{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2KF3SMFR4VXIVL6XUCTIXDOCH2","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":"94cdcdfbae48b106cbb265d5671d849a7d7d8de6f275a8589c6de9e9be156cea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-25T11:09:46Z","title_canon_sha256":"74be1fda6c8ff724a386e07a167de23aca778d7121c8f0efe0cbf960bc78aae9"},"schema_version":"1.0","source":{"id":"1108.5058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5058","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5058v1","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5058","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"2KF3SMFR4VXI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2KF3SMFR4VXIVL6X","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2KF3SMFR","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:f74b7c86438b443720644847e9e246eb5f6b30b53577b002bc9e66f4f0a3da57","target":"graph","created_at":"2026-05-18T04:14:45Z","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":"In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. We motivate our approach by illustrative examples.","authors_text":"Ioan-Lucian Popa, Mihail Megan, Traian Ceausu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-25T11:09:46Z","title":"Exponential dichotomies for linear discrete-time systems in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5058","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":"sha256:58b3c8eb19b89356b29fc5bb9453c838690232c1589e0064fa0185336a6bf77e","target":"record","created_at":"2026-05-18T04:14:45Z","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":"94cdcdfbae48b106cbb265d5671d849a7d7d8de6f275a8589c6de9e9be156cea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-25T11:09:46Z","title_canon_sha256":"74be1fda6c8ff724a386e07a167de23aca778d7121c8f0efe0cbf960bc78aae9"},"schema_version":"1.0","source":{"id":"1108.5058","kind":"arxiv","version":1}},"canonical_sha256":"d28bb930b1e56e8aafd7a0a68b8dc23ea160969b84a8cc40a7f7aafe8e5241d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d28bb930b1e56e8aafd7a0a68b8dc23ea160969b84a8cc40a7f7aafe8e5241d0","first_computed_at":"2026-05-18T04:14:45.487712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:45.487712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qOy6cPGbVvMky3csfMTL8cPjjs1akOZmeXXths5MWVAJsuThN/nLG/3y0wE8EDru8WxxZrLZcwuSaoyYQqQlCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:45.488199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58b3c8eb19b89356b29fc5bb9453c838690232c1589e0064fa0185336a6bf77e","sha256:f74b7c86438b443720644847e9e246eb5f6b30b53577b002bc9e66f4f0a3da57"],"state_sha256":"c4cdce092aa24838c67b17cb788aed02934af6e3b73d3abf020e618bad54af5f"}