{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JMGSPYJP3FAOEAL3RUH43L5FHY","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":"6671b60915b1373e61a3c12375e8f3a89976640822e586f7271b53912400a768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:02:15Z","title_canon_sha256":"f99e59d4423c1c074c1d8c61f0fc8e15b207367527b18a0715f7d6587736a68a"},"schema_version":"1.0","source":{"id":"1310.7773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7773","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7773v2","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7773","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"JMGSPYJP3FAO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JMGSPYJP3FAOEAL3","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JMGSPYJP","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ba6661533c5b0f6668c192ce9625314aa98df933c87fdcb665249d08ad1af9ea","target":"graph","created_at":"2026-05-18T02:41:08Z","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":"The aim of this paper is twofold: (1) On the one hand, the paper revisits the spectral analysis of semigroups in a general Banach space setting. It presents some new and more general versions, and provides comprehensible proofs, of classical results such as the spectral mapping theorem, some (quantified) Weyl's Theorems and the Krein-Rutman Theorem. Motivated by evolution PDE applications, the results apply to a wide and natural class of generators which split as a dissipative part plus a more regular part, without assuming any symmetric structure on the operators nor Hilbert structure on the ","authors_text":"Justine Scher (CEREMADE), St\\'ephane Mischler (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:02:15Z","title":"Spectral analysis of semigroups and growth-fragmentation equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7773","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":"sha256:35e5fd201160900eaf61893fb2eebf5809b461c9d165c9331bdff4b565e935b8","target":"record","created_at":"2026-05-18T02:41:08Z","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":"6671b60915b1373e61a3c12375e8f3a89976640822e586f7271b53912400a768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:02:15Z","title_canon_sha256":"f99e59d4423c1c074c1d8c61f0fc8e15b207367527b18a0715f7d6587736a68a"},"schema_version":"1.0","source":{"id":"1310.7773","kind":"arxiv","version":2}},"canonical_sha256":"4b0d27e12fd940e2017b8d0fcdafa53e1945b2ac3676d8dc692b6ab0f7234141","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0d27e12fd940e2017b8d0fcdafa53e1945b2ac3676d8dc692b6ab0f7234141","first_computed_at":"2026-05-18T02:41:08.874514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:08.874514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTOfpACqQW6cZI/e1swRE1YpUkms+cYyDosd+BDjjN92ydIc4W79s/KhsuU5qiC7aaeqTFYzk4J32TDz1ARvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:08.874888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35e5fd201160900eaf61893fb2eebf5809b461c9d165c9331bdff4b565e935b8","sha256:ba6661533c5b0f6668c192ce9625314aa98df933c87fdcb665249d08ad1af9ea"],"state_sha256":"62c953349a9aa544a1997c92b9e9d7fd6f5664f185360010ff47eed6d0b783a5"}