{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZD45R36M5GAHP5UI4L2NO4IWSB","short_pith_number":"pith:ZD45R36M","canonical_record":{"source":{"id":"1211.2629","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-12T14:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"152f83bb7a3064264f07e47fc9243ce3f6f2e19d773231dcdb772bd2441881aa","abstract_canon_sha256":"8a0255499a3637764dfd25c9e9c214eb5d85f50f884a08d92fe7c31a2ac3da4c"},"schema_version":"1.0"},"canonical_sha256":"c8f9d8efcce98077f688e2f4d77116904dd52c186a55eb5aab7191f0775b20aa","source":{"kind":"arxiv","id":"1211.2629","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2629","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2629v3","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2629","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZD45R36M5GAH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZD45R36M5GAHP5UI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZD45R36M","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZD45R36M5GAHP5UI4L2NO4IWSB","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2629","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-12T14:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"152f83bb7a3064264f07e47fc9243ce3f6f2e19d773231dcdb772bd2441881aa","abstract_canon_sha256":"8a0255499a3637764dfd25c9e9c214eb5d85f50f884a08d92fe7c31a2ac3da4c"},"schema_version":"1.0"},"canonical_sha256":"c8f9d8efcce98077f688e2f4d77116904dd52c186a55eb5aab7191f0775b20aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:47.218996Z","signature_b64":"yPshAWJK26RigdtVA0iW9CxvJicT+CTCdFteI6oga5o31XSBl5jr3J8NhYWmt8IJtqsSOJ9S1/zl9qgfz4MFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8f9d8efcce98077f688e2f4d77116904dd52c186a55eb5aab7191f0775b20aa","last_reissued_at":"2026-05-18T02:48:47.218376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:47.218376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2629","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KFqomf7ez2z2Y88LQpOaUK5ewXX7o19dnOxYOtZ36nhIrXl61msJwMAq8tbSnwldcZQ0zG6aX/O/bGcjBycAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:00:46.073356Z"},"content_sha256":"c298f65ef7e5781907ba57ab8f0a822045cbfd18647d176f71f4b0b0080a1f0d","schema_version":"1.0","event_id":"sha256:c298f65ef7e5781907ba57ab8f0a822045cbfd18647d176f71f4b0b0080a1f0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZD45R36M5GAHP5UI4L2NO4IWSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic modules over Colombeau-generalized numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Guenther Hoermann, Michael Kunzinger, Sanja Konjik","submitted_at":"2012-11-12T14:26:09Z","abstract_excerpt":"We study symplectic linear algebra over the ring $\\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular, we construct symplectic bases for any symplectic form on a free $\\Rt$-module of finite rank. Further, we consider the general problem of eigenvalues for matrices over $\\Kt$ ($\\K=\\R$ or $\\C$) and derive normal forms for Hermitian and skew-symmetric matrices. Our investigations are motivated by applications in non-smooth symplectic geometry and the theory of F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2629","kind":"arxiv","version":3},"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":"2026-05-18T02:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44BZtQSTo+2nOrMGSkeWEGbVopiThKh1gp/iML/cFkse7MdU+xAb7wLblSr635IA51EEuK0RVOOObzdigAHYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:00:46.073719Z"},"content_sha256":"7b037efee95a8dd772be62b9d53fcfc62b0366e0495759c8e4d8bf0efd91d3ac","schema_version":"1.0","event_id":"sha256:7b037efee95a8dd772be62b9d53fcfc62b0366e0495759c8e4d8bf0efd91d3ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZD45R36M5GAHP5UI4L2NO4IWSB/bundle.json","state_url":"https://pith.science/pith/ZD45R36M5GAHP5UI4L2NO4IWSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZD45R36M5GAHP5UI4L2NO4IWSB/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":"2026-05-28T23:00:46Z","links":{"resolver":"https://pith.science/pith/ZD45R36M5GAHP5UI4L2NO4IWSB","bundle":"https://pith.science/pith/ZD45R36M5GAHP5UI4L2NO4IWSB/bundle.json","state":"https://pith.science/pith/ZD45R36M5GAHP5UI4L2NO4IWSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZD45R36M5GAHP5UI4L2NO4IWSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZD45R36M5GAHP5UI4L2NO4IWSB","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":"8a0255499a3637764dfd25c9e9c214eb5d85f50f884a08d92fe7c31a2ac3da4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-12T14:26:09Z","title_canon_sha256":"152f83bb7a3064264f07e47fc9243ce3f6f2e19d773231dcdb772bd2441881aa"},"schema_version":"1.0","source":{"id":"1211.2629","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2629","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2629v3","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2629","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZD45R36M5GAH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZD45R36M5GAHP5UI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZD45R36M","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:7b037efee95a8dd772be62b9d53fcfc62b0366e0495759c8e4d8bf0efd91d3ac","target":"graph","created_at":"2026-05-18T02:48:47Z","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":"We study symplectic linear algebra over the ring $\\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular, we construct symplectic bases for any symplectic form on a free $\\Rt$-module of finite rank. Further, we consider the general problem of eigenvalues for matrices over $\\Kt$ ($\\K=\\R$ or $\\C$) and derive normal forms for Hermitian and skew-symmetric matrices. Our investigations are motivated by applications in non-smooth symplectic geometry and the theory of F","authors_text":"Guenther Hoermann, Michael Kunzinger, Sanja Konjik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-12T14:26:09Z","title":"Symplectic modules over Colombeau-generalized numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2629","kind":"arxiv","version":3},"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:c298f65ef7e5781907ba57ab8f0a822045cbfd18647d176f71f4b0b0080a1f0d","target":"record","created_at":"2026-05-18T02:48:47Z","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":"8a0255499a3637764dfd25c9e9c214eb5d85f50f884a08d92fe7c31a2ac3da4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-12T14:26:09Z","title_canon_sha256":"152f83bb7a3064264f07e47fc9243ce3f6f2e19d773231dcdb772bd2441881aa"},"schema_version":"1.0","source":{"id":"1211.2629","kind":"arxiv","version":3}},"canonical_sha256":"c8f9d8efcce98077f688e2f4d77116904dd52c186a55eb5aab7191f0775b20aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8f9d8efcce98077f688e2f4d77116904dd52c186a55eb5aab7191f0775b20aa","first_computed_at":"2026-05-18T02:48:47.218376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:47.218376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yPshAWJK26RigdtVA0iW9CxvJicT+CTCdFteI6oga5o31XSBl5jr3J8NhYWmt8IJtqsSOJ9S1/zl9qgfz4MFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:47.218996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2629","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c298f65ef7e5781907ba57ab8f0a822045cbfd18647d176f71f4b0b0080a1f0d","sha256:7b037efee95a8dd772be62b9d53fcfc62b0366e0495759c8e4d8bf0efd91d3ac"],"state_sha256":"9295f2eb538d63c3263eaa3378832e47f7eb0b4481c403e8eb63758f9acc1195"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGjibsiqWHyJpreNpt8yu0arQJIBg/MuJF93sICYAO7xSU24xi6EAFNtu3cdIdmrgStt89ThQbQgPaEdVSPmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:00:46.075963Z","bundle_sha256":"57707e847f4f6527de96a24e90cdc59949dd663a5a7fb5c8bae9c1d3ae3fc9b9"}}