{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:E7O4EWM4XOH2PQDAPFTVTGTA3T","short_pith_number":"pith:E7O4EWM4","canonical_record":{"source":{"id":"1804.08006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T18:17:53Z","cross_cats_sorted":[],"title_canon_sha256":"080a7f24fa10e344126baaf7f2b53370c97e27c233cbfe37fc391393121dd90e","abstract_canon_sha256":"2805f1a0485658edb56a05190a46ca77c81017869e37aebfcf6570d886984c40"},"schema_version":"1.0"},"canonical_sha256":"27ddc2599cbb8fa7c0607967599a60dcc3fd3ce65d234dc0b92e9288c3223947","source":{"kind":"arxiv","id":"1804.08006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08006","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08006v1","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08006","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"E7O4EWM4XOH2","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"E7O4EWM4XOH2PQDA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"E7O4EWM4","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:E7O4EWM4XOH2PQDAPFTVTGTA3T","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T18:17:53Z","cross_cats_sorted":[],"title_canon_sha256":"080a7f24fa10e344126baaf7f2b53370c97e27c233cbfe37fc391393121dd90e","abstract_canon_sha256":"2805f1a0485658edb56a05190a46ca77c81017869e37aebfcf6570d886984c40"},"schema_version":"1.0"},"canonical_sha256":"27ddc2599cbb8fa7c0607967599a60dcc3fd3ce65d234dc0b92e9288c3223947","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:49.834297Z","signature_b64":"yxGefJRH/jvKiwNUxxV+DsdJ71WA0AG2RxLvQnT6VuwSA89+J2FOjqx2t15jFArIUVsmFRPAJFbTgKpX1pwYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27ddc2599cbb8fa7c0607967599a60dcc3fd3ce65d234dc0b92e9288c3223947","last_reissued_at":"2026-05-18T00:17:49.833752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:49.833752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08006","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":"2026-05-18T00:17:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVQzeOE/jZf7xfbZN50KOGC4tj5+V9DgRKHolglpBFfx0bxZjadx2FSjOU0yU2g07rokbk54G0+LHk4IzryoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:27:32.851839Z"},"content_sha256":"f12b1ce96719fbc97d9ca6ebf7bd0619e47f8f7ed44c3b9a77c8f3edaf59f7c0","schema_version":"1.0","event_id":"sha256:f12b1ce96719fbc97d9ca6ebf7bd0619e47f8f7ed44c3b9a77c8f3edaf59f7c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:E7O4EWM4XOH2PQDAPFTVTGTA3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher equivariant and invariant topological complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Marzieh Bayeh, Soumen Sarkar","submitted_at":"2018-04-21T18:17:53Z","abstract_excerpt":"In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We compute some of these invariants for moment angle complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08006","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":"2026-05-18T00:17:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQsZ3Nq4x5c4BAYRdcU/4HoRC06lT+2g3u8cWemJe2ms/QJPVvsgfLy7hQ7k8b6z8AADaw5EO36MPFXg8fGoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:27:32.852702Z"},"content_sha256":"50c0ab1aa781f0d1a1ab1d12787aea4656bf4a58888452377c1a7c097ca4482b","schema_version":"1.0","event_id":"sha256:50c0ab1aa781f0d1a1ab1d12787aea4656bf4a58888452377c1a7c097ca4482b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T/bundle.json","state_url":"https://pith.science/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T/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":"2026-05-31T20:27:32Z","links":{"resolver":"https://pith.science/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T","bundle":"https://pith.science/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T/bundle.json","state":"https://pith.science/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7O4EWM4XOH2PQDAPFTVTGTA3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E7O4EWM4XOH2PQDAPFTVTGTA3T","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":"2805f1a0485658edb56a05190a46ca77c81017869e37aebfcf6570d886984c40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T18:17:53Z","title_canon_sha256":"080a7f24fa10e344126baaf7f2b53370c97e27c233cbfe37fc391393121dd90e"},"schema_version":"1.0","source":{"id":"1804.08006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08006","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08006v1","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08006","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"E7O4EWM4XOH2","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"E7O4EWM4XOH2PQDA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"E7O4EWM4","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:50c0ab1aa781f0d1a1ab1d12787aea4656bf4a58888452377c1a7c097ca4482b","target":"graph","created_at":"2026-05-18T00:17:49Z","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 introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We compute some of these invariants for moment angle complexes.","authors_text":"Marzieh Bayeh, Soumen Sarkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T18:17:53Z","title":"Higher equivariant and invariant topological complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08006","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:f12b1ce96719fbc97d9ca6ebf7bd0619e47f8f7ed44c3b9a77c8f3edaf59f7c0","target":"record","created_at":"2026-05-18T00:17:49Z","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":"2805f1a0485658edb56a05190a46ca77c81017869e37aebfcf6570d886984c40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T18:17:53Z","title_canon_sha256":"080a7f24fa10e344126baaf7f2b53370c97e27c233cbfe37fc391393121dd90e"},"schema_version":"1.0","source":{"id":"1804.08006","kind":"arxiv","version":1}},"canonical_sha256":"27ddc2599cbb8fa7c0607967599a60dcc3fd3ce65d234dc0b92e9288c3223947","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27ddc2599cbb8fa7c0607967599a60dcc3fd3ce65d234dc0b92e9288c3223947","first_computed_at":"2026-05-18T00:17:49.833752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:49.833752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxGefJRH/jvKiwNUxxV+DsdJ71WA0AG2RxLvQnT6VuwSA89+J2FOjqx2t15jFArIUVsmFRPAJFbTgKpX1pwYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:49.834297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12b1ce96719fbc97d9ca6ebf7bd0619e47f8f7ed44c3b9a77c8f3edaf59f7c0","sha256:50c0ab1aa781f0d1a1ab1d12787aea4656bf4a58888452377c1a7c097ca4482b"],"state_sha256":"2cfd1053d13be63806efa3df107dcc1b982b12d741b88a308f810565531881b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGSMEibqkwc80kF8COiRwJgzJJyobRxcIqW6G86scK6W1W35Wg6PIHhp406jXNThlAik+51AF/1CLozi79EADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:27:32.857551Z","bundle_sha256":"f042995dba9c1bba37cb6b5c45803b623a5bd0bcd4abbf25311216ed30546450"}}