{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2NULMRTHYOK6PZD65AEZPHL2MF","short_pith_number":"pith:2NULMRTH","canonical_record":{"source":{"id":"1303.7100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-28T11:19:43Z","cross_cats_sorted":[],"title_canon_sha256":"d78a05aa6ee10209e38ec246a593b2b933762d021276495fc5b818cb142e4c5e","abstract_canon_sha256":"8328340dd010928e6036b21e235c6c5b339ff3e2cba5e3b0ca09cdee2015d680"},"schema_version":"1.0"},"canonical_sha256":"d368b64667c395e7e47ee809979d7a61565c97cb6ed6834b537111668f89ba9e","source":{"kind":"arxiv","id":"1303.7100","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7100","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7100v1","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7100","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"2NULMRTHYOK6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2NULMRTHYOK6PZD6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2NULMRTH","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2NULMRTHYOK6PZD65AEZPHL2MF","target":"record","payload":{"canonical_record":{"source":{"id":"1303.7100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-28T11:19:43Z","cross_cats_sorted":[],"title_canon_sha256":"d78a05aa6ee10209e38ec246a593b2b933762d021276495fc5b818cb142e4c5e","abstract_canon_sha256":"8328340dd010928e6036b21e235c6c5b339ff3e2cba5e3b0ca09cdee2015d680"},"schema_version":"1.0"},"canonical_sha256":"d368b64667c395e7e47ee809979d7a61565c97cb6ed6834b537111668f89ba9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:38.252979Z","signature_b64":"kaY1V1L+bfky11ea3ON72C1pXn2j8OdoynStPrxTODnohuyRbTHEDJSvaIUGUkXlkdVQr8p4FDshPPcAtpx9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d368b64667c395e7e47ee809979d7a61565c97cb6ed6834b537111668f89ba9e","last_reissued_at":"2026-05-18T03:29:38.252483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:38.252483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.7100","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSgpd6v1tavCc2NX2IQY4BobSwSI5GYdYPm5ne3dRGhF0/bCPtJe3kZaE6idzVvh9IDtQNBbFkMK/jgh09AcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:14:48.516207Z"},"content_sha256":"7f60bb15dcc585eee3a7f4c2db622706444098155916839e39eb8ec9453da07d","schema_version":"1.0","event_id":"sha256:7f60bb15dcc585eee3a7f4c2db622706444098155916839e39eb8ec9453da07d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2NULMRTHYOK6PZD65AEZPHL2MF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-autonomous Honesty theory in abstract state spaces with applications to linear kinetic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Luisa Arlotti, Mustapha Mokhtar-Kharroubi (LM-Besan\\c{c}on)","submitted_at":"2013-03-28T11:19:43Z","abstract_excerpt":"We provide a honesty theory of substochastic evolution families in real abstract state space, extending to an non-autonomous setting the result obtained for $C_0$-semigroups in our recent contribution \\textit{[On perturbed substochastic semigroups in abstract state spaces, \\textit{Z. Anal. Anwend.} \\textbf{30}, 457--495, 2011]}. The link with the honesty theory of perturbed substochastic semigroups is established. Several applications to non-autonomous linear kinetic equations (linear Boltzmann equation and fragmentation equation) are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7100","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5REskBw39PgFt5P3gWEplZ7ottlbm1VZrwnG3GF4dTbaXIG5Icv/k9fSYd35B4XhNL1sScYbhTyWdagyKxNGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:14:48.516584Z"},"content_sha256":"30107a8ec8701aebd30ff8d8cfeebd8b09a73b89a83125231e186e13d0ecabb0","schema_version":"1.0","event_id":"sha256:30107a8ec8701aebd30ff8d8cfeebd8b09a73b89a83125231e186e13d0ecabb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NULMRTHYOK6PZD65AEZPHL2MF/bundle.json","state_url":"https://pith.science/pith/2NULMRTHYOK6PZD65AEZPHL2MF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NULMRTHYOK6PZD65AEZPHL2MF/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":"2026-06-20T14:14:48Z","links":{"resolver":"https://pith.science/pith/2NULMRTHYOK6PZD65AEZPHL2MF","bundle":"https://pith.science/pith/2NULMRTHYOK6PZD65AEZPHL2MF/bundle.json","state":"https://pith.science/pith/2NULMRTHYOK6PZD65AEZPHL2MF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NULMRTHYOK6PZD65AEZPHL2MF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2NULMRTHYOK6PZD65AEZPHL2MF","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":"8328340dd010928e6036b21e235c6c5b339ff3e2cba5e3b0ca09cdee2015d680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-28T11:19:43Z","title_canon_sha256":"d78a05aa6ee10209e38ec246a593b2b933762d021276495fc5b818cb142e4c5e"},"schema_version":"1.0","source":{"id":"1303.7100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7100","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7100v1","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7100","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"2NULMRTHYOK6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2NULMRTHYOK6PZD6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2NULMRTH","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:30107a8ec8701aebd30ff8d8cfeebd8b09a73b89a83125231e186e13d0ecabb0","target":"graph","created_at":"2026-05-18T03:29:38Z","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 provide a honesty theory of substochastic evolution families in real abstract state space, extending to an non-autonomous setting the result obtained for $C_0$-semigroups in our recent contribution \\textit{[On perturbed substochastic semigroups in abstract state spaces, \\textit{Z. Anal. Anwend.} \\textbf{30}, 457--495, 2011]}. The link with the honesty theory of perturbed substochastic semigroups is established. Several applications to non-autonomous linear kinetic equations (linear Boltzmann equation and fragmentation equation) are provided.","authors_text":"Bertrand Lods, Luisa Arlotti, Mustapha Mokhtar-Kharroubi (LM-Besan\\c{c}on)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-28T11:19:43Z","title":"Non-autonomous Honesty theory in abstract state spaces with applications to linear kinetic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7100","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":"sha256:7f60bb15dcc585eee3a7f4c2db622706444098155916839e39eb8ec9453da07d","target":"record","created_at":"2026-05-18T03:29:38Z","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":"8328340dd010928e6036b21e235c6c5b339ff3e2cba5e3b0ca09cdee2015d680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-28T11:19:43Z","title_canon_sha256":"d78a05aa6ee10209e38ec246a593b2b933762d021276495fc5b818cb142e4c5e"},"schema_version":"1.0","source":{"id":"1303.7100","kind":"arxiv","version":1}},"canonical_sha256":"d368b64667c395e7e47ee809979d7a61565c97cb6ed6834b537111668f89ba9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d368b64667c395e7e47ee809979d7a61565c97cb6ed6834b537111668f89ba9e","first_computed_at":"2026-05-18T03:29:38.252483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:38.252483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kaY1V1L+bfky11ea3ON72C1pXn2j8OdoynStPrxTODnohuyRbTHEDJSvaIUGUkXlkdVQr8p4FDshPPcAtpx9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:38.252979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.7100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f60bb15dcc585eee3a7f4c2db622706444098155916839e39eb8ec9453da07d","sha256:30107a8ec8701aebd30ff8d8cfeebd8b09a73b89a83125231e186e13d0ecabb0"],"state_sha256":"aa651c8b0526bbffceb95a3920d6ad5ca21485a06aa964c54d1c1d11e547dd18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AjGURMTUGLouOD2yp67pOSfH1sj6scaJEAozqn0g7fZpVuEMWPily12/jtGpmM26kH/Qmob/tD09m9vbrZyYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:14:48.518506Z","bundle_sha256":"889da390d19b48678f019ab5680cfb175ce989079c1a193dc4f4dc1372d68a64"}}