{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:P35TISO3QJZ3KIXJCSYL6NJANI","short_pith_number":"pith:P35TISO3","canonical_record":{"source":{"id":"math/0311461","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-11-26T04:43:57Z","cross_cats_sorted":[],"title_canon_sha256":"19a37e466b02c32ef548ef231ce70374ac5514fbfed95c8c3f2f0c3911c9e840","abstract_canon_sha256":"3928d4bc8b9f7790d6fcfdd2122e41e67d9fc6d24516f112a4330ad580e8a1de"},"schema_version":"1.0"},"canonical_sha256":"7efb3449db8273b522e914b0bf35206a255db8b48782526a60aa79c7f7a072d1","source":{"kind":"arxiv","id":"math/0311461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0311461","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0311461v1","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311461","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"P35TISO3QJZ3","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"P35TISO3QJZ3KIXJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"P35TISO3","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:P35TISO3QJZ3KIXJCSYL6NJANI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0311461","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-11-26T04:43:57Z","cross_cats_sorted":[],"title_canon_sha256":"19a37e466b02c32ef548ef231ce70374ac5514fbfed95c8c3f2f0c3911c9e840","abstract_canon_sha256":"3928d4bc8b9f7790d6fcfdd2122e41e67d9fc6d24516f112a4330ad580e8a1de"},"schema_version":"1.0"},"canonical_sha256":"7efb3449db8273b522e914b0bf35206a255db8b48782526a60aa79c7f7a072d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.713612Z","signature_b64":"qjeOqmfExfBSYqVSlHptKSdsQyXrWwYr3TccS0ZTBjBRsB/a2iw+oLRVEWfG4elfzf6Iw5S9QVT+KfwiwL1rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7efb3449db8273b522e914b0bf35206a255db8b48782526a60aa79c7f7a072d1","last_reissued_at":"2026-05-18T01:05:26.713116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.713116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0311461","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":"2026-05-18T01:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCioFxGT4UStHqpL71AIawleUyjq2VIiX3C7lgPey4dnbnXyAts2Nw37Fzp6aX5GThCuvTV/UHp2/UcgJQs1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:27:05.437342Z"},"content_sha256":"bd300ce0b6d52958e84fae8549a33ff62030956931d287c9385c1e2f3a1761cd","schema_version":"1.0","event_id":"sha256:bd300ce0b6d52958e84fae8549a33ff62030956931d287c9385c1e2f3a1761cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:P35TISO3QJZ3KIXJCSYL6NJANI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological stable rank of inclusions of unital C*-algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hiroyuki Osaka, Tamotsu Teruya","submitted_at":"2003-11-26T04:43:57Z","abstract_excerpt":"Let $1 \\in A \\subset B$ be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of $B$ ($= \\tsr(B)$) when $A$ has topological stable rank one. We show that $\\tsr(B) \\leq 2$ when $A$ is a tsr boundedly divisible algebra, in particular, $A$ is a C*-minimal tensor product $UHF \\otimes\n D$ with $\\tsr(D) = 1$. When $G$ is a finite group and $\\alpha$ is an action of $G$ on UHF, we know that a crossed product algebra $UHF \\rtimes_\\alpha G$ has topological stable rank less than or equal to two.\n  These results are affirmative datum to a generaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311461","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":"2026-05-18T01:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fz8szsvc2Aw5yerBySeOm9IMjRjgt+e7mRor9L5rPdUsfmY5+wOHnQbGAQwo5QZUGgfIFrKwJLnmDZyLfKdIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:27:05.437696Z"},"content_sha256":"91993a96563baeb111f1aebf48a917f41f097a1977d0bd8ab498f32c3e73830c","schema_version":"1.0","event_id":"sha256:91993a96563baeb111f1aebf48a917f41f097a1977d0bd8ab498f32c3e73830c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P35TISO3QJZ3KIXJCSYL6NJANI/bundle.json","state_url":"https://pith.science/pith/P35TISO3QJZ3KIXJCSYL6NJANI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P35TISO3QJZ3KIXJCSYL6NJANI/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":"2026-06-02T21:27:05Z","links":{"resolver":"https://pith.science/pith/P35TISO3QJZ3KIXJCSYL6NJANI","bundle":"https://pith.science/pith/P35TISO3QJZ3KIXJCSYL6NJANI/bundle.json","state":"https://pith.science/pith/P35TISO3QJZ3KIXJCSYL6NJANI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P35TISO3QJZ3KIXJCSYL6NJANI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:P35TISO3QJZ3KIXJCSYL6NJANI","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":"3928d4bc8b9f7790d6fcfdd2122e41e67d9fc6d24516f112a4330ad580e8a1de","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2003-11-26T04:43:57Z","title_canon_sha256":"19a37e466b02c32ef548ef231ce70374ac5514fbfed95c8c3f2f0c3911c9e840"},"schema_version":"1.0","source":{"id":"math/0311461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0311461","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0311461v1","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311461","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"P35TISO3QJZ3","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"P35TISO3QJZ3KIXJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"P35TISO3","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:91993a96563baeb111f1aebf48a917f41f097a1977d0bd8ab498f32c3e73830c","target":"graph","created_at":"2026-05-18T01:05:26Z","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 $1 \\in A \\subset B$ be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of $B$ ($= \\tsr(B)$) when $A$ has topological stable rank one. We show that $\\tsr(B) \\leq 2$ when $A$ is a tsr boundedly divisible algebra, in particular, $A$ is a C*-minimal tensor product $UHF \\otimes\n D$ with $\\tsr(D) = 1$. When $G$ is a finite group and $\\alpha$ is an action of $G$ on UHF, we know that a crossed product algebra $UHF \\rtimes_\\alpha G$ has topological stable rank less than or equal to two.\n  These results are affirmative datum to a generaliza","authors_text":"Hiroyuki Osaka, Tamotsu Teruya","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2003-11-26T04:43:57Z","title":"Topological stable rank of inclusions of unital C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311461","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:bd300ce0b6d52958e84fae8549a33ff62030956931d287c9385c1e2f3a1761cd","target":"record","created_at":"2026-05-18T01:05:26Z","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":"3928d4bc8b9f7790d6fcfdd2122e41e67d9fc6d24516f112a4330ad580e8a1de","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2003-11-26T04:43:57Z","title_canon_sha256":"19a37e466b02c32ef548ef231ce70374ac5514fbfed95c8c3f2f0c3911c9e840"},"schema_version":"1.0","source":{"id":"math/0311461","kind":"arxiv","version":1}},"canonical_sha256":"7efb3449db8273b522e914b0bf35206a255db8b48782526a60aa79c7f7a072d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7efb3449db8273b522e914b0bf35206a255db8b48782526a60aa79c7f7a072d1","first_computed_at":"2026-05-18T01:05:26.713116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:26.713116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qjeOqmfExfBSYqVSlHptKSdsQyXrWwYr3TccS0ZTBjBRsB/a2iw+oLRVEWfG4elfzf6Iw5S9QVT+KfwiwL1rAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:26.713612Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0311461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd300ce0b6d52958e84fae8549a33ff62030956931d287c9385c1e2f3a1761cd","sha256:91993a96563baeb111f1aebf48a917f41f097a1977d0bd8ab498f32c3e73830c"],"state_sha256":"6d601bd5bf05e895e3adc63f1cc40bc5f224eed79aeb47c46cdd300cc7893529"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43WAYtwQ7VlMtkHTNVzqAKbdRgZN14KbWrfGt0l2yYnmCVXg+xQX788LS9gyqQz0sxjp7dD5iNHrZCBIR5DaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:27:05.439616Z","bundle_sha256":"68cd1119637d388b9de4063be66fe4c04479aa79c7c097d9d412ed6d16247393"}}