{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2OPTWGDC2PZFCXMHH7KHOTF33G","short_pith_number":"pith:2OPTWGDC","canonical_record":{"source":{"id":"1711.11173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T01:15:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"efdb5951bf38882b934a8a3d4c7e4a44011b895a3cccc9768aec8d35a9341a66","abstract_canon_sha256":"a47b26ff281a2e14a28bd2cabeb5d80cd2dc92a42a0506c09a6bbb47820656b4"},"schema_version":"1.0"},"canonical_sha256":"d39f3b1862d3f2515d873fd4774cbbd9a06d01223c130dced1dd033c6e3f5db3","source":{"kind":"arxiv","id":"1711.11173","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11173","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11173v2","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11173","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"2OPTWGDC2PZF","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2OPTWGDC2PZFCXMH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2OPTWGDC","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2OPTWGDC2PZFCXMHH7KHOTF33G","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T01:15:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"efdb5951bf38882b934a8a3d4c7e4a44011b895a3cccc9768aec8d35a9341a66","abstract_canon_sha256":"a47b26ff281a2e14a28bd2cabeb5d80cd2dc92a42a0506c09a6bbb47820656b4"},"schema_version":"1.0"},"canonical_sha256":"d39f3b1862d3f2515d873fd4774cbbd9a06d01223c130dced1dd033c6e3f5db3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:36.216217Z","signature_b64":"BjBNM0sDDl/vTRUF7MSeYCH9Jv+ETEalzObb4aArHIyr7giy7ro8FTYKmYtkPDS97YmZzfhdOsEYnVlEsPZGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d39f3b1862d3f2515d873fd4774cbbd9a06d01223c130dced1dd033c6e3f5db3","last_reissued_at":"2026-05-18T00:08:36.215385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:36.215385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11173","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":"2026-05-18T00:08:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"js5ByPZ3SeRn3DbppnP4OYf71Fn/VjUVwPoeX+rAmasHkUAwLIkmCVbDlhY0nVxuBM+gh7ccGE3tqDnEKb4DBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:19:54.796698Z"},"content_sha256":"87f9897de94e8757c69efb1894086dd5635fbc67fe92e3197e7566175b3ffc01","schema_version":"1.0","event_id":"sha256:87f9897de94e8757c69efb1894086dd5635fbc67fe92e3197e7566175b3ffc01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2OPTWGDC2PZFCXMHH7KHOTF33G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On periodicity and hypercyclic weighted translation operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Kui-Yo Chen","submitted_at":"2017-11-30T01:15:25Z","abstract_excerpt":"We use the generization of Weyl's equidistribution theorem to characterize several necessary conditions of hypercyclic weighted translation operators with periodic element."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11173","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":"2026-05-18T00:08:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SHkcB1TZW6yib72cAQbT+dQjkpxh/3aS8NUltfAPtu7SPY8u2Tf/lFrf0hyPFDUG3Z6kkx6NTuvxR792qUkvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:19:54.797039Z"},"content_sha256":"33859ad5b58c23966ef623a6dd091f0460e62891e9162394bc748e72df55224d","schema_version":"1.0","event_id":"sha256:33859ad5b58c23966ef623a6dd091f0460e62891e9162394bc748e72df55224d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2OPTWGDC2PZFCXMHH7KHOTF33G/bundle.json","state_url":"https://pith.science/pith/2OPTWGDC2PZFCXMHH7KHOTF33G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2OPTWGDC2PZFCXMHH7KHOTF33G/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":"2026-06-01T08:19:54Z","links":{"resolver":"https://pith.science/pith/2OPTWGDC2PZFCXMHH7KHOTF33G","bundle":"https://pith.science/pith/2OPTWGDC2PZFCXMHH7KHOTF33G/bundle.json","state":"https://pith.science/pith/2OPTWGDC2PZFCXMHH7KHOTF33G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2OPTWGDC2PZFCXMHH7KHOTF33G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2OPTWGDC2PZFCXMHH7KHOTF33G","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":"a47b26ff281a2e14a28bd2cabeb5d80cd2dc92a42a0506c09a6bbb47820656b4","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T01:15:25Z","title_canon_sha256":"efdb5951bf38882b934a8a3d4c7e4a44011b895a3cccc9768aec8d35a9341a66"},"schema_version":"1.0","source":{"id":"1711.11173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11173","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11173v2","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11173","created_at":"2026-05-18T00:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"2OPTWGDC2PZF","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2OPTWGDC2PZFCXMH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2OPTWGDC","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:33859ad5b58c23966ef623a6dd091f0460e62891e9162394bc748e72df55224d","target":"graph","created_at":"2026-05-18T00:08:36Z","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 use the generization of Weyl's equidistribution theorem to characterize several necessary conditions of hypercyclic weighted translation operators with periodic element.","authors_text":"Kui-Yo Chen","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T01:15:25Z","title":"On periodicity and hypercyclic weighted translation operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11173","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":"sha256:87f9897de94e8757c69efb1894086dd5635fbc67fe92e3197e7566175b3ffc01","target":"record","created_at":"2026-05-18T00:08:36Z","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":"a47b26ff281a2e14a28bd2cabeb5d80cd2dc92a42a0506c09a6bbb47820656b4","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T01:15:25Z","title_canon_sha256":"efdb5951bf38882b934a8a3d4c7e4a44011b895a3cccc9768aec8d35a9341a66"},"schema_version":"1.0","source":{"id":"1711.11173","kind":"arxiv","version":2}},"canonical_sha256":"d39f3b1862d3f2515d873fd4774cbbd9a06d01223c130dced1dd033c6e3f5db3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d39f3b1862d3f2515d873fd4774cbbd9a06d01223c130dced1dd033c6e3f5db3","first_computed_at":"2026-05-18T00:08:36.215385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:36.215385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BjBNM0sDDl/vTRUF7MSeYCH9Jv+ETEalzObb4aArHIyr7giy7ro8FTYKmYtkPDS97YmZzfhdOsEYnVlEsPZGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:36.216217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87f9897de94e8757c69efb1894086dd5635fbc67fe92e3197e7566175b3ffc01","sha256:33859ad5b58c23966ef623a6dd091f0460e62891e9162394bc748e72df55224d"],"state_sha256":"5f26944da0232bec15c7497a752a8f3cf00daa884758bb81410fb95aac8a63fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciHOz6TJBCZcwW7r2ncxJyKJz4CI3YrQqkdTd2YkH1A3k/Y/4YM+gzaoZXbUtUPvVrjPwvRF2gFsmjmAFCdiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:19:54.799150Z","bundle_sha256":"aebcdb2cd8b22723f682d398f3b4b735925271840a84adaf3f6233e775a5cc07"}}