{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:43SNEFLMDQEWB3LHTLDGUPFEE7","short_pith_number":"pith:43SNEFLM","canonical_record":{"source":{"id":"1301.1378","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-01-08T01:57:09Z","cross_cats_sorted":["cs.GR"],"title_canon_sha256":"13c074c6a667539eec68217aa0b17911f1233812e05350551d88f686f8503df7","abstract_canon_sha256":"8cb4d5e54e9363ed901df95c2ded74d64abc77a2b601b934db417024fabf6cf1"},"schema_version":"1.0"},"canonical_sha256":"e6e4d2156c1c0960ed679ac66a3ca427e423dc5bfa26e946aef55114060a9ae6","source":{"kind":"arxiv","id":"1301.1378","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1378","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1378v2","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1378","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"43SNEFLMDQEW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"43SNEFLMDQEWB3LH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"43SNEFLM","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:43SNEFLMDQEWB3LHTLDGUPFEE7","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1378","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-01-08T01:57:09Z","cross_cats_sorted":["cs.GR"],"title_canon_sha256":"13c074c6a667539eec68217aa0b17911f1233812e05350551d88f686f8503df7","abstract_canon_sha256":"8cb4d5e54e9363ed901df95c2ded74d64abc77a2b601b934db417024fabf6cf1"},"schema_version":"1.0"},"canonical_sha256":"e6e4d2156c1c0960ed679ac66a3ca427e423dc5bfa26e946aef55114060a9ae6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:33.270021Z","signature_b64":"zkHUcqAKGXsbjvk9w9SbHHyQF+uvBtY8LXDA/jpQiXVREHI4FYoDfFIQIsHdw59jgo6E6ej2Q+ym1ryZi9FvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6e4d2156c1c0960ed679ac66a3ca427e423dc5bfa26e946aef55114060a9ae6","last_reissued_at":"2026-05-18T02:18:33.269515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:33.269515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1378","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":"2026-05-18T02:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOANU6racO5ZvWXIYiPP3QxePI6bHzGbQ+MBD9h0GB+JSlStz7cBQ93ZHlCJCUQFRLQAW3zkJOVXLp1qSK5hDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:06:55.186361Z"},"content_sha256":"7792e247132440608703464c1d34b29960e00876324aa49c3b824b3f720c0d6b","schema_version":"1.0","event_id":"sha256:7792e247132440608703464c1d34b29960e00876324aa49c3b824b3f720c0d6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:43SNEFLMDQEWB3LHTLDGUPFEE7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Apollonian Circumcircles of IFS Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GR"],"primary_cat":"cs.CG","authors_text":"J\\'ozsef Vass","submitted_at":"2013-01-08T01:57:09Z","abstract_excerpt":"Euclidean triangles and IFS fractals seem to be disparate geometrical concepts, unless we consider the Sierpi\\'{n}ski gasket, which is a self-similar collection of triangles. The \"circumcircle\" hints at a direct link, as it can be derived for three-map IFS fractals in general, defined in an Apollonian manner. Following this path, one may discover a broader relationship between polygons and IFS fractals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1378","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":"2026-05-18T02:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARZ5t8jer91iYqj8N4bbOD1UGGk7rCZ0ZX6Yfd5C+no+5lbbHuUtEDBHdKkgprpcgvFKrpkgXZbRnVOG9wwMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:06:55.186981Z"},"content_sha256":"9fb4897631be11f75cc299fc46acde685db29b798054908e19c09c3fde0dcf16","schema_version":"1.0","event_id":"sha256:9fb4897631be11f75cc299fc46acde685db29b798054908e19c09c3fde0dcf16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/43SNEFLMDQEWB3LHTLDGUPFEE7/bundle.json","state_url":"https://pith.science/pith/43SNEFLMDQEWB3LHTLDGUPFEE7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/43SNEFLMDQEWB3LHTLDGUPFEE7/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":"2026-06-08T06:06:55Z","links":{"resolver":"https://pith.science/pith/43SNEFLMDQEWB3LHTLDGUPFEE7","bundle":"https://pith.science/pith/43SNEFLMDQEWB3LHTLDGUPFEE7/bundle.json","state":"https://pith.science/pith/43SNEFLMDQEWB3LHTLDGUPFEE7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/43SNEFLMDQEWB3LHTLDGUPFEE7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:43SNEFLMDQEWB3LHTLDGUPFEE7","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":"8cb4d5e54e9363ed901df95c2ded74d64abc77a2b601b934db417024fabf6cf1","cross_cats_sorted":["cs.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-01-08T01:57:09Z","title_canon_sha256":"13c074c6a667539eec68217aa0b17911f1233812e05350551d88f686f8503df7"},"schema_version":"1.0","source":{"id":"1301.1378","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1378","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1378v2","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1378","created_at":"2026-05-18T02:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"43SNEFLMDQEW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"43SNEFLMDQEWB3LH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"43SNEFLM","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:9fb4897631be11f75cc299fc46acde685db29b798054908e19c09c3fde0dcf16","target":"graph","created_at":"2026-05-18T02:18:33Z","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":"Euclidean triangles and IFS fractals seem to be disparate geometrical concepts, unless we consider the Sierpi\\'{n}ski gasket, which is a self-similar collection of triangles. The \"circumcircle\" hints at a direct link, as it can be derived for three-map IFS fractals in general, defined in an Apollonian manner. Following this path, one may discover a broader relationship between polygons and IFS fractals.","authors_text":"J\\'ozsef Vass","cross_cats":["cs.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-01-08T01:57:09Z","title":"Apollonian Circumcircles of IFS Fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1378","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":"sha256:7792e247132440608703464c1d34b29960e00876324aa49c3b824b3f720c0d6b","target":"record","created_at":"2026-05-18T02:18:33Z","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":"8cb4d5e54e9363ed901df95c2ded74d64abc77a2b601b934db417024fabf6cf1","cross_cats_sorted":["cs.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-01-08T01:57:09Z","title_canon_sha256":"13c074c6a667539eec68217aa0b17911f1233812e05350551d88f686f8503df7"},"schema_version":"1.0","source":{"id":"1301.1378","kind":"arxiv","version":2}},"canonical_sha256":"e6e4d2156c1c0960ed679ac66a3ca427e423dc5bfa26e946aef55114060a9ae6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6e4d2156c1c0960ed679ac66a3ca427e423dc5bfa26e946aef55114060a9ae6","first_computed_at":"2026-05-18T02:18:33.269515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:33.269515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zkHUcqAKGXsbjvk9w9SbHHyQF+uvBtY8LXDA/jpQiXVREHI4FYoDfFIQIsHdw59jgo6E6ej2Q+ym1ryZi9FvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:33.270021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1378","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7792e247132440608703464c1d34b29960e00876324aa49c3b824b3f720c0d6b","sha256:9fb4897631be11f75cc299fc46acde685db29b798054908e19c09c3fde0dcf16"],"state_sha256":"78c90db6f581ad855170addb0588d0045a66842580b2d281d15ba2bf14d2b642"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHlU/0nZoZnSJoagx8FSftkQjfkEi0dBby0ZdnTPprj4r8nyfEejNFekynqfplfnNtcaxmi0NjrwleG7q7LWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:06:55.190879Z","bundle_sha256":"ca9487145841fd953da57473b9b6c326b4ffbed25a81097f18c153ecc2b4e09b"}}