{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YQ4WLODBPXEIKV47JQKDTQ4PR4","short_pith_number":"pith:YQ4WLODB","schema_version":"1.0","canonical_sha256":"c43965b8617dc885579f4c1439c38f8f11d11157092346e803738598f0d2ee77","source":{"kind":"arxiv","id":"1311.0971","version":1},"attestation_state":"computed","paper":{"title":"Transport semigroup associated to positive boundary conditions of unit norm: a Dyson-Phillips approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Luisa Arlotti","submitted_at":"2013-11-05T05:34:41Z","abstract_excerpt":"We revisit our study of general transport operator with general force field and general invariant measure by considering, in the $L^1$ setting, the linear transport operator $\\T_H$ associated to a linear and positive boundary operator $H$ of unit norm. It is known that in this case an extension of $\\T_H$ generates a substochastic (i.e. positive contraction) $C_0$-semigroup $(V_H(t))_{t\\geq 0}$. We show here that $(V_H(t))_{t\\geq 0}$ is the smallest substochastic $C_0$-semigroup with the above mentioned property and provides a representation of $(V_H(t))_{t \\geq 0}$ as the sum of an expansion s"},"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":"1311.0971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-05T05:34:41Z","cross_cats_sorted":[],"title_canon_sha256":"936d7c741999d48a927285e7d568d61c41a84d6cbce4af1cec1dc37b231f912d","abstract_canon_sha256":"0621cfd9f117f5ab705ea62043290ac1701b95d561f708b38b490eebe618c6e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:55.873554Z","signature_b64":"AskL3LKGObzWMXrbLBsYMJDLG8M4U96eeZNpRJe8vvXyRZdFqpTbvWcsiBjLaMv8vn83CWdHhoKfjR16eWjYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c43965b8617dc885579f4c1439c38f8f11d11157092346e803738598f0d2ee77","last_reissued_at":"2026-05-18T03:07:55.872896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:55.872896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transport semigroup associated to positive boundary conditions of unit norm: a Dyson-Phillips approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Luisa Arlotti","submitted_at":"2013-11-05T05:34:41Z","abstract_excerpt":"We revisit our study of general transport operator with general force field and general invariant measure by considering, in the $L^1$ setting, the linear transport operator $\\T_H$ associated to a linear and positive boundary operator $H$ of unit norm. It is known that in this case an extension of $\\T_H$ generates a substochastic (i.e. positive contraction) $C_0$-semigroup $(V_H(t))_{t\\geq 0}$. We show here that $(V_H(t))_{t\\geq 0}$ is the smallest substochastic $C_0$-semigroup with the above mentioned property and provides a representation of $(V_H(t))_{t \\geq 0}$ as the sum of an expansion s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0971","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":"1311.0971","created_at":"2026-05-18T03:07:55.873006+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0971v1","created_at":"2026-05-18T03:07:55.873006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0971","created_at":"2026-05-18T03:07:55.873006+00:00"},{"alias_kind":"pith_short_12","alias_value":"YQ4WLODBPXEI","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YQ4WLODBPXEIKV47","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YQ4WLODB","created_at":"2026-05-18T12:28:09.283467+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/YQ4WLODBPXEIKV47JQKDTQ4PR4","json":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4.json","graph_json":"https://pith.science/api/pith-number/YQ4WLODBPXEIKV47JQKDTQ4PR4/graph.json","events_json":"https://pith.science/api/pith-number/YQ4WLODBPXEIKV47JQKDTQ4PR4/events.json","paper":"https://pith.science/paper/YQ4WLODB"},"agent_actions":{"view_html":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4","download_json":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4.json","view_paper":"https://pith.science/paper/YQ4WLODB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0971&json=true","fetch_graph":"https://pith.science/api/pith-number/YQ4WLODBPXEIKV47JQKDTQ4PR4/graph.json","fetch_events":"https://pith.science/api/pith-number/YQ4WLODBPXEIKV47JQKDTQ4PR4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4/action/storage_attestation","attest_author":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4/action/author_attestation","sign_citation":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4/action/citation_signature","submit_replication":"https://pith.science/pith/YQ4WLODBPXEIKV47JQKDTQ4PR4/action/replication_record"}},"created_at":"2026-05-18T03:07:55.873006+00:00","updated_at":"2026-05-18T03:07:55.873006+00:00"}