{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DZEUXROBHJ75YLLGC26A2NLILM","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":"32a6089f05c65fba8586729ba2edd9f028b97a1aaafa4b6fda66310e59443942","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-20T16:48:53Z","title_canon_sha256":"8aaa2a13e37d9c3aa1da4b2638e42ab4612074aa9fca2588ee17c543c1a81fc0"},"schema_version":"1.0","source":{"id":"1212.5135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5135","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5135v1","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5135","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"pith_short_12","alias_value":"DZEUXROBHJ75","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DZEUXROBHJ75YLLG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DZEUXROB","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:4bbed335ffdde0475f7a6bac6774d9ce4fa8f8b2b6222333424080e2b9a07b53","target":"graph","created_at":"2026-05-18T03:38:03Z","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":"For totally ergodic Z^2-actions a collection of weak limits provide the set {2,4, ..., 2 ^ n} of spectral multiplicities for their tensor product. Our conditions allow to obtain a similar result for mixing actions via some limit procedure.","authors_text":"R. A. Konev, V. V. Ryzhikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-20T16:48:53Z","title":"On spectral multiplicities {2, 4,..., 2^n} for totally ergodic Z^2-actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5135","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":"sha256:6184b4850fd6f1bf091c0c2e9ed60fa72f380255cbdbb6db520738c76b78ea15","target":"record","created_at":"2026-05-18T03:38:03Z","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":"32a6089f05c65fba8586729ba2edd9f028b97a1aaafa4b6fda66310e59443942","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-20T16:48:53Z","title_canon_sha256":"8aaa2a13e37d9c3aa1da4b2638e42ab4612074aa9fca2588ee17c543c1a81fc0"},"schema_version":"1.0","source":{"id":"1212.5135","kind":"arxiv","version":1}},"canonical_sha256":"1e494bc5c13a7fdc2d6616bc0d35685b2fdf8b7bb215805ac6a47e63dd6d2c27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e494bc5c13a7fdc2d6616bc0d35685b2fdf8b7bb215805ac6a47e63dd6d2c27","first_computed_at":"2026-05-18T03:38:03.715014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:03.715014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RX0D9BLvE1IQ9/5LIFxQULbFduy/oxYASAxt2KuFdcY0iW4HL/Ju/WpmGXvOA1CAtWOydRocqfn/1CUZ14JYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:03.715745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6184b4850fd6f1bf091c0c2e9ed60fa72f380255cbdbb6db520738c76b78ea15","sha256:4bbed335ffdde0475f7a6bac6774d9ce4fa8f8b2b6222333424080e2b9a07b53"],"state_sha256":"fbc58af741005e488441e6112589edce9f9d40bf68ef1928279ad77e30961db9"}