature_b64":"XlVBuXzpnwVvFxhwThFZrLAubbjsM43/B78LesbzgxHzfvKlZetRNUM+VIlQGvFdm7PTLvnwQ8K3tv11nljnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bc8aef9c81993fe8166eee44d75b942b037711206cad9d576f4c79ee6055c96","last_reissued_at":"2026-05-18T02:32:05.675140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:05.675140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1975","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":"2026-05-18T02:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbRSjioU0JaJbwFrsJ2sSkmeBXpbb0T19RHeSE/i9tG/ABUnasmPalAy+tGWP+rvuCdh6f+0mj4OGz9bzPHFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:57:00.346085Z"},"content_sha256":"38cb990ba9a23b1394e0d886e6f2af33aaa046e44f7232b10df2564e3dfeb191","schema_version":"1.0","event_id":"sha256:38cb990ba9a23b1394e0d886e6f2af33aaa046e44f7232b10df2564e3dfeb191"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FPEK56OIDGJ75ALG53SE25NZIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On cut sets of attractors of iterated function systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GN","authors_text":"Beno\\^it Loridant, J\\\"org Thuswaldner, Jun Luo, Tarek Sellami","submitted_at":"2014-12-05T12:08:48Z","abstract_excerpt":"In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a criterion for the existence of cut points of IFS attractors. If the IFS attractors are self-affine tiles, our results become algorithmically checkable and can be used to exhibit cut points with the help of Hata graphs. This enables us to construct cut points of some self-affine tiles studied in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1975","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":"2026-05-18T02:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxqkf2fcvQTPfrRFpGMVR/lHwdUkv9fOnBNXwYRGpcWVAbjUUEMkkXgs4RJqpoJ1o/dkC/hTxvurGy1hF8buAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:57:00.346868Z"},"content_sha256":"c4e66feed3ae109478f2d110d4d8d0aca5511bf0fb890e3991141ba4a764fb57","schema_version":"1.0","event_id":"sha256:c4e66feed3ae109478f2d110d4d8d0aca5511bf0fb890e3991141ba4a764fb57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPEK56OIDGJ75ALG53SE25NZIK/bundle.json","state_url":"https://pith.science/pith/FPEK56OIDGJ75ALG53SE25NZIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPEK56OIDGJ75ALG53SE25NZIK/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":"2026-06-11T22:57:00Z","links":{"resolver":"https://pith.science/pith/FPEK56OIDGJ75ALG53SE25NZIK","bundle":"https://pith.science/pith/FPEK56OIDGJ75ALG53SE25NZIK/bundle.json","state":"https://pith.science/pith/FPEK56OIDGJ75ALG53SE25NZIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPEK56OIDGJ75ALG53SE25NZIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FPEK56OIDGJ75ALG53SE25NZIK","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":"b90a7623a303c89ae38a1775555954a048ac07103e42b2278489242b52f26689","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-12-05T12:08:48Z","title_canon_sha256":"0e15fa8bc56b237be5276021e9c86c881e7e9088279bd9cb104cb46f05ea4420"},"schema_version":"1.0","source":{"id":"1412.1975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1975","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1975v1","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1975","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"FPEK56OIDGJ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FPEK56OIDGJ75ALG","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FPEK56OI","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:c4e66feed3ae109478f2d110d4d8d0aca5511bf0fb890e3991141ba4a764fb57","target":"graph","created_at":"2026-05-18T02:32:05Z","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":"In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a criterion for the existence of cut points of IFS attractors. If the IFS attractors are self-affine tiles, our results become algorithmically checkable and can be used to exhibit cut points with the help of Hata graphs. This enables us to construct cut points of some self-affine tiles studied in the literature.","authors_text":"Beno\\^it Loridant, J\\\"org Thuswaldner, Jun Luo, Tarek Sellami","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-12-05T12:08:48Z","title":"On cut sets of attractors of iterated function systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1975","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":"sha256:38cb990ba9a23b1394e0d886e6f2af33aaa046e44f7232b10df2564e3dfeb191","target":"record","created_at":"2026-05-18T02:32:05Z","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":"b90a7623a303c89ae38a1775555954a048ac07103e42b2278489242b52f26689","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-12-05T12:08:48Z","title_canon_sha256":"0e15fa8bc56b237be5276021e9c86c881e7e9088279bd9cb104cb46f05ea4420"},"schema_version":"1.0","source":{"id":"1412.1975","kind":"arxiv","version":1}},"canonical_sha256":"2bc8aef9c81993fe8166eee44d75b942b037711206cad9d576f4c79ee6055c96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bc8aef9c81993fe8166eee44d75b942b037711206cad9d576f4c79ee6055c96","first_computed_at":"2026-05-18T02:32:05.675140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:05.675140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XlVBuXzpnwVvFxhwThFZrLAubbjsM43/B78LesbzgxHzfvKlZetRNUM+VIlQGvFdm7PTLvnwQ8K3tv11nljnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:05.675529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38cb990ba9a23b1394e0d886e6f2af33aaa046e44f7232b10df2564e3dfeb191","sha256:c4e66feed3ae109478f2d110d4d8d0aca5511bf0fb890e3991141ba4a764fb57"],"state_sha256":"e50b83af715138b2d9ea6fb4eb9bc27591c7b3bf456f7b01c8e686680c9e412c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+PrkD7tleomZiuPV3rAmGVbtZi/NrrmZDEDnHNFVWxycyziyrsz7H6pM0d+C2h+S8rA48m3Al6H3xly/HKsODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:57:00.350862Z","bundle_sha256":"75f71f4f386fa45c5835c36d1ca480d189e79221bbd66a96242bfb6801807cf1"}}