{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WD74RL6KBSBE734WFQIIT35TET","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":"2652fbe60059e809f2baa3953f8fbc19f69450757b207854773cbf5568309b9f","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-10T00:41:58Z","title_canon_sha256":"d8350f3419532674729512c3eead9b687def0902e104d539aa962e80c1cce0dc"},"schema_version":"1.0","source":{"id":"1308.2263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2263","created_at":"2026-05-18T01:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2263v2","created_at":"2026-05-18T01:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2263","created_at":"2026-05-18T01:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"WD74RL6KBSBE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WD74RL6KBSBE734W","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WD74RL6K","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:6a1c4bd006a1010a40b2badd9b9d00e57aaee031dcc389d0d1b0da0ab6160b69","target":"graph","created_at":"2026-05-18T01:14:18Z","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 give a survey of various results about the topology of oriented Grassmannian bundles related to the exceptional Lie group G_2. Some of these results are new. We give self-contained proofs here. One often encounters these spaces when studying submanifolds of manifolds with calibrated geometries. For the sake of completeness we decided to collect them here in a self-contained way to be easily accessible for future usage in calibrated geometry. As an application we deduce existence of certain special 3 and 4 dimensional submanifolds of G_2 manifolds with special properties, which","authors_text":"Mustafa Kalafat, Selman Akbulut","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-10T00:41:58Z","title":"Algebraic topology of $G_2$ manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2263","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:bcb1765644876bbe0530026cd3efdb6c9f495c36e493c56937e3149eeaae0f55","target":"record","created_at":"2026-05-18T01:14:18Z","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":"2652fbe60059e809f2baa3953f8fbc19f69450757b207854773cbf5568309b9f","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-10T00:41:58Z","title_canon_sha256":"d8350f3419532674729512c3eead9b687def0902e104d539aa962e80c1cce0dc"},"schema_version":"1.0","source":{"id":"1308.2263","kind":"arxiv","version":2}},"canonical_sha256":"b0ffc8afca0c824fef962c1089efb324fc82bc15e247e80f22d23d54b03a6302","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0ffc8afca0c824fef962c1089efb324fc82bc15e247e80f22d23d54b03a6302","first_computed_at":"2026-05-18T01:14:18.483074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:18.483074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7DzLU59FdYpoZg6hvSc+N7dnWKx4yO5UH33dJLTAHehB8Ue+7LYqF871DhyDaYv3cAufiibLHXQ05YtNbpPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:18.483779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcb1765644876bbe0530026cd3efdb6c9f495c36e493c56937e3149eeaae0f55","sha256:6a1c4bd006a1010a40b2badd9b9d00e57aaee031dcc389d0d1b0da0ab6160b69"],"state_sha256":"0544adb141f17d6bd81e3c8a2f1b58ae4750dc8d5af8f1bcaa847d7e6f3589dd"}