{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:23Y36QPODJM5WXAMR37OUKIUM4","short_pith_number":"pith:23Y36QPO","canonical_record":{"source":{"id":"1705.03784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T14:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"8377243e3dd4b79a6f73a41d4a6acbd605f46011852d1423598f3676bf901ca3","abstract_canon_sha256":"e6573a6904f963a8dba3bdc8483682c3cc37da73d7646769d73290549a1b4fe4"},"schema_version":"1.0"},"canonical_sha256":"d6f1bf41ee1a59db5c0c8efeea2914671c22a1ece9ed5242fc2db09e37174ea2","source":{"kind":"arxiv","id":"1705.03784","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03784","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03784v1","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03784","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"23Y36QPODJM5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"23Y36QPODJM5WXAM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"23Y36QPO","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:23Y36QPODJM5WXAMR37OUKIUM4","target":"record","payload":{"canonical_record":{"source":{"id":"1705.03784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T14:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"8377243e3dd4b79a6f73a41d4a6acbd605f46011852d1423598f3676bf901ca3","abstract_canon_sha256":"e6573a6904f963a8dba3bdc8483682c3cc37da73d7646769d73290549a1b4fe4"},"schema_version":"1.0"},"canonical_sha256":"d6f1bf41ee1a59db5c0c8efeea2914671c22a1ece9ed5242fc2db09e37174ea2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:43.040898Z","signature_b64":"17gFzF7BLo00XqtawUe1G69y6v7R9UoZX6Zwiqst5SddQlxPAn5jjJUn7h+WOfSF/XE/GeV9e2qg85kLyzeaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6f1bf41ee1a59db5c0c8efeea2914671c22a1ece9ed5242fc2db09e37174ea2","last_reissued_at":"2026-05-18T00:44:43.040464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:43.040464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.03784","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":"2026-05-18T00:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEYvKkdrRBMRZAvTjK3mxhIXBroEH3pUJyEXEc0ipYV6HtSsFrsX1OxhJrvG2CsNDK4pfvJjhw7DQuZksBx2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:52:06.854822Z"},"content_sha256":"e0360d6150101e94e49364dc2a193f24128e68494857fc503ade76d8d7acbb45","schema_version":"1.0","event_id":"sha256:e0360d6150101e94e49364dc2a193f24128e68494857fc503ade76d8d7acbb45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:23Y36QPODJM5WXAMR37OUKIUM4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On invariant measures associated to weakly coupled systems of Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Davide Addona, Luca Lorenzi, Luciana Angiuli","submitted_at":"2017-05-10T14:06:15Z","abstract_excerpt":"In this paper, we deal with weakly coupled elliptic systems $\\boldsymbol{\\mathcal A}$ with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup $({\\bf T}(t))_{t\\ge 0}$ associated to $\\boldsymbol{\\mathcal A}$ in $C_b(\\mathbb R^d;\\mathbb R^m)$. We also show some relevant properties of the extension of $({\\bf T}(t))_{t\\ge 0}$ to the $L^p$-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of $({\\bf T}(t))_{t\\ge 0}$ as $t$ tends to $+\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03784","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":"2026-05-18T00:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KJf4XrJ8rSbcFESZeS/gPsdnA51lrFiT41X6ybSAgQDwTWuVHx/e/yYM86+7qFnA7UA9x9y2q3wB4AhIkFT7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:52:06.855175Z"},"content_sha256":"0901cb9a538f632fd1575f4157f395f371ec09450de0031c3266b2b751729cf5","schema_version":"1.0","event_id":"sha256:0901cb9a538f632fd1575f4157f395f371ec09450de0031c3266b2b751729cf5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23Y36QPODJM5WXAMR37OUKIUM4/bundle.json","state_url":"https://pith.science/pith/23Y36QPODJM5WXAMR37OUKIUM4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23Y36QPODJM5WXAMR37OUKIUM4/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":"2026-06-25T22:52:06Z","links":{"resolver":"https://pith.science/pith/23Y36QPODJM5WXAMR37OUKIUM4","bundle":"https://pith.science/pith/23Y36QPODJM5WXAMR37OUKIUM4/bundle.json","state":"https://pith.science/pith/23Y36QPODJM5WXAMR37OUKIUM4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23Y36QPODJM5WXAMR37OUKIUM4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:23Y36QPODJM5WXAMR37OUKIUM4","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":"e6573a6904f963a8dba3bdc8483682c3cc37da73d7646769d73290549a1b4fe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T14:06:15Z","title_canon_sha256":"8377243e3dd4b79a6f73a41d4a6acbd605f46011852d1423598f3676bf901ca3"},"schema_version":"1.0","source":{"id":"1705.03784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03784","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03784v1","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03784","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"23Y36QPODJM5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"23Y36QPODJM5WXAM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"23Y36QPO","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:0901cb9a538f632fd1575f4157f395f371ec09450de0031c3266b2b751729cf5","target":"graph","created_at":"2026-05-18T00:44:43Z","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":"In this paper, we deal with weakly coupled elliptic systems $\\boldsymbol{\\mathcal A}$ with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup $({\\bf T}(t))_{t\\ge 0}$ associated to $\\boldsymbol{\\mathcal A}$ in $C_b(\\mathbb R^d;\\mathbb R^m)$. We also show some relevant properties of the extension of $({\\bf T}(t))_{t\\ge 0}$ to the $L^p$-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of $({\\bf T}(t))_{t\\ge 0}$ as $t$ tends to $+\\infty$.","authors_text":"Davide Addona, Luca Lorenzi, Luciana Angiuli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T14:06:15Z","title":"On invariant measures associated to weakly coupled systems of Kolmogorov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03784","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:e0360d6150101e94e49364dc2a193f24128e68494857fc503ade76d8d7acbb45","target":"record","created_at":"2026-05-18T00:44:43Z","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":"e6573a6904f963a8dba3bdc8483682c3cc37da73d7646769d73290549a1b4fe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-10T14:06:15Z","title_canon_sha256":"8377243e3dd4b79a6f73a41d4a6acbd605f46011852d1423598f3676bf901ca3"},"schema_version":"1.0","source":{"id":"1705.03784","kind":"arxiv","version":1}},"canonical_sha256":"d6f1bf41ee1a59db5c0c8efeea2914671c22a1ece9ed5242fc2db09e37174ea2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6f1bf41ee1a59db5c0c8efeea2914671c22a1ece9ed5242fc2db09e37174ea2","first_computed_at":"2026-05-18T00:44:43.040464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:43.040464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"17gFzF7BLo00XqtawUe1G69y6v7R9UoZX6Zwiqst5SddQlxPAn5jjJUn7h+WOfSF/XE/GeV9e2qg85kLyzeaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:43.040898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0360d6150101e94e49364dc2a193f24128e68494857fc503ade76d8d7acbb45","sha256:0901cb9a538f632fd1575f4157f395f371ec09450de0031c3266b2b751729cf5"],"state_sha256":"932230890396335704735353a31c89284aea3d2ac99811679f796030a167bfa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swRY0ohzB9A/tDMmuh8AFOjShXSse0dYtcqsFQvPngc81AK+yX8dvxudVWZY22VNIKzPlD+nQqMSvlw49Ke8Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:52:06.857387Z","bundle_sha256":"21a1e214aede13b1e68d49a0ca5413c79fb02b5b2568e0cc25170b38fbba2e0f"}}