{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NUH3CRI77AQQYU2M665ELGB2L6","short_pith_number":"pith:NUH3CRI7","canonical_record":{"source":{"id":"1512.04589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-14T22:20:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b1b6828358ee28022406b1ae3531404bde8ad8769fc79b35398b8755486a7553","abstract_canon_sha256":"caecc00ca8f4d552240415d9828adec9555b1bf4eeea9097509219e97e5803f4"},"schema_version":"1.0"},"canonical_sha256":"6d0fb1451ff8210c534cf7ba45983a5f84b106936a6f8d29315c05dd6ad51625","source":{"kind":"arxiv","id":"1512.04589","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04589","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04589v3","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04589","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"NUH3CRI77AQQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUH3CRI77AQQYU2M","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUH3CRI7","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NUH3CRI77AQQYU2M665ELGB2L6","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-14T22:20:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b1b6828358ee28022406b1ae3531404bde8ad8769fc79b35398b8755486a7553","abstract_canon_sha256":"caecc00ca8f4d552240415d9828adec9555b1bf4eeea9097509219e97e5803f4"},"schema_version":"1.0"},"canonical_sha256":"6d0fb1451ff8210c534cf7ba45983a5f84b106936a6f8d29315c05dd6ad51625","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:55.442326Z","signature_b64":"KmjTKSf1r91aMZcMo/QNUKtJszunPAkopq6jWYTBv1y2BWSJyZOw+pn+UoFW39Y8Q3rp2mL5VMnswxxkNCERDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d0fb1451ff8210c534cf7ba45983a5f84b106936a6f8d29315c05dd6ad51625","last_reissued_at":"2026-05-18T00:17:55.441754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:55.441754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04589","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R3jkut+iOtpIMr5qFPSOtSqy+drIzIAO66dzvXSdY8+JN5COq1/qsI3b/SLwXzB5Hpzi6aGhCu+YZXic1FZXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:14:46.589233Z"},"content_sha256":"630a8ca0bcfff06ad06f84b649e10bad3f161eb4e0e1b098363fa2905c171580","schema_version":"1.0","event_id":"sha256:630a8ca0bcfff06ad06f84b649e10bad3f161eb4e0e1b098363fa2905c171580"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NUH3CRI77AQQYU2M665ELGB2L6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$C_0$-sequentially equicontinuous semigroups: theory and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Mauro Rosestolato, Salvatore Federico","submitted_at":"2015-12-14T22:20:22Z","abstract_excerpt":"We present and apply a theory of one parameter $C_0$-semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker notion of sequential equicontinuity, we prove the basic results of the classical theory of $C_0$-equicontinuous semigroups: we show that the semigroup is uniquely identified by its generator and we provide a generation theorem in the spirit of the celebrated Hille-Yosida theorem. Then, we particularize the theory in some functional spaces and identify two locally convex topologies that allow to gather u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04589","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ec4CCzzrFTcoWM6FVIPCEdy8HAAdtIpXiLww9ArDGNj5BUByfeQ4kEHEHHpFjn4+r7G2mC3YHr9jUxdZCgKSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:14:46.589875Z"},"content_sha256":"d8cf4db5960f6103bca33123b1efd8ddb5ef378dcce047c6a6a27420049d176c","schema_version":"1.0","event_id":"sha256:d8cf4db5960f6103bca33123b1efd8ddb5ef378dcce047c6a6a27420049d176c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUH3CRI77AQQYU2M665ELGB2L6/bundle.json","state_url":"https://pith.science/pith/NUH3CRI77AQQYU2M665ELGB2L6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUH3CRI77AQQYU2M665ELGB2L6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T11:14:46Z","links":{"resolver":"https://pith.science/pith/NUH3CRI77AQQYU2M665ELGB2L6","bundle":"https://pith.science/pith/NUH3CRI77AQQYU2M665ELGB2L6/bundle.json","state":"https://pith.science/pith/NUH3CRI77AQQYU2M665ELGB2L6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUH3CRI77AQQYU2M665ELGB2L6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NUH3CRI77AQQYU2M665ELGB2L6","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":"caecc00ca8f4d552240415d9828adec9555b1bf4eeea9097509219e97e5803f4","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-14T22:20:22Z","title_canon_sha256":"b1b6828358ee28022406b1ae3531404bde8ad8769fc79b35398b8755486a7553"},"schema_version":"1.0","source":{"id":"1512.04589","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04589","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04589v3","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04589","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"NUH3CRI77AQQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUH3CRI77AQQYU2M","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUH3CRI7","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:d8cf4db5960f6103bca33123b1efd8ddb5ef378dcce047c6a6a27420049d176c","target":"graph","created_at":"2026-05-18T00:17:55Z","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":"We present and apply a theory of one parameter $C_0$-semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker notion of sequential equicontinuity, we prove the basic results of the classical theory of $C_0$-equicontinuous semigroups: we show that the semigroup is uniquely identified by its generator and we provide a generation theorem in the spirit of the celebrated Hille-Yosida theorem. Then, we particularize the theory in some functional spaces and identify two locally convex topologies that allow to gather u","authors_text":"Mauro Rosestolato, Salvatore Federico","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-14T22:20:22Z","title":"$C_0$-sequentially equicontinuous semigroups: theory and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04589","kind":"arxiv","version":3},"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":"sha256:630a8ca0bcfff06ad06f84b649e10bad3f161eb4e0e1b098363fa2905c171580","target":"record","created_at":"2026-05-18T00:17:55Z","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":"caecc00ca8f4d552240415d9828adec9555b1bf4eeea9097509219e97e5803f4","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-14T22:20:22Z","title_canon_sha256":"b1b6828358ee28022406b1ae3531404bde8ad8769fc79b35398b8755486a7553"},"schema_version":"1.0","source":{"id":"1512.04589","kind":"arxiv","version":3}},"canonical_sha256":"6d0fb1451ff8210c534cf7ba45983a5f84b106936a6f8d29315c05dd6ad51625","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d0fb1451ff8210c534cf7ba45983a5f84b106936a6f8d29315c05dd6ad51625","first_computed_at":"2026-05-18T00:17:55.441754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:55.441754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KmjTKSf1r91aMZcMo/QNUKtJszunPAkopq6jWYTBv1y2BWSJyZOw+pn+UoFW39Y8Q3rp2mL5VMnswxxkNCERDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:55.442326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04589","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:630a8ca0bcfff06ad06f84b649e10bad3f161eb4e0e1b098363fa2905c171580","sha256:d8cf4db5960f6103bca33123b1efd8ddb5ef378dcce047c6a6a27420049d176c"],"state_sha256":"8f3b465dc4848395376080fae7f1312a2ba5ceb0596e5bb674bacfaf81c8a752"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hKXjZzsWQgoYupkU/GBYSFQOX+jDwvTOP88mw8rh5+v1Am0g8b27gN3iqk6kFFEf08uCVXgz1WmAJUu9hP0LAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:14:46.594338Z","bundle_sha256":"817bae66d2e05b0e1b737d24533f22261225ce7fcf36def43a45cd2ea9e19a41"}}