{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6XNSAD7HGCDKWE7NR62HRFAJJI","short_pith_number":"pith:6XNSAD7H","schema_version":"1.0","canonical_sha256":"f5db200fe73086ab13ed8fb47894094a224d60af0ba74e5180d76bee515ae242","source":{"kind":"arxiv","id":"1609.08498","version":1},"attestation_state":"computed","paper":{"title":"Towards a Perron--Frobenius Theory for Eventually Positive Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Jochen Gl\\\"uck","submitted_at":"2016-09-27T15:33:59Z","abstract_excerpt":"This article is a contribution to the spectral theory of so-called eventually positive operators, i.e.\\ operators $T$ which may not be positive but whose powers $T^n$ become positive for large enough $n$. While the spectral theory of such operators is well understood in finite dimensions, the infinite dimensional case has received much less attention in the literature.\n  We show that several sensible notions of \"eventual positivity\" can be defined in the infinite dimensional setting, and in contrast to the finite dimensional case those notions do not in general coincide. We then prove a variet"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.08498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-09-27T15:33:59Z","cross_cats_sorted":[],"title_canon_sha256":"d5060c8c0151692f1d6d7c5b5b5477a1763caf9232fc27485abd05cfa0e0127a","abstract_canon_sha256":"fecfcd9f946001ff5a02b9f885848b30a7843b73a9cee5d49c833eb6f556d100"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:45.775277Z","signature_b64":"KsWg0922KhsQFJYV+fnWPiApidMb+6HVW7RURQTiz19x97FnT/08XPNqDhqltmmHiSkkUY00O8+hzAnB6cd8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5db200fe73086ab13ed8fb47894094a224d60af0ba74e5180d76bee515ae242","last_reissued_at":"2026-05-18T01:03:45.774893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:45.774893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a Perron--Frobenius Theory for Eventually Positive Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Jochen Gl\\\"uck","submitted_at":"2016-09-27T15:33:59Z","abstract_excerpt":"This article is a contribution to the spectral theory of so-called eventually positive operators, i.e.\\ operators $T$ which may not be positive but whose powers $T^n$ become positive for large enough $n$. While the spectral theory of such operators is well understood in finite dimensions, the infinite dimensional case has received much less attention in the literature.\n  We show that several sensible notions of \"eventual positivity\" can be defined in the infinite dimensional setting, and in contrast to the finite dimensional case those notions do not in general coincide. We then prove a variet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08498","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.08498","created_at":"2026-05-18T01:03:45.774949+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.08498v1","created_at":"2026-05-18T01:03:45.774949+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08498","created_at":"2026-05-18T01:03:45.774949+00:00"},{"alias_kind":"pith_short_12","alias_value":"6XNSAD7HGCDK","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"6XNSAD7HGCDKWE7N","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"6XNSAD7H","created_at":"2026-05-18T12:30:04.600751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI","json":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI.json","graph_json":"https://pith.science/api/pith-number/6XNSAD7HGCDKWE7NR62HRFAJJI/graph.json","events_json":"https://pith.science/api/pith-number/6XNSAD7HGCDKWE7NR62HRFAJJI/events.json","paper":"https://pith.science/paper/6XNSAD7H"},"agent_actions":{"view_html":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI","download_json":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI.json","view_paper":"https://pith.science/paper/6XNSAD7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.08498&json=true","fetch_graph":"https://pith.science/api/pith-number/6XNSAD7HGCDKWE7NR62HRFAJJI/graph.json","fetch_events":"https://pith.science/api/pith-number/6XNSAD7HGCDKWE7NR62HRFAJJI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI/action/storage_attestation","attest_author":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI/action/author_attestation","sign_citation":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI/action/citation_signature","submit_replication":"https://pith.science/pith/6XNSAD7HGCDKWE7NR62HRFAJJI/action/replication_record"}},"created_at":"2026-05-18T01:03:45.774949+00:00","updated_at":"2026-05-18T01:03:45.774949+00:00"}