{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Z4ZEPNSICPWXWSF5PALBDXZ4FX","short_pith_number":"pith:Z4ZEPNSI","canonical_record":{"source":{"id":"1805.02572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-07T15:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"5a375dfff92602c6b9af951456b7546b4e399c0defa8bf520e9c2c3ad713a672","abstract_canon_sha256":"0edc76cb002c67284dc37451ed924b9b36e20a8e27033df300ef7e4528cf82de"},"schema_version":"1.0"},"canonical_sha256":"cf3247b64813ed7b48bd781611df3c2dfee882d8eba6365be41220842cff9f9c","source":{"kind":"arxiv","id":"1805.02572","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02572","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02572v1","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02572","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"Z4ZEPNSICPWX","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z4ZEPNSICPWXWSF5","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z4ZEPNSI","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Z4ZEPNSICPWXWSF5PALBDXZ4FX","target":"record","payload":{"canonical_record":{"source":{"id":"1805.02572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-07T15:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"5a375dfff92602c6b9af951456b7546b4e399c0defa8bf520e9c2c3ad713a672","abstract_canon_sha256":"0edc76cb002c67284dc37451ed924b9b36e20a8e27033df300ef7e4528cf82de"},"schema_version":"1.0"},"canonical_sha256":"cf3247b64813ed7b48bd781611df3c2dfee882d8eba6365be41220842cff9f9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:39.621287Z","signature_b64":"4m5IU31yzUUn/bwWWSa3mMnVFEQyamjbURg4A8TMXhuzX9fd1lXDQKmMypuAc2C/ZIl4MgfFMXVvCsEMjgC5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf3247b64813ed7b48bd781611df3c2dfee882d8eba6365be41220842cff9f9c","last_reissued_at":"2026-05-18T00:16:39.620839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:39.620839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.02572","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":"2026-05-18T00:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWzzvDdd8fFqB+anzGWqVOTlYeYIlHHlii/nvFR7t83MjIyDjdA8tUUby69uj91sZ+sDET9bIIWma0WRZvrSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:21:27.366607Z"},"content_sha256":"34094eaf98781589d7195c26b55c5471a0624fc517617963b28a112d7c6b4a62","schema_version":"1.0","event_id":"sha256:34094eaf98781589d7195c26b55c5471a0624fc517617963b28a112d7c6b4a62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Z4ZEPNSICPWXWSF5PALBDXZ4FX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational Complexity of Space-Bounded Real Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marcos Villagra, Masaki Nakanishi","submitted_at":"2018-05-07T15:28:31Z","abstract_excerpt":"In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic irrational numbers which seem to required linear space. We characterized the complexity of space-bounded real numbers by quantifying the space complexities of tally sets. The latter result introduces a technique to prove the space complexity of real numbers by studying its corresponding tally sets, which is arguably a more natural approach. Results of this work pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02572","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":"2026-05-18T00:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QN0gtMJ+GpOO0mLXnEUvT15af4p2yE/YdwMNf9cP8xOSin+m8a3IIcGF6sAECl5cMJXUTzJWqhfXQz2g4JjeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:21:27.367241Z"},"content_sha256":"b9cd5c69aa73f3f82cc6079ae12873a6b4e7d559ca21cf223e61cf24d51e6802","schema_version":"1.0","event_id":"sha256:b9cd5c69aa73f3f82cc6079ae12873a6b4e7d559ca21cf223e61cf24d51e6802"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX/bundle.json","state_url":"https://pith.science/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX/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":"2026-06-02T14:21:27Z","links":{"resolver":"https://pith.science/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX","bundle":"https://pith.science/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX/bundle.json","state":"https://pith.science/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4ZEPNSICPWXWSF5PALBDXZ4FX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z4ZEPNSICPWXWSF5PALBDXZ4FX","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":"0edc76cb002c67284dc37451ed924b9b36e20a8e27033df300ef7e4528cf82de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-07T15:28:31Z","title_canon_sha256":"5a375dfff92602c6b9af951456b7546b4e399c0defa8bf520e9c2c3ad713a672"},"schema_version":"1.0","source":{"id":"1805.02572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02572","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02572v1","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02572","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"Z4ZEPNSICPWX","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z4ZEPNSICPWXWSF5","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z4ZEPNSI","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:b9cd5c69aa73f3f82cc6079ae12873a6b4e7d559ca21cf223e61cf24d51e6802","target":"graph","created_at":"2026-05-18T00:16:39Z","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 work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic irrational numbers which seem to required linear space. We characterized the complexity of space-bounded real numbers by quantifying the space complexities of tally sets. The latter result introduces a technique to prove the space complexity of real numbers by studying its corresponding tally sets, which is arguably a more natural approach. Results of this work pre","authors_text":"Marcos Villagra, Masaki Nakanishi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-07T15:28:31Z","title":"Computational Complexity of Space-Bounded Real Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02572","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":"sha256:34094eaf98781589d7195c26b55c5471a0624fc517617963b28a112d7c6b4a62","target":"record","created_at":"2026-05-18T00:16:39Z","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":"0edc76cb002c67284dc37451ed924b9b36e20a8e27033df300ef7e4528cf82de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-05-07T15:28:31Z","title_canon_sha256":"5a375dfff92602c6b9af951456b7546b4e399c0defa8bf520e9c2c3ad713a672"},"schema_version":"1.0","source":{"id":"1805.02572","kind":"arxiv","version":1}},"canonical_sha256":"cf3247b64813ed7b48bd781611df3c2dfee882d8eba6365be41220842cff9f9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf3247b64813ed7b48bd781611df3c2dfee882d8eba6365be41220842cff9f9c","first_computed_at":"2026-05-18T00:16:39.620839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:39.620839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4m5IU31yzUUn/bwWWSa3mMnVFEQyamjbURg4A8TMXhuzX9fd1lXDQKmMypuAc2C/ZIl4MgfFMXVvCsEMjgC5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:39.621287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34094eaf98781589d7195c26b55c5471a0624fc517617963b28a112d7c6b4a62","sha256:b9cd5c69aa73f3f82cc6079ae12873a6b4e7d559ca21cf223e61cf24d51e6802"],"state_sha256":"895b8e4a7d271532a5b2b82364e9e668177b8ddce8c0ae2e6557d185f8a1856d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZSmr9NTtph7tbtxOjrmDeDEGBZQA9TXPKze3V9ET26MA5eHtgWNF/xOU3+2kc9UjEV8p8lfI+VIRaoqLr9JzBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:21:27.370593Z","bundle_sha256":"b5e1256c402fcc9dc2d4b5d2bfd481ba6fc9ff38e0e7e87ca330c30547911bdd"}}