{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:SW6YFRXFZJ4J2PAJUCGUFL6UXZ","short_pith_number":"pith:SW6YFRXF","canonical_record":{"source":{"id":"0810.3619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-20T17:47:12Z","cross_cats_sorted":[],"title_canon_sha256":"3c6ffb983184bc57a4f70e10fcb6f89c733dedb5ec47eec2a607751039afb5b2","abstract_canon_sha256":"b81e59fd2202755a3d8bacdcc3b506d0b4909b09f311e276bb57d3de951d0ee2"},"schema_version":"1.0"},"canonical_sha256":"95bd82c6e5ca789d3c09a08d42afd4be5948fd6906264831f0556aaba82ec2c9","source":{"kind":"arxiv","id":"0810.3619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3619","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3619v1","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3619","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"SW6YFRXFZJ4J","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SW6YFRXFZJ4J2PAJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SW6YFRXF","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:SW6YFRXFZJ4J2PAJUCGUFL6UXZ","target":"record","payload":{"canonical_record":{"source":{"id":"0810.3619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-20T17:47:12Z","cross_cats_sorted":[],"title_canon_sha256":"3c6ffb983184bc57a4f70e10fcb6f89c733dedb5ec47eec2a607751039afb5b2","abstract_canon_sha256":"b81e59fd2202755a3d8bacdcc3b506d0b4909b09f311e276bb57d3de951d0ee2"},"schema_version":"1.0"},"canonical_sha256":"95bd82c6e5ca789d3c09a08d42afd4be5948fd6906264831f0556aaba82ec2c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:23.886305Z","signature_b64":"ydznHg1mkZEuHxrkqpORVH4J5K5SYb6aNdJxnQAtrOE7Abl2+3lVcRHtQnnAAuaWfukwqstkVZ4SOyAX8ODRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95bd82c6e5ca789d3c09a08d42afd4be5948fd6906264831f0556aaba82ec2c9","last_reissued_at":"2026-05-18T02:15:23.885585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:23.885585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.3619","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":"2026-05-18T02:15:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIqzaPBJSJHAS+sJH3uU6UO2euI7ujaXr961//bglVoiDgDnwqqCotVF1lUAmqhRG3u9gnmMzZHgV2fxYua5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:41:12.597257Z"},"content_sha256":"65542cfc2dd0cead6031535551718f090659c2c9fe849044d2868f338c17da7e","schema_version":"1.0","event_id":"sha256:65542cfc2dd0cead6031535551718f090659c2c9fe849044d2868f338c17da7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:SW6YFRXFZJ4J2PAJUCGUFL6UXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On regularization methods of EM-Kaczmarz type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Antonio Leitao, Elena Resmerita, Markus Haltmeier","submitted_at":"2008-10-20T17:47:12Z","abstract_excerpt":"We consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established ordered-subsets expectation-maximization iteration (OS-EM). We show monotonicity properties of the methods and present a numerical experiment which indicates that the extended OS-EM methods we propose are much faster than the standard EM algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3619","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":"2026-05-18T02:15:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eo9tRHgjXWyrEoQeABwGw0LmEvhIqPMvK+UCDoo7GSS0mSeLbybYYzocpFtDDQ9RlF2dZpCS02C1RpCt+leJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:41:12.597612Z"},"content_sha256":"c387c04040e704ba4ab43019bb99c1b8c9043ba485f23bc822e2964da9b1390f","schema_version":"1.0","event_id":"sha256:c387c04040e704ba4ab43019bb99c1b8c9043ba485f23bc822e2964da9b1390f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ/bundle.json","state_url":"https://pith.science/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ/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":"2026-06-12T01:41:12Z","links":{"resolver":"https://pith.science/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ","bundle":"https://pith.science/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ/bundle.json","state":"https://pith.science/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SW6YFRXFZJ4J2PAJUCGUFL6UXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:SW6YFRXFZJ4J2PAJUCGUFL6UXZ","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":"b81e59fd2202755a3d8bacdcc3b506d0b4909b09f311e276bb57d3de951d0ee2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-20T17:47:12Z","title_canon_sha256":"3c6ffb983184bc57a4f70e10fcb6f89c733dedb5ec47eec2a607751039afb5b2"},"schema_version":"1.0","source":{"id":"0810.3619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3619","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3619v1","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3619","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"SW6YFRXFZJ4J","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SW6YFRXFZJ4J2PAJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SW6YFRXF","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c387c04040e704ba4ab43019bb99c1b8c9043ba485f23bc822e2964da9b1390f","target":"graph","created_at":"2026-05-18T02:15:23Z","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 consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established ordered-subsets expectation-maximization iteration (OS-EM). We show monotonicity properties of the methods and present a numerical experiment which indicates that the extended OS-EM methods we propose are much faster than the standard EM algorithm.","authors_text":"Antonio Leitao, Elena Resmerita, Markus Haltmeier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-20T17:47:12Z","title":"On regularization methods of EM-Kaczmarz type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3619","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":"sha256:65542cfc2dd0cead6031535551718f090659c2c9fe849044d2868f338c17da7e","target":"record","created_at":"2026-05-18T02:15:23Z","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":"b81e59fd2202755a3d8bacdcc3b506d0b4909b09f311e276bb57d3de951d0ee2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-20T17:47:12Z","title_canon_sha256":"3c6ffb983184bc57a4f70e10fcb6f89c733dedb5ec47eec2a607751039afb5b2"},"schema_version":"1.0","source":{"id":"0810.3619","kind":"arxiv","version":1}},"canonical_sha256":"95bd82c6e5ca789d3c09a08d42afd4be5948fd6906264831f0556aaba82ec2c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95bd82c6e5ca789d3c09a08d42afd4be5948fd6906264831f0556aaba82ec2c9","first_computed_at":"2026-05-18T02:15:23.885585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:23.885585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ydznHg1mkZEuHxrkqpORVH4J5K5SYb6aNdJxnQAtrOE7Abl2+3lVcRHtQnnAAuaWfukwqstkVZ4SOyAX8ODRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:23.886305Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.3619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65542cfc2dd0cead6031535551718f090659c2c9fe849044d2868f338c17da7e","sha256:c387c04040e704ba4ab43019bb99c1b8c9043ba485f23bc822e2964da9b1390f"],"state_sha256":"a2f05de8d15f357265c02b07c6dcff49bbd98850c2f1fb58b8a9e4665e68c6d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9m0vtmTmWt+UucBjOZnfUjDpiFurbEkgu1hVV1j6ofx2ys/Mw3OhBU3oIRr9g+h5OhvHtrS+Lw7Crpgx9lAAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:41:12.599468Z","bundle_sha256":"9e9ae58d0926fd4c518d34983bd42324f9e635d31bb86a1b7c5c30ba49a87e8c"}}