{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DE6XQ6JQ3I2OQSQZQXIFG3SWUF","short_pith_number":"pith:DE6XQ6JQ","canonical_record":{"source":{"id":"1004.1133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-07T16:59:24Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"8b07ad3688f972beb2797d14f01d3dc1aaa63922830ccc0874b63ceaf188fd4e","abstract_canon_sha256":"01a8871848223ac61f1d2679f5270909d2370f5500f33f0e39fa9642d7a200c1"},"schema_version":"1.0"},"canonical_sha256":"193d787930da34e84a1985d0536e56a1773555a0d366a298dd5ab95062a9d938","source":{"kind":"arxiv","id":"1004.1133","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1133","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1133v2","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1133","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"DE6XQ6JQ3I2O","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DE6XQ6JQ3I2OQSQZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DE6XQ6JQ","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DE6XQ6JQ3I2OQSQZQXIFG3SWUF","target":"record","payload":{"canonical_record":{"source":{"id":"1004.1133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-07T16:59:24Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"8b07ad3688f972beb2797d14f01d3dc1aaa63922830ccc0874b63ceaf188fd4e","abstract_canon_sha256":"01a8871848223ac61f1d2679f5270909d2370f5500f33f0e39fa9642d7a200c1"},"schema_version":"1.0"},"canonical_sha256":"193d787930da34e84a1985d0536e56a1773555a0d366a298dd5ab95062a9d938","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:30.014866Z","signature_b64":"6k6/KQmjgHIg6mUH99mnB0WqJ2bZ48/b0u1UowyXX3aelvxQRxDFQoDjTMgb+fWyhi6kxMfiM6/5r+tzM3bYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"193d787930da34e84a1985d0536e56a1773555a0d366a298dd5ab95062a9d938","last_reissued_at":"2026-05-18T04:21:30.014495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:30.014495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.1133","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJ4VRUJAI3XOqu5TV1oFrpUr8QIxhBp7hWKZDINTDkQMDR1cBe9AuiIM3Yl/k8vPDftpXOYAWV3Y/jTLCsBkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:27:18.107881Z"},"content_sha256":"5ec71e65bb14f85f76cef0e1ebb49996079fbdc423498107c1d5722c94b032a4","schema_version":"1.0","event_id":"sha256:5ec71e65bb14f85f76cef0e1ebb49996079fbdc423498107c1d5722c94b032a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DE6XQ6JQ3I2OQSQZQXIFG3SWUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite reduction and Morse index estimates for mechanical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Alessandro Sfondrini, Franco Cardin, Giuseppe De Marco","submitted_at":"2010-04-07T16:59:24Z","abstract_excerpt":"A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1133","kind":"arxiv","version":2},"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":"2026-05-18T04:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5DZH/vuJd/iM9Xp8CueZ21oXCVrvgw11wBwxCHYC7q98QexEhaKb5qk+JfS6Ld0s+196KM1NhN88D+Dm+n2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:27:18.108546Z"},"content_sha256":"f6041f9ac5638e7dfc88bca804156b608ea55dbcc953f3fc71f32d0f97c263ba","schema_version":"1.0","event_id":"sha256:f6041f9ac5638e7dfc88bca804156b608ea55dbcc953f3fc71f32d0f97c263ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF/bundle.json","state_url":"https://pith.science/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF/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":"2026-06-11T17:27:18Z","links":{"resolver":"https://pith.science/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF","bundle":"https://pith.science/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF/bundle.json","state":"https://pith.science/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DE6XQ6JQ3I2OQSQZQXIFG3SWUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DE6XQ6JQ3I2OQSQZQXIFG3SWUF","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":"01a8871848223ac61f1d2679f5270909d2370f5500f33f0e39fa9642d7a200c1","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-07T16:59:24Z","title_canon_sha256":"8b07ad3688f972beb2797d14f01d3dc1aaa63922830ccc0874b63ceaf188fd4e"},"schema_version":"1.0","source":{"id":"1004.1133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1133","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1133v2","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1133","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"DE6XQ6JQ3I2O","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DE6XQ6JQ3I2OQSQZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DE6XQ6JQ","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:f6041f9ac5638e7dfc88bca804156b608ea55dbcc953f3fc71f32d0f97c263ba","target":"graph","created_at":"2026-05-18T04:21:30Z","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":"A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.","authors_text":"Alessandro Sfondrini, Franco Cardin, Giuseppe De Marco","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-07T16:59:24Z","title":"Finite reduction and Morse index estimates for mechanical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1133","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":"sha256:5ec71e65bb14f85f76cef0e1ebb49996079fbdc423498107c1d5722c94b032a4","target":"record","created_at":"2026-05-18T04:21:30Z","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":"01a8871848223ac61f1d2679f5270909d2370f5500f33f0e39fa9642d7a200c1","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-07T16:59:24Z","title_canon_sha256":"8b07ad3688f972beb2797d14f01d3dc1aaa63922830ccc0874b63ceaf188fd4e"},"schema_version":"1.0","source":{"id":"1004.1133","kind":"arxiv","version":2}},"canonical_sha256":"193d787930da34e84a1985d0536e56a1773555a0d366a298dd5ab95062a9d938","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"193d787930da34e84a1985d0536e56a1773555a0d366a298dd5ab95062a9d938","first_computed_at":"2026-05-18T04:21:30.014495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:30.014495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6k6/KQmjgHIg6mUH99mnB0WqJ2bZ48/b0u1UowyXX3aelvxQRxDFQoDjTMgb+fWyhi6kxMfiM6/5r+tzM3bYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:30.014866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ec71e65bb14f85f76cef0e1ebb49996079fbdc423498107c1d5722c94b032a4","sha256:f6041f9ac5638e7dfc88bca804156b608ea55dbcc953f3fc71f32d0f97c263ba"],"state_sha256":"e673937cf83844e18005459d5255ff290c683e177a488145fd586832d9fd0430"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yrp3f8tS8ZyD9nXOV9loERlLdqgaUpN7lGFCu5nTkVR22zemW+LJlYugfv8EVYKQrBEaSNZvZjN2TMLp5fQcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:27:18.112075Z","bundle_sha256":"8130bd39fe4ec5c47c4aa60b95afc666e728c2caacaa70f60950d52ff525ba4a"}}