{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:M3LNLDHKZPAMXQPSWH6KTBXTBL","short_pith_number":"pith:M3LNLDHK","canonical_record":{"source":{"id":"1110.5608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-25T18:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"797067f72c35b20fdb3eba239392315aec6021f8c6f2abe7efc865ce0a38e529","abstract_canon_sha256":"e38069b46c61e224c7f90186421f6bec22a5d917c15170679b6a669b0a0731ac"},"schema_version":"1.0"},"canonical_sha256":"66d6d58ceacbc0cbc1f2b1fca986f30adedff79dc59f81dfd14d6c455feaffe1","source":{"kind":"arxiv","id":"1110.5608","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5608","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5608v1","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5608","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"M3LNLDHKZPAM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M3LNLDHKZPAMXQPS","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M3LNLDHK","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:M3LNLDHKZPAMXQPSWH6KTBXTBL","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-25T18:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"797067f72c35b20fdb3eba239392315aec6021f8c6f2abe7efc865ce0a38e529","abstract_canon_sha256":"e38069b46c61e224c7f90186421f6bec22a5d917c15170679b6a669b0a0731ac"},"schema_version":"1.0"},"canonical_sha256":"66d6d58ceacbc0cbc1f2b1fca986f30adedff79dc59f81dfd14d6c455feaffe1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:22.513382Z","signature_b64":"NeXZqlr0+/CuTYbvOyg78nzx8e8D0KUMtxEXrdsxgG90LPstsU4S5Io8j7oYO2ML5TlzcopDciH2HoaidR/EAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66d6d58ceacbc0cbc1f2b1fca986f30adedff79dc59f81dfd14d6c455feaffe1","last_reissued_at":"2026-05-18T04:10:22.512940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:22.512940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5608","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":"2026-05-18T04:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8y1VjbkJ4TTit0wi0y9X6NVoWft3nhT3pnMMP4KPGtsSxgMK+oihBLzWja/jN+96hVZRo0WReAmirelWBTahAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:41:54.976719Z"},"content_sha256":"078e8610e6dd7650d912dcf97c323382965b92d4fe39840b7598b91177234c10","schema_version":"1.0","event_id":"sha256:078e8610e6dd7650d912dcf97c323382965b92d4fe39840b7598b91177234c10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:M3LNLDHKZPAMXQPSWH6KTBXTBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Hermitian Cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Igor Kriz, Po Hu","submitted_at":"2011-10-25T18:50:51Z","abstract_excerpt":"Extending our method for investigating Real cobordism (which was recently used by Hill, Hopkins and Ravenel in their solution of the Kervaire invariant 1 problem), we investigate the $RO(G)$-graded homotopy groups of a (non-complete) $\\Z/2\\times \\Z/2$-equivariant spectrum called topological Hermitian cobordism. The methods of this paper may be useful in computing the homotopy groups of other $G$-equivariant spectra where $G\\neq \\Z/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5608","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":"2026-05-18T04:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1dhvdaN3DoINILgOy2+HRbmYTTh4MO7z/OFgJWcw28C0KHon+PXhL0MNWvb+icZfMID0nwLuSktFpfbVr5HDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:41:54.977059Z"},"content_sha256":"f3ea9ca3c72c4679dcde52c679782138ef0dee2cffba38dcff3e94617eba02b1","schema_version":"1.0","event_id":"sha256:f3ea9ca3c72c4679dcde52c679782138ef0dee2cffba38dcff3e94617eba02b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL/bundle.json","state_url":"https://pith.science/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL/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":"2026-06-22T11:41:54Z","links":{"resolver":"https://pith.science/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL","bundle":"https://pith.science/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL/bundle.json","state":"https://pith.science/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3LNLDHKZPAMXQPSWH6KTBXTBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:M3LNLDHKZPAMXQPSWH6KTBXTBL","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":"e38069b46c61e224c7f90186421f6bec22a5d917c15170679b6a669b0a0731ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-25T18:50:51Z","title_canon_sha256":"797067f72c35b20fdb3eba239392315aec6021f8c6f2abe7efc865ce0a38e529"},"schema_version":"1.0","source":{"id":"1110.5608","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5608","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5608v1","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5608","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"M3LNLDHKZPAM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M3LNLDHKZPAMXQPS","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M3LNLDHK","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:f3ea9ca3c72c4679dcde52c679782138ef0dee2cffba38dcff3e94617eba02b1","target":"graph","created_at":"2026-05-18T04:10:22Z","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":"Extending our method for investigating Real cobordism (which was recently used by Hill, Hopkins and Ravenel in their solution of the Kervaire invariant 1 problem), we investigate the $RO(G)$-graded homotopy groups of a (non-complete) $\\Z/2\\times \\Z/2$-equivariant spectrum called topological Hermitian cobordism. The methods of this paper may be useful in computing the homotopy groups of other $G$-equivariant spectra where $G\\neq \\Z/2$.","authors_text":"Igor Kriz, Po Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-25T18:50:51Z","title":"Topological Hermitian Cobordism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5608","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":"sha256:078e8610e6dd7650d912dcf97c323382965b92d4fe39840b7598b91177234c10","target":"record","created_at":"2026-05-18T04:10:22Z","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":"e38069b46c61e224c7f90186421f6bec22a5d917c15170679b6a669b0a0731ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-25T18:50:51Z","title_canon_sha256":"797067f72c35b20fdb3eba239392315aec6021f8c6f2abe7efc865ce0a38e529"},"schema_version":"1.0","source":{"id":"1110.5608","kind":"arxiv","version":1}},"canonical_sha256":"66d6d58ceacbc0cbc1f2b1fca986f30adedff79dc59f81dfd14d6c455feaffe1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66d6d58ceacbc0cbc1f2b1fca986f30adedff79dc59f81dfd14d6c455feaffe1","first_computed_at":"2026-05-18T04:10:22.512940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:22.512940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NeXZqlr0+/CuTYbvOyg78nzx8e8D0KUMtxEXrdsxgG90LPstsU4S5Io8j7oYO2ML5TlzcopDciH2HoaidR/EAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:22.513382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5608","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:078e8610e6dd7650d912dcf97c323382965b92d4fe39840b7598b91177234c10","sha256:f3ea9ca3c72c4679dcde52c679782138ef0dee2cffba38dcff3e94617eba02b1"],"state_sha256":"2a063571a79b7b7f9693de004861533a04b930380128cce60ca1800f08e547f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6utHJlNQerXRHsSswIpHl7RhGNy05B9XUNTffSse4dmV9UNobW5UJWJhSepYEVB5T/YG1Q+BLkbc+aCi2zpIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:41:54.978927Z","bundle_sha256":"c92b5463112029d9b34b3ee2dc5b3d758ebb28792d20e503b57b518102a1ae3c"}}