{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:22L46ELJKWQESMKGAZTI4VLCHQ","short_pith_number":"pith:22L46ELJ","canonical_record":{"source":{"id":"1511.05374","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-17T12:19:32Z","cross_cats_sorted":["math.CA","math.SP"],"title_canon_sha256":"abe9fd1d0a2a9434a643753e79518400ad4a8b19c2030076fd3a99231d0b4b8e","abstract_canon_sha256":"8ee99f6b569a91d30faf98ea0beb0244a4604935ea60de952f952dc76702849d"},"schema_version":"1.0"},"canonical_sha256":"d697cf116955a049314606668e55623c1fd8606d554ee5108a135b8c974742a8","source":{"kind":"arxiv","id":"1511.05374","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05374","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05374v3","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05374","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"pith_short_12","alias_value":"22L46ELJKWQE","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"22L46ELJKWQESMKG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"22L46ELJ","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:22L46ELJKWQESMKGAZTI4VLCHQ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05374","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-17T12:19:32Z","cross_cats_sorted":["math.CA","math.SP"],"title_canon_sha256":"abe9fd1d0a2a9434a643753e79518400ad4a8b19c2030076fd3a99231d0b4b8e","abstract_canon_sha256":"8ee99f6b569a91d30faf98ea0beb0244a4604935ea60de952f952dc76702849d"},"schema_version":"1.0"},"canonical_sha256":"d697cf116955a049314606668e55623c1fd8606d554ee5108a135b8c974742a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:07.796304Z","signature_b64":"w/gXVvy26a9DGHGlzjV4U3xPIuPirI2jHr+Ixi+rGHTvKT24/zDKb/X8mqDuMyRdIwWbxEjt0lzmdwsAVBWfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d697cf116955a049314606668e55623c1fd8606d554ee5108a135b8c974742a8","last_reissued_at":"2026-05-17T23:54:07.795737Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:07.795737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05374","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":"2026-05-17T23:54:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGq9Z+g7CxJRm3bQEFL3iMfRITTPpG9J2kzosCr43bA5AwohCiC5137+B5vNorz165ipcHQ1ySuzrl+cYz5FAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:22:26.030981Z"},"content_sha256":"4cc5f4d3a07668ba37548cd05dc54d910bfbf545136349ef6fc2b447970a9b83","schema_version":"1.0","event_id":"sha256:4cc5f4d3a07668ba37548cd05dc54d910bfbf545136349ef6fc2b447970a9b83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:22L46ELJKWQESMKGAZTI4VLCHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics for infinite systems of differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.SP"],"primary_cat":"math.FA","authors_text":"David Seifert, Lassi Paunonen","submitted_at":"2015-11-17T12:19:32Z","abstract_excerpt":"This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a characterisation, in terms of convergence of certain Ces\\`aro averages, of those initial values which lead to convergent solutions. Moreover, we obtain estimates on the rate of convergence for solutions whose initial values satisfy a stronger ergodic condition. These results rely on a detailed spectral analysis of the operator describing the system, which is made "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05374","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":"2026-05-17T23:54:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9GRD6JdjXF255cpiavNfeUA5HNEdNDJm/JZTeKoqphA0kYiFmOfBvuJ9t7CkUuiHKiiAYq6DspBEkOrd8FhwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:22:26.031346Z"},"content_sha256":"bfa069b40872def54e0f1ef569629c011653b1a7a8e71e59bf53bf192d28f340","schema_version":"1.0","event_id":"sha256:bfa069b40872def54e0f1ef569629c011653b1a7a8e71e59bf53bf192d28f340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22L46ELJKWQESMKGAZTI4VLCHQ/bundle.json","state_url":"https://pith.science/pith/22L46ELJKWQESMKGAZTI4VLCHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22L46ELJKWQESMKGAZTI4VLCHQ/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":"2026-06-24T07:22:26Z","links":{"resolver":"https://pith.science/pith/22L46ELJKWQESMKGAZTI4VLCHQ","bundle":"https://pith.science/pith/22L46ELJKWQESMKGAZTI4VLCHQ/bundle.json","state":"https://pith.science/pith/22L46ELJKWQESMKGAZTI4VLCHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22L46ELJKWQESMKGAZTI4VLCHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:22L46ELJKWQESMKGAZTI4VLCHQ","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":"8ee99f6b569a91d30faf98ea0beb0244a4604935ea60de952f952dc76702849d","cross_cats_sorted":["math.CA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-17T12:19:32Z","title_canon_sha256":"abe9fd1d0a2a9434a643753e79518400ad4a8b19c2030076fd3a99231d0b4b8e"},"schema_version":"1.0","source":{"id":"1511.05374","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05374","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05374v3","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05374","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"pith_short_12","alias_value":"22L46ELJKWQE","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"22L46ELJKWQESMKG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"22L46ELJ","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:bfa069b40872def54e0f1ef569629c011653b1a7a8e71e59bf53bf192d28f340","target":"graph","created_at":"2026-05-17T23:54:07Z","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":"This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a characterisation, in terms of convergence of certain Ces\\`aro averages, of those initial values which lead to convergent solutions. Moreover, we obtain estimates on the rate of convergence for solutions whose initial values satisfy a stronger ergodic condition. These results rely on a detailed spectral analysis of the operator describing the system, which is made ","authors_text":"David Seifert, Lassi Paunonen","cross_cats":["math.CA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-17T12:19:32Z","title":"Asymptotics for infinite systems of differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05374","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":"sha256:4cc5f4d3a07668ba37548cd05dc54d910bfbf545136349ef6fc2b447970a9b83","target":"record","created_at":"2026-05-17T23:54:07Z","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":"8ee99f6b569a91d30faf98ea0beb0244a4604935ea60de952f952dc76702849d","cross_cats_sorted":["math.CA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-17T12:19:32Z","title_canon_sha256":"abe9fd1d0a2a9434a643753e79518400ad4a8b19c2030076fd3a99231d0b4b8e"},"schema_version":"1.0","source":{"id":"1511.05374","kind":"arxiv","version":3}},"canonical_sha256":"d697cf116955a049314606668e55623c1fd8606d554ee5108a135b8c974742a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d697cf116955a049314606668e55623c1fd8606d554ee5108a135b8c974742a8","first_computed_at":"2026-05-17T23:54:07.795737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:07.795737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w/gXVvy26a9DGHGlzjV4U3xPIuPirI2jHr+Ixi+rGHTvKT24/zDKb/X8mqDuMyRdIwWbxEjt0lzmdwsAVBWfCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:07.796304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05374","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cc5f4d3a07668ba37548cd05dc54d910bfbf545136349ef6fc2b447970a9b83","sha256:bfa069b40872def54e0f1ef569629c011653b1a7a8e71e59bf53bf192d28f340"],"state_sha256":"091567ca8c50060411312a04f5f3e270c28017464f5373d595e6b8d46d8e93dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQz0kSEcV+cgFfZkTlpfQVSgQFc/opz7VhOk/CETSY92UUS5/hKYLMDoPoTGoe1x5H+C+2FKcZNm9QrJY1/9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:22:26.033353Z","bundle_sha256":"8834ad85d47960a825a725f08fa621d4bebdf69d5a95cb1765017bb71ea2f460"}}