{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CXASQX4M2HAG6B7YOE6JHPFUSL","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":"a0ab34d2c54e419163dacef9db5433a723126fde608e9105b2f35885e053e98b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-15T16:44:22Z","title_canon_sha256":"c83960d17d2d71adde47c099f8b0ec5ab886dc6535411881433d4ff7d925c1ad"},"schema_version":"1.0","source":{"id":"1601.03992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03992","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03992v1","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03992","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"CXASQX4M2HAG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CXASQX4M2HAG6B7Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CXASQX4M","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:fd92b45ee872648a662164a728a0476132bddf61a209ef898e02e1bdd7b65851","target":"graph","created_at":"2026-05-18T01:22:49Z","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":"For $J$-hermitian operators on a Krein space $(\\mathcal{K},J)$ satisfying an adequate Fredholm property, a global Krein signature is shown to be a homotopy invariant. It is argued that this global signature is a generalization of the Noether index. When the Krein space has a supplementary Real structure, the sets of $J$-hermitian Fredholm operators with Real symmetry can be retracted to certain of the classifying spaces of Atiyah and Singer. Secondary $\\mathbb{Z}_2$-invariants are introduced to label their connected components. Related invariants are also analyzed for $J$-unitary operators.","authors_text":"Carlos Villegas-Blas, Hermann Schulz-Baldes","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-15T16:44:22Z","title":"Signatures for $J$-hermitians and $J$-unitaries on Krein spaces with Real structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03992","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":"sha256:87562b416cce20e77c5a83bbca23de6d966b5d9f68a21d309cacc7798aaf1451","target":"record","created_at":"2026-05-18T01:22:49Z","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":"a0ab34d2c54e419163dacef9db5433a723126fde608e9105b2f35885e053e98b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-15T16:44:22Z","title_canon_sha256":"c83960d17d2d71adde47c099f8b0ec5ab886dc6535411881433d4ff7d925c1ad"},"schema_version":"1.0","source":{"id":"1601.03992","kind":"arxiv","version":1}},"canonical_sha256":"15c1285f8cd1c06f07f8713c93bcb492dd40f0faf00056c772b3c024860e035d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15c1285f8cd1c06f07f8713c93bcb492dd40f0faf00056c772b3c024860e035d","first_computed_at":"2026-05-18T01:22:49.550497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:49.550497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"slNPQ6Uvk8cojykFek9gBbJpbGiaZSQS7MQXg3bX0KoBA66RTMZVVC4ZVKMFfZMNZZ1yXoGeEbOPIh5GKf6qAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:49.551131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87562b416cce20e77c5a83bbca23de6d966b5d9f68a21d309cacc7798aaf1451","sha256:fd92b45ee872648a662164a728a0476132bddf61a209ef898e02e1bdd7b65851"],"state_sha256":"4504362542441942d8875a43819c1d5f1242bdf101e8c1c4a2f79302a8f1b489"}