{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DNDXEXIZWCXIQSBNQWLZAZNTL6","short_pith_number":"pith:DNDXEXIZ","canonical_record":{"source":{"id":"1108.0293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T12:06:09Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"1c2d3fbf2d14b2693f7e1215ca728d18ac8d35721a9ae6e4799ee0125be8d788","abstract_canon_sha256":"f4c0b107cd5060b4c8659989b3993a7695f516002fe50ec320f1be2d7fbd34f1"},"schema_version":"1.0"},"canonical_sha256":"1b47725d19b0ae88482d85979065b35f88478684f07b29169d4af8ad9c6a982c","source":{"kind":"arxiv","id":"1108.0293","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0293","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0293v2","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0293","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"DNDXEXIZWCXI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DNDXEXIZWCXIQSBN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DNDXEXIZ","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DNDXEXIZWCXIQSBNQWLZAZNTL6","target":"record","payload":{"canonical_record":{"source":{"id":"1108.0293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T12:06:09Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"1c2d3fbf2d14b2693f7e1215ca728d18ac8d35721a9ae6e4799ee0125be8d788","abstract_canon_sha256":"f4c0b107cd5060b4c8659989b3993a7695f516002fe50ec320f1be2d7fbd34f1"},"schema_version":"1.0"},"canonical_sha256":"1b47725d19b0ae88482d85979065b35f88478684f07b29169d4af8ad9c6a982c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:55.374343Z","signature_b64":"BHnqHFu5pJ2WlAW57zstzYofT/gEfR3c9lACALk+PsvP983Uaf2YTCjRkZfGSNDrglIqsFTA7JrWaPHpbcO5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b47725d19b0ae88482d85979065b35f88478684f07b29169d4af8ad9c6a982c","last_reissued_at":"2026-05-18T03:03:55.373659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:55.373659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.0293","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":"2026-05-18T03:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zrYY+cZB2aJx4t/902Az546DuLxA8H9jUl9yaVlPkCOkCAqBHZMuuljmcsY3dCbqFYEr7mlw117aUUeKgA6HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:44:42.182770Z"},"content_sha256":"5699b85e877a4f8190ca710581dc13e92ae4b2b02309ce2f1f38e26fbe525c70","schema_version":"1.0","event_id":"sha256:5699b85e877a4f8190ca710581dc13e92ae4b2b02309ce2f1f38e26fbe525c70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DNDXEXIZWCXIQSBNQWLZAZNTL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of iterated $S^1$-bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AT","authors_text":"Jong Bum Lee, Mikiya Masuda","submitted_at":"2011-08-01T12:06:09Z","abstract_excerpt":"In this paper we investigate what kind of manifolds arise as the total spaces of iterated $S^1$-bundles. A real Bott tower studied in \\cite{CMO}, \\cite{KM} and \\cite{KN} is an example of an iterated $S^1$-bundle. We show that the total space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A real Bott manifold, which is the total space of a real Bott tower, provides an example of a closed flat Riemannian manifold. We also show that real Bott manifolds are the only closed flat Riemannian manifolds obtained from iterated $\\bbr{P}^1$-bundles. Finally we classify the homeomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0293","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":"2026-05-18T03:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"buxNa65xf67Q9VKEPmeNTwIEBUIYZRxAfLOXwsFFnzRdxBBQ83Fp6JjtDZm5EF+ybi5txxqTj+EIiuAtSoN6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:44:42.183107Z"},"content_sha256":"d564ae13ddbc01a12771e22cce02b6f22003962e9053ad405cc2b2fc872568d3","schema_version":"1.0","event_id":"sha256:d564ae13ddbc01a12771e22cce02b6f22003962e9053ad405cc2b2fc872568d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6/bundle.json","state_url":"https://pith.science/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6/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":"2026-06-09T10:44:42Z","links":{"resolver":"https://pith.science/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6","bundle":"https://pith.science/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6/bundle.json","state":"https://pith.science/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNDXEXIZWCXIQSBNQWLZAZNTL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DNDXEXIZWCXIQSBNQWLZAZNTL6","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":"f4c0b107cd5060b4c8659989b3993a7695f516002fe50ec320f1be2d7fbd34f1","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T12:06:09Z","title_canon_sha256":"1c2d3fbf2d14b2693f7e1215ca728d18ac8d35721a9ae6e4799ee0125be8d788"},"schema_version":"1.0","source":{"id":"1108.0293","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0293","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0293v2","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0293","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"DNDXEXIZWCXI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DNDXEXIZWCXIQSBN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DNDXEXIZ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:d564ae13ddbc01a12771e22cce02b6f22003962e9053ad405cc2b2fc872568d3","target":"graph","created_at":"2026-05-18T03:03:55Z","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 paper we investigate what kind of manifolds arise as the total spaces of iterated $S^1$-bundles. A real Bott tower studied in \\cite{CMO}, \\cite{KM} and \\cite{KN} is an example of an iterated $S^1$-bundle. We show that the total space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A real Bott manifold, which is the total space of a real Bott tower, provides an example of a closed flat Riemannian manifold. We also show that real Bott manifolds are the only closed flat Riemannian manifolds obtained from iterated $\\bbr{P}^1$-bundles. Finally we classify the homeomorph","authors_text":"Jong Bum Lee, Mikiya Masuda","cross_cats":["math.DG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T12:06:09Z","title":"Topology of iterated $S^1$-bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0293","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":"sha256:5699b85e877a4f8190ca710581dc13e92ae4b2b02309ce2f1f38e26fbe525c70","target":"record","created_at":"2026-05-18T03:03:55Z","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":"f4c0b107cd5060b4c8659989b3993a7695f516002fe50ec320f1be2d7fbd34f1","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T12:06:09Z","title_canon_sha256":"1c2d3fbf2d14b2693f7e1215ca728d18ac8d35721a9ae6e4799ee0125be8d788"},"schema_version":"1.0","source":{"id":"1108.0293","kind":"arxiv","version":2}},"canonical_sha256":"1b47725d19b0ae88482d85979065b35f88478684f07b29169d4af8ad9c6a982c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b47725d19b0ae88482d85979065b35f88478684f07b29169d4af8ad9c6a982c","first_computed_at":"2026-05-18T03:03:55.373659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:55.373659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BHnqHFu5pJ2WlAW57zstzYofT/gEfR3c9lACALk+PsvP983Uaf2YTCjRkZfGSNDrglIqsFTA7JrWaPHpbcO5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:55.374343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0293","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5699b85e877a4f8190ca710581dc13e92ae4b2b02309ce2f1f38e26fbe525c70","sha256:d564ae13ddbc01a12771e22cce02b6f22003962e9053ad405cc2b2fc872568d3"],"state_sha256":"e9915e749e0e0f12a303ec5cf8ab6bf455a0ea64f808a8894be5c281e41b24a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMCcQl5CQIpk5yVE1vZUT++Tcrh/QP0qRDy8oaInHymlUdRSOkQceK2HoEndXsJV2UHmiJvL4iR6VzDQAB7PAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:44:42.185008Z","bundle_sha256":"cd62f39ac76fece7e3079768166806de1ade028829e6a726a32cddc2c28a5ca0"}}