{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:E5ENFT66MV5PDFQ4KYMXHQELOR","short_pith_number":"pith:E5ENFT66","canonical_record":{"source":{"id":"1302.4599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-02-19T13:07:41Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"573495a66aa103ae128b871d6e6413281769f5236bc22ab0cf0e6fdc60f64246","abstract_canon_sha256":"2fb93ee0ae330831cd115ab60c96cfd06ed9600a66653625e5f086c185caaaae"},"schema_version":"1.0"},"canonical_sha256":"2748d2cfde657af1961c561973c08b744982874db67e1a727580391cb8e0fe36","source":{"kind":"arxiv","id":"1302.4599","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4599","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4599v1","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4599","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"E5ENFT66MV5P","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E5ENFT66MV5PDFQ4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E5ENFT66","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:E5ENFT66MV5PDFQ4KYMXHQELOR","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-02-19T13:07:41Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"573495a66aa103ae128b871d6e6413281769f5236bc22ab0cf0e6fdc60f64246","abstract_canon_sha256":"2fb93ee0ae330831cd115ab60c96cfd06ed9600a66653625e5f086c185caaaae"},"schema_version":"1.0"},"canonical_sha256":"2748d2cfde657af1961c561973c08b744982874db67e1a727580391cb8e0fe36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:12.791033Z","signature_b64":"vIrZCcxHE2x3cnWVojnyhnFVdZrbJ4Mp36G4HTn1IceMBygw9GgIRSmEocoKWI0ahaLsBcagR+111ekj91apCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2748d2cfde657af1961c561973c08b744982874db67e1a727580391cb8e0fe36","last_reissued_at":"2026-05-18T03:33:12.790150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:12.790150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4599","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":"2026-05-18T03:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxWHAwyN25Ih+zPcTqC5u7W3Kh76dEg173c92RCipuIfMIHNezcXwQm8pNEFWxgiUksEDrNhuwaNpdODF8TsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:51:42.161210Z"},"content_sha256":"1ab62dc504b8c0f02fe0d383b347a23686663fc5724ae221782491311bc05f3c","schema_version":"1.0","event_id":"sha256:1ab62dc504b8c0f02fe0d383b347a23686663fc5724ae221782491311bc05f3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:E5ENFT66MV5PDFQ4KYMXHQELOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform boundedness of pretangent spaces and local strong one-side porosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey, Viktoriia Bilet","submitted_at":"2013-02-19T13:07:41Z","abstract_excerpt":"Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \\in X, whose degree of convergence is comparable with a given scaling sequence (r_n), r_n\\downarrow 0. We say that (r_n) is normal if there is (x_n) such that |d(x_n,p)-r_n|=o(r_n) for n\\to\\infty. Let Omega_{p}^{X}(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from Omega_{p}^{X}(n) are uniformly bounded if and only if {d(x,p:x\\in X}is a so-called completely strongly porous set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4599","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":"2026-05-18T03:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DRXlu488nFzhmuZOqAv2ZhaTqP0JFSc+bY4XbrFqYN2nlcfulEPR0kamvAKZzqG2lTLG3I2Pyo5fJUSGsFLMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:51:42.161612Z"},"content_sha256":"52304731bff9e451487085b44df65dab475a66a73c7c4cb5b86efc63a35d6360","schema_version":"1.0","event_id":"sha256:52304731bff9e451487085b44df65dab475a66a73c7c4cb5b86efc63a35d6360"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/bundle.json","state_url":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/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":"2026-06-05T18:51:42Z","links":{"resolver":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR","bundle":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/bundle.json","state":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E5ENFT66MV5PDFQ4KYMXHQELOR","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":"2fb93ee0ae330831cd115ab60c96cfd06ed9600a66653625e5f086c185caaaae","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-02-19T13:07:41Z","title_canon_sha256":"573495a66aa103ae128b871d6e6413281769f5236bc22ab0cf0e6fdc60f64246"},"schema_version":"1.0","source":{"id":"1302.4599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4599","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4599v1","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4599","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"E5ENFT66MV5P","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E5ENFT66MV5PDFQ4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E5ENFT66","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:52304731bff9e451487085b44df65dab475a66a73c7c4cb5b86efc63a35d6360","target":"graph","created_at":"2026-05-18T03:33:12Z","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":"Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \\in X, whose degree of convergence is comparable with a given scaling sequence (r_n), r_n\\downarrow 0. We say that (r_n) is normal if there is (x_n) such that |d(x_n,p)-r_n|=o(r_n) for n\\to\\infty. Let Omega_{p}^{X}(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from Omega_{p}^{X}(n) are uniformly bounded if and only if {d(x,p:x\\in X}is a so-called completely strongly porous set.","authors_text":"Oleksiy Dovgoshey, Viktoriia Bilet","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-02-19T13:07:41Z","title":"Uniform boundedness of pretangent spaces and local strong one-side porosity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4599","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":"sha256:1ab62dc504b8c0f02fe0d383b347a23686663fc5724ae221782491311bc05f3c","target":"record","created_at":"2026-05-18T03:33:12Z","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":"2fb93ee0ae330831cd115ab60c96cfd06ed9600a66653625e5f086c185caaaae","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-02-19T13:07:41Z","title_canon_sha256":"573495a66aa103ae128b871d6e6413281769f5236bc22ab0cf0e6fdc60f64246"},"schema_version":"1.0","source":{"id":"1302.4599","kind":"arxiv","version":1}},"canonical_sha256":"2748d2cfde657af1961c561973c08b744982874db67e1a727580391cb8e0fe36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2748d2cfde657af1961c561973c08b744982874db67e1a727580391cb8e0fe36","first_computed_at":"2026-05-18T03:33:12.790150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:12.790150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vIrZCcxHE2x3cnWVojnyhnFVdZrbJ4Mp36G4HTn1IceMBygw9GgIRSmEocoKWI0ahaLsBcagR+111ekj91apCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:12.791033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ab62dc504b8c0f02fe0d383b347a23686663fc5724ae221782491311bc05f3c","sha256:52304731bff9e451487085b44df65dab475a66a73c7c4cb5b86efc63a35d6360"],"state_sha256":"d89a85fe90e9ae47d78dd48563acb00ac7af910a3f11b68b15fbda3d7ec1a45d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tv/XHs8nhXzp4bhAxFmG872TO0Y0Aj27QgMb6snuT3IM18IjFSOmq30mj2xKBvPIW6q9ZWTD2b9p2SOaMaVBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:51:42.163618Z","bundle_sha256":"efef25bbffdc54f57c72786e45e196565b1e81412a389d42a5e9646f5fb4b59e"}}