{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HCPMFILXETAIYEPK2PJSFHI4UU","short_pith_number":"pith:HCPMFILX","canonical_record":{"source":{"id":"1303.1076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T15:48:57Z","cross_cats_sorted":[],"title_canon_sha256":"d5549b652c37a728df41b45501dd3f21fcbb93c7dceb92c2fe9701956a429ea4","abstract_canon_sha256":"6074732838f54ac582592b88143d97f7495552eda347302a18c27ca5987ddef5"},"schema_version":"1.0"},"canonical_sha256":"389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed","source":{"kind":"arxiv","id":"1303.1076","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1076","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1076v2","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1076","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"HCPMFILXETAI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HCPMFILXETAIYEPK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HCPMFILX","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HCPMFILXETAIYEPK2PJSFHI4UU","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T15:48:57Z","cross_cats_sorted":[],"title_canon_sha256":"d5549b652c37a728df41b45501dd3f21fcbb93c7dceb92c2fe9701956a429ea4","abstract_canon_sha256":"6074732838f54ac582592b88143d97f7495552eda347302a18c27ca5987ddef5"},"schema_version":"1.0"},"canonical_sha256":"389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:43.384552Z","signature_b64":"Cu3bdFtWV9xVIFCcoANEhnPMgdDCxhYQ8qXE6bAyk9eTBKRNygDKzKbGGvyRnL4aga00gHacrsxeonVCFqY1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed","last_reissued_at":"2026-05-18T03:15:43.383844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:43.383844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1076","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":"2026-05-18T03:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8X+I5PQSfELMyDl3NJh/FE57LZZT6RSizkKgDDCHcT/0rrfPG4FIANW/BnPSBKjfTzyVZyc9O2IjnDw8ZaADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:12:51.547137Z"},"content_sha256":"d96ee8d81f6316fe95b8fa6e30b1bdbb74baa8d592a69716cb02814f077e6179","schema_version":"1.0","event_id":"sha256:d96ee8d81f6316fe95b8fa6e30b1bdbb74baa8d592a69716cb02814f077e6179"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HCPMFILXETAIYEPK2PJSFHI4UU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inner product spaces and Krein spaces in the quaternionic setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Alpay, Fabrizio Colombo, Irene Sabadini","submitted_at":"2013-03-05T15:48:57Z","abstract_excerpt":"In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1076","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":"2026-05-18T03:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLrpnJMZ8bNNXVzDr5K2HHHpwUAhKMsdpLhLOW73//FEAVMXv6q3jVh9h6otMrwht4/3uUEk6U1GtB9C6+AECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:12:51.547495Z"},"content_sha256":"2369fbe64ade54d65a8e2b88d74bbd6b8dffca0d4fbf96cbf7c2022588f6d56d","schema_version":"1.0","event_id":"sha256:2369fbe64ade54d65a8e2b88d74bbd6b8dffca0d4fbf96cbf7c2022588f6d56d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCPMFILXETAIYEPK2PJSFHI4UU/bundle.json","state_url":"https://pith.science/pith/HCPMFILXETAIYEPK2PJSFHI4UU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCPMFILXETAIYEPK2PJSFHI4UU/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":"2026-06-02T01:12:51Z","links":{"resolver":"https://pith.science/pith/HCPMFILXETAIYEPK2PJSFHI4UU","bundle":"https://pith.science/pith/HCPMFILXETAIYEPK2PJSFHI4UU/bundle.json","state":"https://pith.science/pith/HCPMFILXETAIYEPK2PJSFHI4UU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCPMFILXETAIYEPK2PJSFHI4UU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HCPMFILXETAIYEPK2PJSFHI4UU","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":"6074732838f54ac582592b88143d97f7495552eda347302a18c27ca5987ddef5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T15:48:57Z","title_canon_sha256":"d5549b652c37a728df41b45501dd3f21fcbb93c7dceb92c2fe9701956a429ea4"},"schema_version":"1.0","source":{"id":"1303.1076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1076","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1076v2","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1076","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"HCPMFILXETAI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HCPMFILXETAIYEPK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HCPMFILX","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:2369fbe64ade54d65a8e2b88d74bbd6b8dffca0d4fbf96cbf7c2022588f6d56d","target":"graph","created_at":"2026-05-18T03:15:43Z","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":"In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper.","authors_text":"Daniel Alpay, Fabrizio Colombo, Irene Sabadini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T15:48:57Z","title":"Inner product spaces and Krein spaces in the quaternionic setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1076","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:d96ee8d81f6316fe95b8fa6e30b1bdbb74baa8d592a69716cb02814f077e6179","target":"record","created_at":"2026-05-18T03:15:43Z","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":"6074732838f54ac582592b88143d97f7495552eda347302a18c27ca5987ddef5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T15:48:57Z","title_canon_sha256":"d5549b652c37a728df41b45501dd3f21fcbb93c7dceb92c2fe9701956a429ea4"},"schema_version":"1.0","source":{"id":"1303.1076","kind":"arxiv","version":2}},"canonical_sha256":"389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"389ec2a17724c08c11ead3d3229d1ca5079398ed37a848e318578bc1cc1967ed","first_computed_at":"2026-05-18T03:15:43.383844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:43.383844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cu3bdFtWV9xVIFCcoANEhnPMgdDCxhYQ8qXE6bAyk9eTBKRNygDKzKbGGvyRnL4aga00gHacrsxeonVCFqY1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:43.384552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d96ee8d81f6316fe95b8fa6e30b1bdbb74baa8d592a69716cb02814f077e6179","sha256:2369fbe64ade54d65a8e2b88d74bbd6b8dffca0d4fbf96cbf7c2022588f6d56d"],"state_sha256":"d23ddd0e70a4b320e6e7eb11a7115bf72c4cf671ebdeeaa7a687580190cfc8ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1IA+Eh5Wy1sgv7yjUwp/5qLECN5xnxwgBHYUdXvhCF3PLMPi+00l2mBSWRCg6a44DviQYtXZ2ZdQv00BoxnDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:12:51.549444Z","bundle_sha256":"01028bed847273315140cbeb617b45e064880d2ee253129ca460999979ccb659"}}