{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JACCPVBVGCTFK4N4WJQGUH3YBC","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":"adced017da0f639784e7dc4d459ed5dc901df20c11a4419bb989521a2d7afa80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-27T12:42:11Z","title_canon_sha256":"cb7ecf583cd0727aaf95faabfe57333343c11531a648d13fe38a1a1c0af2f8a6"},"schema_version":"1.0","source":{"id":"2505.21123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21123","created_at":"2026-07-05T11:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21123v2","created_at":"2026-07-05T11:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21123","created_at":"2026-07-05T11:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"JACCPVBVGCTF","created_at":"2026-07-05T11:20:12Z"},{"alias_kind":"pith_short_16","alias_value":"JACCPVBVGCTFK4N4","created_at":"2026-07-05T11:20:12Z"},{"alias_kind":"pith_short_8","alias_value":"JACCPVBV","created_at":"2026-07-05T11:20:12Z"}],"graph_snapshots":[{"event_id":"sha256:b3a4531055bbdc188aa3998de512748c0c007b7abd9bec1b0b3fd426d75e5a53","target":"graph","created_at":"2026-07-05T11:20:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.21123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of linear relations.","authors_text":"Maximiliano Contino, M. Laura Arias, Stefania Marcantognini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-27T12:42:11Z","title":"Factorizations of linear relations by idempotents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21123","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:d54b3be98966a535e2917470bd6931ba9092da0f3bf5260ba614ff03ac8fe8d1","target":"record","created_at":"2026-07-05T11:20:12Z","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":"adced017da0f639784e7dc4d459ed5dc901df20c11a4419bb989521a2d7afa80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-27T12:42:11Z","title_canon_sha256":"cb7ecf583cd0727aaf95faabfe57333343c11531a648d13fe38a1a1c0af2f8a6"},"schema_version":"1.0","source":{"id":"2505.21123","kind":"arxiv","version":2}},"canonical_sha256":"480427d43530a65571bcb2606a1f7808a9f0987febf7b935fff06866166cb96d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480427d43530a65571bcb2606a1f7808a9f0987febf7b935fff06866166cb96d","first_computed_at":"2026-07-05T11:20:12.457885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:12.457885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ch7gvlMJKFqBZ6FJSbQikT+Ku7Y61B0Fb4X0yLfjQ8YpIxWlUl1A2P9zzbJD/X2gJB5eKQ4dEhRp/elZ0NuWCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:12.458327Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d54b3be98966a535e2917470bd6931ba9092da0f3bf5260ba614ff03ac8fe8d1","sha256:b3a4531055bbdc188aa3998de512748c0c007b7abd9bec1b0b3fd426d75e5a53"],"state_sha256":"3d09bbffefc9a5dacfbb7de97e6817339cc3d49b54058b01efee0a54d12ecf2e"}