{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ABFHP3WETQI5W5IHNKYJ2BTZQD","short_pith_number":"pith:ABFHP3WE","canonical_record":{"source":{"id":"1007.0113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-01T09:48:24Z","cross_cats_sorted":[],"title_canon_sha256":"bf09f3e1e04cb2286b87e3a80fc13b097d35fd5acc5b8000b2465590934562c9","abstract_canon_sha256":"51873e7e023bac3f087f97d76ed81cc88b228bda17f21cf27b9197048c21d930"},"schema_version":"1.0"},"canonical_sha256":"004a77eec49c11db75076ab09d067980ecbdffb0baa0a6b9464696d7d3d2586a","source":{"kind":"arxiv","id":"1007.0113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0113","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0113v1","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0113","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"ABFHP3WETQI5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ABFHP3WETQI5W5IH","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ABFHP3WE","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ABFHP3WETQI5W5IHNKYJ2BTZQD","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-01T09:48:24Z","cross_cats_sorted":[],"title_canon_sha256":"bf09f3e1e04cb2286b87e3a80fc13b097d35fd5acc5b8000b2465590934562c9","abstract_canon_sha256":"51873e7e023bac3f087f97d76ed81cc88b228bda17f21cf27b9197048c21d930"},"schema_version":"1.0"},"canonical_sha256":"004a77eec49c11db75076ab09d067980ecbdffb0baa0a6b9464696d7d3d2586a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:22.948275Z","signature_b64":"+nzTO4EZHxJwi+leLhvKVzrL/lsA/Tw9ET7gJowOcDht02fgxcO3dAfsXbphtSd/Syb5N1meWCQISb5688CTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"004a77eec49c11db75076ab09d067980ecbdffb0baa0a6b9464696d7d3d2586a","last_reissued_at":"2026-05-18T00:37:22.947645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:22.947645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0113","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":"2026-05-18T00:37:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXKGireAstpwiTrjQZmx4/FFtr+x6JkHxwxOseTdbzWHkn2lVhlvTvWKp3XzIiH+bcGcn3kGWnRJLmMmyuHOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:38:27.942586Z"},"content_sha256":"53cc5cb7d1038cd1a56ba4485e076c83cac32010b8c9d9274575965659a0f4ce","schema_version":"1.0","event_id":"sha256:53cc5cb7d1038cd1a56ba4485e076c83cac32010b8c9d9274575965659a0f4ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ABFHP3WETQI5W5IHNKYJ2BTZQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert Modules - Square Roots of Positive Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael Skeide","submitted_at":"2010-07-01T09:48:24Z","abstract_excerpt":"We reflect on the notions of positivity and square roots. We review many examples which underline our thesis that square roots of positive maps related to *-algebras are Hilbert modules. As a result of our considerations we discuss requirements a notion of positivity on a *-algebra should fulfill and derive some basic consequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0113","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":"2026-05-18T00:37:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bsOVCBCa+92vEvgnenngHQYF2Mm100v8fEpzKjDBqDmMKhTcKay2wIDxFI32YyKlHYnXeul1qkYnXd8dh6WzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:38:27.943248Z"},"content_sha256":"57d9486c7e7b35eb20605c5abf0cdedebf50ff1d8f49f2fd17956329215da81f","schema_version":"1.0","event_id":"sha256:57d9486c7e7b35eb20605c5abf0cdedebf50ff1d8f49f2fd17956329215da81f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD/bundle.json","state_url":"https://pith.science/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD/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":"2026-06-11T10:38:27Z","links":{"resolver":"https://pith.science/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD","bundle":"https://pith.science/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD/bundle.json","state":"https://pith.science/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABFHP3WETQI5W5IHNKYJ2BTZQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ABFHP3WETQI5W5IHNKYJ2BTZQD","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":"51873e7e023bac3f087f97d76ed81cc88b228bda17f21cf27b9197048c21d930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-01T09:48:24Z","title_canon_sha256":"bf09f3e1e04cb2286b87e3a80fc13b097d35fd5acc5b8000b2465590934562c9"},"schema_version":"1.0","source":{"id":"1007.0113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0113","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0113v1","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0113","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"ABFHP3WETQI5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ABFHP3WETQI5W5IH","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ABFHP3WE","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:57d9486c7e7b35eb20605c5abf0cdedebf50ff1d8f49f2fd17956329215da81f","target":"graph","created_at":"2026-05-18T00:37:22Z","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 reflect on the notions of positivity and square roots. We review many examples which underline our thesis that square roots of positive maps related to *-algebras are Hilbert modules. As a result of our considerations we discuss requirements a notion of positivity on a *-algebra should fulfill and derive some basic consequences.","authors_text":"Michael Skeide","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-01T09:48:24Z","title":"Hilbert Modules - Square Roots of Positive Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0113","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":"sha256:53cc5cb7d1038cd1a56ba4485e076c83cac32010b8c9d9274575965659a0f4ce","target":"record","created_at":"2026-05-18T00:37:22Z","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":"51873e7e023bac3f087f97d76ed81cc88b228bda17f21cf27b9197048c21d930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-01T09:48:24Z","title_canon_sha256":"bf09f3e1e04cb2286b87e3a80fc13b097d35fd5acc5b8000b2465590934562c9"},"schema_version":"1.0","source":{"id":"1007.0113","kind":"arxiv","version":1}},"canonical_sha256":"004a77eec49c11db75076ab09d067980ecbdffb0baa0a6b9464696d7d3d2586a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"004a77eec49c11db75076ab09d067980ecbdffb0baa0a6b9464696d7d3d2586a","first_computed_at":"2026-05-18T00:37:22.947645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:22.947645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nzTO4EZHxJwi+leLhvKVzrL/lsA/Tw9ET7gJowOcDht02fgxcO3dAfsXbphtSd/Syb5N1meWCQISb5688CTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:22.948275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53cc5cb7d1038cd1a56ba4485e076c83cac32010b8c9d9274575965659a0f4ce","sha256:57d9486c7e7b35eb20605c5abf0cdedebf50ff1d8f49f2fd17956329215da81f"],"state_sha256":"abccd5298016d878e8650e518f0e13d1bf9143e88fb8e56104694a195b27065e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRzSYlRYwKZC82GFBxTPEcQnkUtwEhhoarCesb5+EsF7jJAA/wB46gMtkb1/NSEvm0x9eEyvno9YfVq4sb/RAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:38:27.947136Z","bundle_sha256":"13aa0b28ef946b37e6e2cf77853b028522e37ca25109d5cf391e127a80262aec"}}