{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FU45N4UARYRS6CJTJ76QLL2QH3","short_pith_number":"pith:FU45N4UA","canonical_record":{"source":{"id":"1803.03753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-10T04:12:32Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2ce2a71d9edcd4e3975ec1d68915db9b42322a425fad17a650f3a3131c118c92","abstract_canon_sha256":"c2d740c668025537fd46d65577fb88ad959b6dcbd7bb0bb38f0c83600eaf3c46"},"schema_version":"1.0"},"canonical_sha256":"2d39d6f2808e232f09334ffd05af503eff6211af581cbb57ffb31938a7ccffdc","source":{"kind":"arxiv","id":"1803.03753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03753","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03753v1","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03753","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"FU45N4UARYRS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FU45N4UARYRS6CJT","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FU45N4UA","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FU45N4UARYRS6CJTJ76QLL2QH3","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-10T04:12:32Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2ce2a71d9edcd4e3975ec1d68915db9b42322a425fad17a650f3a3131c118c92","abstract_canon_sha256":"c2d740c668025537fd46d65577fb88ad959b6dcbd7bb0bb38f0c83600eaf3c46"},"schema_version":"1.0"},"canonical_sha256":"2d39d6f2808e232f09334ffd05af503eff6211af581cbb57ffb31938a7ccffdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:33.884934Z","signature_b64":"s1AVcLe6xzagTy7bIn0KGBwcYfwii8OeZFTsaW/YdxbZ62sB98KPer4xs6NBxSUj+yjJ+jznIxqfQdBZ8WzdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d39d6f2808e232f09334ffd05af503eff6211af581cbb57ffb31938a7ccffdc","last_reissued_at":"2026-05-18T00:21:33.884475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:33.884475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03753","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":"2026-05-18T00:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvQVL2ak1zDy7ARYFl7LWH9dWDxo/SpzBTerAnK8Cfwm5wlIau0rMzSV8Ga//xHfdMH2WULnSQ2Xus6St86UDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:23:11.500394Z"},"content_sha256":"06f551cb8e364915ea270a1b400ebba5172f69501602f1f89f508a6f885f3f44","schema_version":"1.0","event_id":"sha256:06f551cb8e364915ea270a1b400ebba5172f69501602f1f89f508a6f885f3f44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FU45N4UARYRS6CJTJ76QLL2QH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a metric generalization of the $tt$-degrees and effective dimension theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Takayuki Kihara","submitted_at":"2018-03-10T04:12:32Z","abstract_excerpt":"In this article, we study an analogue of $tt$-reducibility for points in computable metric spaces. We characterize the notion of the metric $tt$-degree in the context of first-level Borel isomorphism. Then, we study this concept from the perspectives of effective topological dimension theory and of effective fractal dimension theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03753","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":"2026-05-18T00:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+6D/nWSDpqCLU74Y5f+SkL73eEN0NtuxV/8Bm5qZBgc6+LVJG8yu4b5tZ63jLZXzST+hkRk+ZH10Uan1uJhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:23:11.501068Z"},"content_sha256":"669c8f77d23c35cbebc7204cdbd3c42c08094dd484ccf2a2325276368888abfa","schema_version":"1.0","event_id":"sha256:669c8f77d23c35cbebc7204cdbd3c42c08094dd484ccf2a2325276368888abfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FU45N4UARYRS6CJTJ76QLL2QH3/bundle.json","state_url":"https://pith.science/pith/FU45N4UARYRS6CJTJ76QLL2QH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FU45N4UARYRS6CJTJ76QLL2QH3/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":"2026-05-31T10:23:11Z","links":{"resolver":"https://pith.science/pith/FU45N4UARYRS6CJTJ76QLL2QH3","bundle":"https://pith.science/pith/FU45N4UARYRS6CJTJ76QLL2QH3/bundle.json","state":"https://pith.science/pith/FU45N4UARYRS6CJTJ76QLL2QH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FU45N4UARYRS6CJTJ76QLL2QH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FU45N4UARYRS6CJTJ76QLL2QH3","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":"c2d740c668025537fd46d65577fb88ad959b6dcbd7bb0bb38f0c83600eaf3c46","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-10T04:12:32Z","title_canon_sha256":"2ce2a71d9edcd4e3975ec1d68915db9b42322a425fad17a650f3a3131c118c92"},"schema_version":"1.0","source":{"id":"1803.03753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03753","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03753v1","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03753","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"FU45N4UARYRS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FU45N4UARYRS6CJT","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FU45N4UA","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:669c8f77d23c35cbebc7204cdbd3c42c08094dd484ccf2a2325276368888abfa","target":"graph","created_at":"2026-05-18T00:21:33Z","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":"In this article, we study an analogue of $tt$-reducibility for points in computable metric spaces. We characterize the notion of the metric $tt$-degree in the context of first-level Borel isomorphism. Then, we study this concept from the perspectives of effective topological dimension theory and of effective fractal dimension theory.","authors_text":"Takayuki Kihara","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-10T04:12:32Z","title":"On a metric generalization of the $tt$-degrees and effective dimension theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03753","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":"sha256:06f551cb8e364915ea270a1b400ebba5172f69501602f1f89f508a6f885f3f44","target":"record","created_at":"2026-05-18T00:21:33Z","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":"c2d740c668025537fd46d65577fb88ad959b6dcbd7bb0bb38f0c83600eaf3c46","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-10T04:12:32Z","title_canon_sha256":"2ce2a71d9edcd4e3975ec1d68915db9b42322a425fad17a650f3a3131c118c92"},"schema_version":"1.0","source":{"id":"1803.03753","kind":"arxiv","version":1}},"canonical_sha256":"2d39d6f2808e232f09334ffd05af503eff6211af581cbb57ffb31938a7ccffdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d39d6f2808e232f09334ffd05af503eff6211af581cbb57ffb31938a7ccffdc","first_computed_at":"2026-05-18T00:21:33.884475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:33.884475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s1AVcLe6xzagTy7bIn0KGBwcYfwii8OeZFTsaW/YdxbZ62sB98KPer4xs6NBxSUj+yjJ+jznIxqfQdBZ8WzdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:33.884934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06f551cb8e364915ea270a1b400ebba5172f69501602f1f89f508a6f885f3f44","sha256:669c8f77d23c35cbebc7204cdbd3c42c08094dd484ccf2a2325276368888abfa"],"state_sha256":"f2e8863d96a1d68edf39bc2bc041ca983d9da7a820fb25a51788108016f17c13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwVZaiDcCgxU5c+4IN+91TMbSlyvy25dX86h6zByHMsRrLHfF8vNR7Lyj9iJrjFrn3z+pzljGwvzgUIGVpObBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:23:11.504635Z","bundle_sha256":"6bd6cd576bbc24de88c716a0f61564956e7948c6c84d1afaefa7eac217ff2d91"}}