{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TJG56H33MLF3BCCRRHYECTFBWR","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":"2f0363ee42c6f4acb3eb96ce1608cf62376901810d98f679a5c5755aacad21d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-09T18:14:30Z","title_canon_sha256":"151270ccdac50fdb54d5dee7b4ceb8f0f602f8189d11d7aab2738ba14b574eb1"},"schema_version":"1.0","source":{"id":"1502.02586","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02586","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02586v2","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02586","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"TJG56H33MLF3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TJG56H33MLF3BCCR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TJG56H33","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:db4cb7c6615d9c387e1b00a5c572ca212e4dde0dd6a1ddb8e1a874474f2a6bcd","target":"graph","created_at":"2026-05-18T01:04:01Z","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":"We study the lower bounds and upper bounds for LS-category and equivariant LS-category. In particular we compute both invariants for torus manifolds. There are some examples to show the sharpness of conditions in the theorems. Moreover the equivariant LS-category of the product space is discussed and counterexamples of some previous results are given.","authors_text":"Marzieh Bayeh, Soumen Sarkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-09T18:14:30Z","title":"Some Aspects of Equivariant LS-category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02586","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":"sha256:3d1d7e1959d546d0088de94288e6497d56c3dd118313299419c33064965f720a","target":"record","created_at":"2026-05-18T01:04:01Z","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":"2f0363ee42c6f4acb3eb96ce1608cf62376901810d98f679a5c5755aacad21d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-09T18:14:30Z","title_canon_sha256":"151270ccdac50fdb54d5dee7b4ceb8f0f602f8189d11d7aab2738ba14b574eb1"},"schema_version":"1.0","source":{"id":"1502.02586","kind":"arxiv","version":2}},"canonical_sha256":"9a4ddf1f7b62cbb0885189f0414ca1b4709db0a57796d4c75743709f83b420c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a4ddf1f7b62cbb0885189f0414ca1b4709db0a57796d4c75743709f83b420c5","first_computed_at":"2026-05-18T01:04:01.370604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:01.370604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4wIaF6jxuF+YI3LEWoAH2a9botI978A8jsnr1ailNFi2iU1lhnAnlNSUYOsImFZYGs0oQc9MCGA2F90mfW7RCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:01.371200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02586","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d1d7e1959d546d0088de94288e6497d56c3dd118313299419c33064965f720a","sha256:db4cb7c6615d9c387e1b00a5c572ca212e4dde0dd6a1ddb8e1a874474f2a6bcd"],"state_sha256":"6184b358e6320704cf6f7d034dfebba732f9b347124321ad908fdeaa68ac46e8"}