{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6RSIWYAKFVX4VACLAFOHC2FCOO","short_pith_number":"pith:6RSIWYAK","canonical_record":{"source":{"id":"1810.02619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-05T11:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"d776c3d9738b1905fe293aaf91dca49947162f9c243ba09badf067d83d3a7644","abstract_canon_sha256":"40c701d2be189d3a2eee774e19470b47716137458427cd8ce2f13071c6f0a2c3"},"schema_version":"1.0"},"canonical_sha256":"f4648b600a2d6fca804b015c7168a273bce2b161b4d264f96b1fbdd8063b5dcb","source":{"kind":"arxiv","id":"1810.02619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02619","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02619v1","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02619","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"6RSIWYAKFVX4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6RSIWYAKFVX4VACL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6RSIWYAK","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6RSIWYAKFVX4VACLAFOHC2FCOO","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-05T11:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"d776c3d9738b1905fe293aaf91dca49947162f9c243ba09badf067d83d3a7644","abstract_canon_sha256":"40c701d2be189d3a2eee774e19470b47716137458427cd8ce2f13071c6f0a2c3"},"schema_version":"1.0"},"canonical_sha256":"f4648b600a2d6fca804b015c7168a273bce2b161b4d264f96b1fbdd8063b5dcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:01.189750Z","signature_b64":"qn/2qGwhMFgkIR2V1jO1Yf6BEp+Ei5d6lLiAMRBHrIy2Y8TOKr/5/k2Ln3Hvv0iOsSiQvjVFHN4XOdVTak0zAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4648b600a2d6fca804b015c7168a273bce2b161b4d264f96b1fbdd8063b5dcb","last_reissued_at":"2026-05-18T00:04:01.189196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:01.189196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02619","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O/HtwVoTdovAQKMfLIXxlSDwtsa9nepLI0nJzL/GOceHXtT0y/gGyyeSuyHUGxoK46EBD+pZcfuFMMCakiWXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:39:33.581220Z"},"content_sha256":"fac3d625e2a9aaa2606af97f1ae5c5cedfd0c2f9cc97ea0dff0bbcff8a99c324","schema_version":"1.0","event_id":"sha256:fac3d625e2a9aaa2606af97f1ae5c5cedfd0c2f9cc97ea0dff0bbcff8a99c324"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6RSIWYAKFVX4VACLAFOHC2FCOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operators on anti-dual pairs: Generalized Krein--von Neumann extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tam\\'as Titkos, Zsigmond Tarcsay","submitted_at":"2018-10-05T11:29:57Z","abstract_excerpt":"The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The concept of anti-duality carries an adequate structure to define positivity in a natural way, and is still general enough to cover numerous important areas where the Hilbert space theory cannot be applied. Our running example -- illustrating the applicability of the general setting to spaces bearing poor geometrical features -- comes from noncommutative inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02619","kind":"arxiv","version":1},"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":"2026-05-18T00:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jws9iSfxxkMVMbUUuhvY26B8GnAE1PD17q4UWu4HdG/MTkeFicpRXPKlony/YutN2rWCL5HkXWNs9zyXtwPjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:39:33.581910Z"},"content_sha256":"c747c2466b810032889dcedf4ce600b40bff8c7de7c6404b4fcf7a6725e192c6","schema_version":"1.0","event_id":"sha256:c747c2466b810032889dcedf4ce600b40bff8c7de7c6404b4fcf7a6725e192c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6RSIWYAKFVX4VACLAFOHC2FCOO/bundle.json","state_url":"https://pith.science/pith/6RSIWYAKFVX4VACLAFOHC2FCOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6RSIWYAKFVX4VACLAFOHC2FCOO/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":"2026-05-30T19:39:33Z","links":{"resolver":"https://pith.science/pith/6RSIWYAKFVX4VACLAFOHC2FCOO","bundle":"https://pith.science/pith/6RSIWYAKFVX4VACLAFOHC2FCOO/bundle.json","state":"https://pith.science/pith/6RSIWYAKFVX4VACLAFOHC2FCOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6RSIWYAKFVX4VACLAFOHC2FCOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6RSIWYAKFVX4VACLAFOHC2FCOO","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":"40c701d2be189d3a2eee774e19470b47716137458427cd8ce2f13071c6f0a2c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-05T11:29:57Z","title_canon_sha256":"d776c3d9738b1905fe293aaf91dca49947162f9c243ba09badf067d83d3a7644"},"schema_version":"1.0","source":{"id":"1810.02619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02619","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02619v1","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02619","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"6RSIWYAKFVX4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6RSIWYAKFVX4VACL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6RSIWYAK","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:c747c2466b810032889dcedf4ce600b40bff8c7de7c6404b4fcf7a6725e192c6","target":"graph","created_at":"2026-05-18T00:04:01Z","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":"The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The concept of anti-duality carries an adequate structure to define positivity in a natural way, and is still general enough to cover numerous important areas where the Hilbert space theory cannot be applied. Our running example -- illustrating the applicability of the general setting to spaces bearing poor geometrical features -- comes from noncommutative inte","authors_text":"Tam\\'as Titkos, Zsigmond Tarcsay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-05T11:29:57Z","title":"Operators on anti-dual pairs: Generalized Krein--von Neumann extension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02619","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:fac3d625e2a9aaa2606af97f1ae5c5cedfd0c2f9cc97ea0dff0bbcff8a99c324","target":"record","created_at":"2026-05-18T00:04:01Z","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":"40c701d2be189d3a2eee774e19470b47716137458427cd8ce2f13071c6f0a2c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-05T11:29:57Z","title_canon_sha256":"d776c3d9738b1905fe293aaf91dca49947162f9c243ba09badf067d83d3a7644"},"schema_version":"1.0","source":{"id":"1810.02619","kind":"arxiv","version":1}},"canonical_sha256":"f4648b600a2d6fca804b015c7168a273bce2b161b4d264f96b1fbdd8063b5dcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4648b600a2d6fca804b015c7168a273bce2b161b4d264f96b1fbdd8063b5dcb","first_computed_at":"2026-05-18T00:04:01.189196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:01.189196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qn/2qGwhMFgkIR2V1jO1Yf6BEp+Ei5d6lLiAMRBHrIy2Y8TOKr/5/k2Ln3Hvv0iOsSiQvjVFHN4XOdVTak0zAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:01.189750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fac3d625e2a9aaa2606af97f1ae5c5cedfd0c2f9cc97ea0dff0bbcff8a99c324","sha256:c747c2466b810032889dcedf4ce600b40bff8c7de7c6404b4fcf7a6725e192c6"],"state_sha256":"45cabb87a1ab4023bf1619516d37b4399351773ed397efa7f19f54f69b49bb19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpgvhejC4Gri0r1OrAMlugOcUUhGReredmRLBP/EhokuV197CkhG32AAdmVnKqYrzn9rCACi4HVGv+VHWArDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:39:33.585351Z","bundle_sha256":"fb1cda3fe188997c7d3739eb578c9f109cb10a625776ebfb21e7c7f9640a067b"}}