{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VQ7SE2R3VDHFX32U2PZDQ54U2X","short_pith_number":"pith:VQ7SE2R3","canonical_record":{"source":{"id":"1804.10239","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-26T18:34:59Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"20ad68f6482abbbe86621b402fe60bfabeeccaa1d4d22f34df1e9b7eb666760b","abstract_canon_sha256":"11032feca5dcd3e498d23752a39c85f0290c17eb91575739112f46299aa014b0"},"schema_version":"1.0"},"canonical_sha256":"ac3f226a3ba8ce5bef54d3f2387794d5fbe23d5e80e8362ff803fcfa4f8d646e","source":{"kind":"arxiv","id":"1804.10239","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10239","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10239v2","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10239","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"VQ7SE2R3VDHF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VQ7SE2R3VDHFX32U","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VQ7SE2R3","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VQ7SE2R3VDHFX32U2PZDQ54U2X","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10239","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-26T18:34:59Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"20ad68f6482abbbe86621b402fe60bfabeeccaa1d4d22f34df1e9b7eb666760b","abstract_canon_sha256":"11032feca5dcd3e498d23752a39c85f0290c17eb91575739112f46299aa014b0"},"schema_version":"1.0"},"canonical_sha256":"ac3f226a3ba8ce5bef54d3f2387794d5fbe23d5e80e8362ff803fcfa4f8d646e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:00.205178Z","signature_b64":"HRGShyhSGOoMxWUzyoYRyHJrwnwA2PZ9xRjJD7pEtcOWSiFKwpww4Hpbc2Mmnz4uwcfQylNwG5fTk5qLkY0hDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac3f226a3ba8ce5bef54d3f2387794d5fbe23d5e80e8362ff803fcfa4f8d646e","last_reissued_at":"2026-05-17T23:44:00.204596Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:00.204596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10239","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":"2026-05-17T23:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2G5V15VvsiXp5NkQqBiGXVuOyK22IurT468Z1f8NgGTiZe/xFC8jeCrJooI97QOyMG4qIebAQjSlwMkw8SE2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:44:22.838421Z"},"content_sha256":"8faa2abb714cf7467378770e067b3d73c8a288bad60edd5cc4cbc9f17f795333","schema_version":"1.0","event_id":"sha256:8faa2abb714cf7467378770e067b3d73c8a288bad60edd5cc4cbc9f17f795333"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VQ7SE2R3VDHFX32U2PZDQ54U2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-removability of the Sierpinski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.MG","authors_text":"Dimitrios Ntalampekos","submitted_at":"2018-04-26T18:34:59Z","abstract_excerpt":"We prove that the Sierpi\\'nski gasket is non-removable for quasiconformal maps, thus answering a question of Bishop. The proof involves a new technique of constructing an exceptional homeomorphism from $\\mathbb R^2$ into some non-planar surface $S$, and then embedding this surface quasisymmetrically back into the plane by using the celebrated Bonk-Kleiner Theorem arXiv:math/0107171. We also prove that all homeomorphic copies of the Sierpi\\'nski gasket are non-removable for continuous Sobolev functions of the class $W^{1,p}$ for $1\\leq p\\leq 2$, thus complementing and sharpening the results of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10239","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":"2026-05-17T23:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SqNYXNg65SP7DSV5Vf0HnD68qJDCXYB8NvlyT+Pz1tVyPgpf+bQennGzJRrYaHsy5fcsUKRyc9oI+qDOF3p6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:44:22.839171Z"},"content_sha256":"01cc4eddc5e3280c216e8915afb09111f88fd187f11324f01a206f7df26c36a2","schema_version":"1.0","event_id":"sha256:01cc4eddc5e3280c216e8915afb09111f88fd187f11324f01a206f7df26c36a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X/bundle.json","state_url":"https://pith.science/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X/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":"2026-05-22T05:44:22Z","links":{"resolver":"https://pith.science/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X","bundle":"https://pith.science/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X/bundle.json","state":"https://pith.science/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQ7SE2R3VDHFX32U2PZDQ54U2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VQ7SE2R3VDHFX32U2PZDQ54U2X","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":"11032feca5dcd3e498d23752a39c85f0290c17eb91575739112f46299aa014b0","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-26T18:34:59Z","title_canon_sha256":"20ad68f6482abbbe86621b402fe60bfabeeccaa1d4d22f34df1e9b7eb666760b"},"schema_version":"1.0","source":{"id":"1804.10239","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10239","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10239v2","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10239","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"VQ7SE2R3VDHF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VQ7SE2R3VDHFX32U","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VQ7SE2R3","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:01cc4eddc5e3280c216e8915afb09111f88fd187f11324f01a206f7df26c36a2","target":"graph","created_at":"2026-05-17T23:44:00Z","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 prove that the Sierpi\\'nski gasket is non-removable for quasiconformal maps, thus answering a question of Bishop. The proof involves a new technique of constructing an exceptional homeomorphism from $\\mathbb R^2$ into some non-planar surface $S$, and then embedding this surface quasisymmetrically back into the plane by using the celebrated Bonk-Kleiner Theorem arXiv:math/0107171. We also prove that all homeomorphic copies of the Sierpi\\'nski gasket are non-removable for continuous Sobolev functions of the class $W^{1,p}$ for $1\\leq p\\leq 2$, thus complementing and sharpening the results of ","authors_text":"Dimitrios Ntalampekos","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-26T18:34:59Z","title":"Non-removability of the Sierpinski Gasket"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10239","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":"sha256:8faa2abb714cf7467378770e067b3d73c8a288bad60edd5cc4cbc9f17f795333","target":"record","created_at":"2026-05-17T23:44:00Z","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":"11032feca5dcd3e498d23752a39c85f0290c17eb91575739112f46299aa014b0","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-26T18:34:59Z","title_canon_sha256":"20ad68f6482abbbe86621b402fe60bfabeeccaa1d4d22f34df1e9b7eb666760b"},"schema_version":"1.0","source":{"id":"1804.10239","kind":"arxiv","version":2}},"canonical_sha256":"ac3f226a3ba8ce5bef54d3f2387794d5fbe23d5e80e8362ff803fcfa4f8d646e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac3f226a3ba8ce5bef54d3f2387794d5fbe23d5e80e8362ff803fcfa4f8d646e","first_computed_at":"2026-05-17T23:44:00.204596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:00.204596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HRGShyhSGOoMxWUzyoYRyHJrwnwA2PZ9xRjJD7pEtcOWSiFKwpww4Hpbc2Mmnz4uwcfQylNwG5fTk5qLkY0hDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:00.205178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10239","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8faa2abb714cf7467378770e067b3d73c8a288bad60edd5cc4cbc9f17f795333","sha256:01cc4eddc5e3280c216e8915afb09111f88fd187f11324f01a206f7df26c36a2"],"state_sha256":"359fa4299b0735a8a164a2fda24f7e20721d58ced409566ac18d4c196a0c67a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckp0OW/9f+aQQ3ezkzj9m5TchLyitf6iKsmqCo86PAhELm6io0cWN8LJ7ELpyBmQ2HS+ddGPJarpUkN5WD3VAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T05:44:22.843247Z","bundle_sha256":"bc31fe9d70d0b96b71bdf638ce1a30468f4ad3fba80d22e94cb9ba02ec823636"}}