{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z7VXIUPQ6BL2W3CFDQVZZYPDW5","short_pith_number":"pith:Z7VXIUPQ","canonical_record":{"source":{"id":"1504.06801","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-04-26T11:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"3cd9713cfbff9ca1df86c1e5e7852159a38508fe8662d9c8f04ffee9f5fc1813","abstract_canon_sha256":"1d0dc310b04bf475c5778d8568631e71dd2b2d19d24ede5deff59eb23e60e9d2"},"schema_version":"1.0"},"canonical_sha256":"cfeb7451f0f057ab6c451c2b9ce1e3b760a269a4167e8f31734308eeaa9eee4c","source":{"kind":"arxiv","id":"1504.06801","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06801","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06801v3","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06801","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z7VXIUPQ6BL2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z7VXIUPQ6BL2W3CF","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z7VXIUPQ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z7VXIUPQ6BL2W3CFDQVZZYPDW5","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06801","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-04-26T11:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"3cd9713cfbff9ca1df86c1e5e7852159a38508fe8662d9c8f04ffee9f5fc1813","abstract_canon_sha256":"1d0dc310b04bf475c5778d8568631e71dd2b2d19d24ede5deff59eb23e60e9d2"},"schema_version":"1.0"},"canonical_sha256":"cfeb7451f0f057ab6c451c2b9ce1e3b760a269a4167e8f31734308eeaa9eee4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:16.550362Z","signature_b64":"j1ghgv59yQIbwRcepQZFPqSPVTciml34Xj2/EM7VXinax8TT+2wl1Ut+RxuEYUWAaKcyYZZOP85/Qe8XkOheDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfeb7451f0f057ab6c451c2b9ce1e3b760a269a4167e8f31734308eeaa9eee4c","last_reissued_at":"2026-05-18T01:23:16.549827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:16.549827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06801","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oG+J3ky9qvqCcxBFDRjhh7IHiKH38MWLBJAC0ugMwrwKa8p/hFQH+8fgoDXXgiM4sdVOuRsFvBQ3eBc9FipMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:31:41.402278Z"},"content_sha256":"43825d5a3a28e5f8d73ea92ed37a4ca0c1c2efb9a6ec04933bdff45e31b85a87","schema_version":"1.0","event_id":"sha256:43825d5a3a28e5f8d73ea92ed37a4ca0c1c2efb9a6ec04933bdff45e31b85a87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z7VXIUPQ6BL2W3CFDQVZZYPDW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Five-Collinear Sierpinski Gasket is Not Self-Similar","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sheng Zhang","submitted_at":"2015-04-26T11:01:20Z","abstract_excerpt":"A geometrical conclusion: Sierpinski gasket, two Sierpinski gaskets in a line, three Sierpinski gaskets in a line, and four Sierpinski gaskets in a line are self-similar, but five Sierpinski gaskets in a line is not, which is proved in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06801","kind":"arxiv","version":3},"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":"2026-05-18T01:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttWdXopMlBumQr6wUu89zGPTujY/IcsUTkf81E1u52+569ikuOpXR8TvaOzlrpdKZMBVZSF5dwJHGDPIuA7KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:31:41.402916Z"},"content_sha256":"2a34a801017490e6199dca6a409c4ad3b0f6f36d6b59499c06aa9e99165e1cbc","schema_version":"1.0","event_id":"sha256:2a34a801017490e6199dca6a409c4ad3b0f6f36d6b59499c06aa9e99165e1cbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5/bundle.json","state_url":"https://pith.science/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5/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":"2026-06-04T11:31:41Z","links":{"resolver":"https://pith.science/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5","bundle":"https://pith.science/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5/bundle.json","state":"https://pith.science/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7VXIUPQ6BL2W3CFDQVZZYPDW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z7VXIUPQ6BL2W3CFDQVZZYPDW5","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":"1d0dc310b04bf475c5778d8568631e71dd2b2d19d24ede5deff59eb23e60e9d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-04-26T11:01:20Z","title_canon_sha256":"3cd9713cfbff9ca1df86c1e5e7852159a38508fe8662d9c8f04ffee9f5fc1813"},"schema_version":"1.0","source":{"id":"1504.06801","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06801","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06801v3","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06801","created_at":"2026-05-18T01:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z7VXIUPQ6BL2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z7VXIUPQ6BL2W3CF","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z7VXIUPQ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:2a34a801017490e6199dca6a409c4ad3b0f6f36d6b59499c06aa9e99165e1cbc","target":"graph","created_at":"2026-05-18T01:23:16Z","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":"A geometrical conclusion: Sierpinski gasket, two Sierpinski gaskets in a line, three Sierpinski gaskets in a line, and four Sierpinski gaskets in a line are self-similar, but five Sierpinski gaskets in a line is not, which is proved in this paper.","authors_text":"Sheng Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-04-26T11:01:20Z","title":"Five-Collinear Sierpinski Gasket is Not Self-Similar"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06801","kind":"arxiv","version":3},"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":"sha256:43825d5a3a28e5f8d73ea92ed37a4ca0c1c2efb9a6ec04933bdff45e31b85a87","target":"record","created_at":"2026-05-18T01:23:16Z","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":"1d0dc310b04bf475c5778d8568631e71dd2b2d19d24ede5deff59eb23e60e9d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2015-04-26T11:01:20Z","title_canon_sha256":"3cd9713cfbff9ca1df86c1e5e7852159a38508fe8662d9c8f04ffee9f5fc1813"},"schema_version":"1.0","source":{"id":"1504.06801","kind":"arxiv","version":3}},"canonical_sha256":"cfeb7451f0f057ab6c451c2b9ce1e3b760a269a4167e8f31734308eeaa9eee4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfeb7451f0f057ab6c451c2b9ce1e3b760a269a4167e8f31734308eeaa9eee4c","first_computed_at":"2026-05-18T01:23:16.549827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:16.549827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1ghgv59yQIbwRcepQZFPqSPVTciml34Xj2/EM7VXinax8TT+2wl1Ut+RxuEYUWAaKcyYZZOP85/Qe8XkOheDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:16.550362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06801","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43825d5a3a28e5f8d73ea92ed37a4ca0c1c2efb9a6ec04933bdff45e31b85a87","sha256:2a34a801017490e6199dca6a409c4ad3b0f6f36d6b59499c06aa9e99165e1cbc"],"state_sha256":"3a50f830533d1e0f8f96615eeacc9b9a150c6b0b2b2ee1a25c921b338b21c90c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbtxXOEE5XrTm0a9xwzYd3yJHduwYzMDjC9+bmaEw/NZFTwmzXtvvExYWcEyqhyGxTfOfFauDNG5y49/ekLSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T11:31:41.405872Z","bundle_sha256":"d1cfdc3456b239c24292ea2567c9ec6e37aa5da4623f8d78f2dfc8cdf75c38d2"}}