{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YPQGDPXP4PH7FE66TXD56SND3H","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":"951b159357d28b24081b9b463fddb46c265dd87af541118adf942e3ed0db8bef","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-05-24T12:20:07Z","title_canon_sha256":"4a894eb797df173aff68094a552f90cbafe89f8db79ae8f921b17772d1c3b17d"},"schema_version":"1.0","source":{"id":"0905.3897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3897","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3897v2","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3897","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"YPQGDPXP4PH7","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YPQGDPXP4PH7FE66","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YPQGDPXP","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:ab4b9851ac66609791ba3fefd1e18f92cf5b496d8b898e775af295b1cf81213a","target":"graph","created_at":"2026-05-18T03:17:44Z","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 a family of functionals defined on a Hilbert manifold and smoothly depending on a compact finite dimensional manifold, we give a sufficient condition on the parameter space in such a way the family bifurcate from the trivial branch.","authors_text":"Alessandro Portaluri","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-05-24T12:20:07Z","title":"A $K$-theoretical invariant and bifurcation for a parameterized family of functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3897","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":"sha256:4901ac83da59ae58ea92129b45be275ed8412520dcac5fc5d33d1f2e67ed0acd","target":"record","created_at":"2026-05-18T03:17:44Z","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":"951b159357d28b24081b9b463fddb46c265dd87af541118adf942e3ed0db8bef","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-05-24T12:20:07Z","title_canon_sha256":"4a894eb797df173aff68094a552f90cbafe89f8db79ae8f921b17772d1c3b17d"},"schema_version":"1.0","source":{"id":"0905.3897","kind":"arxiv","version":2}},"canonical_sha256":"c3e061beefe3cff293de9dc7df49a3d9e0d6996efb57d4c5ceddaeaeca7a671d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3e061beefe3cff293de9dc7df49a3d9e0d6996efb57d4c5ceddaeaeca7a671d","first_computed_at":"2026-05-18T03:17:44.970530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:44.970530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywjkGx8kcFMBGuS7l75gz15JILEUMEed4ajO72fCPuhH2wrptFe/l+cq3c0vwSn0YcX2qmWwPKds5FjrTut1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:44.971076Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4901ac83da59ae58ea92129b45be275ed8412520dcac5fc5d33d1f2e67ed0acd","sha256:ab4b9851ac66609791ba3fefd1e18f92cf5b496d8b898e775af295b1cf81213a"],"state_sha256":"e46513f49c62899ce9d1007221f03595833009ff39541b8464cbff93d9b2f9a3"}