{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AJJG2R2XM2NHSIQD7O5F4WVH2K","short_pith_number":"pith:AJJG2R2X","canonical_record":{"source":{"id":"1506.06893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T08:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"b0162c86794d3c2825fff271bbb6fcb8030e4d18c65a473853bb9a9c12208cb4","abstract_canon_sha256":"9ba6f946eb539be7986aa2ec312f7f2a2645767b48cbb3019a6964ea01a2dc31"},"schema_version":"1.0"},"canonical_sha256":"02526d4757669a792203fbba5e5aa7d2abb75684d712dd2024d20cf1496a977b","source":{"kind":"arxiv","id":"1506.06893","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06893","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06893v2","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06893","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"AJJG2R2XM2NH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJJG2R2XM2NHSIQD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJJG2R2X","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AJJG2R2XM2NHSIQD7O5F4WVH2K","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T08:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"b0162c86794d3c2825fff271bbb6fcb8030e4d18c65a473853bb9a9c12208cb4","abstract_canon_sha256":"9ba6f946eb539be7986aa2ec312f7f2a2645767b48cbb3019a6964ea01a2dc31"},"schema_version":"1.0"},"canonical_sha256":"02526d4757669a792203fbba5e5aa7d2abb75684d712dd2024d20cf1496a977b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:20.512035Z","signature_b64":"htqy3tH0a8QBZUJQeKPszXx6g/3dDqz9A8YnTk3PTOv9VFs7anQOJ94GQbvyyN/sQe4fp7qNCyRCTAk+clsyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02526d4757669a792203fbba5e5aa7d2abb75684d712dd2024d20cf1496a977b","last_reissued_at":"2026-05-18T01:19:20.511515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:20.511515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06893","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfZ2DqveEMlOKDWnYfLsJ+RsSaVHKmiA/Lu219CPF2inV2RzGzTsgcMRVBVY/b4GOWxA+xPTKC06c37/n1A2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:06:59.397977Z"},"content_sha256":"e2b09501d12548650843b64347166a9b8be1e49f3c7931299b1a05f6c907992b","schema_version":"1.0","event_id":"sha256:e2b09501d12548650843b64347166a9b8be1e49f3c7931299b1a05f6c907992b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AJJG2R2XM2NHSIQD7O5F4WVH2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-inhomogeneous jump processes and variable order operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo, Costantino Ricciuti, Enzo Orsingher","submitted_at":"2015-06-23T08:07:10Z","abstract_excerpt":"In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not L\\'evy processes, they somehow generalize subordinators in the sense that their Laplace exponents are possibly different Bern\\v{s}tein functions for each time $t$. By means of these processes, a generalization of subordinate semigroups in the sense of Bochner is proposed. Because of time-inhomogeneity, two-parameter semigroups (propagators) arise and we provide a Phillips formula which leads to time dependent generators. The inverse processes are also investigate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06893","kind":"arxiv","version":2},"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":"2026-05-18T01:19:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1fDVEE14kSky95DuSJe6f6pN3OzMZeKXGQdOmycd2Am1dbmjk/tZ/biqaJr2ZhNwOE1BE7MhFBVLLVQ03674BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:06:59.398345Z"},"content_sha256":"a60e4b3abd38d91486003d07c82efa9da4a1971d8c000f113a829ea9c4fb3200","schema_version":"1.0","event_id":"sha256:a60e4b3abd38d91486003d07c82efa9da4a1971d8c000f113a829ea9c4fb3200"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K/bundle.json","state_url":"https://pith.science/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K/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":"2026-05-28T11:06:59Z","links":{"resolver":"https://pith.science/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K","bundle":"https://pith.science/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K/bundle.json","state":"https://pith.science/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJJG2R2XM2NHSIQD7O5F4WVH2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AJJG2R2XM2NHSIQD7O5F4WVH2K","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":"9ba6f946eb539be7986aa2ec312f7f2a2645767b48cbb3019a6964ea01a2dc31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T08:07:10Z","title_canon_sha256":"b0162c86794d3c2825fff271bbb6fcb8030e4d18c65a473853bb9a9c12208cb4"},"schema_version":"1.0","source":{"id":"1506.06893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06893","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06893v2","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06893","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"AJJG2R2XM2NH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJJG2R2XM2NHSIQD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJJG2R2X","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:a60e4b3abd38d91486003d07c82efa9da4a1971d8c000f113a829ea9c4fb3200","target":"graph","created_at":"2026-05-18T01:19:20Z","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 introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not L\\'evy processes, they somehow generalize subordinators in the sense that their Laplace exponents are possibly different Bern\\v{s}tein functions for each time $t$. By means of these processes, a generalization of subordinate semigroups in the sense of Bochner is proposed. Because of time-inhomogeneity, two-parameter semigroups (propagators) arise and we provide a Phillips formula which leads to time dependent generators. The inverse processes are also investigate","authors_text":"Bruno Toaldo, Costantino Ricciuti, Enzo Orsingher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T08:07:10Z","title":"Time-inhomogeneous jump processes and variable order operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06893","kind":"arxiv","version":2},"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:e2b09501d12548650843b64347166a9b8be1e49f3c7931299b1a05f6c907992b","target":"record","created_at":"2026-05-18T01:19:20Z","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":"9ba6f946eb539be7986aa2ec312f7f2a2645767b48cbb3019a6964ea01a2dc31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T08:07:10Z","title_canon_sha256":"b0162c86794d3c2825fff271bbb6fcb8030e4d18c65a473853bb9a9c12208cb4"},"schema_version":"1.0","source":{"id":"1506.06893","kind":"arxiv","version":2}},"canonical_sha256":"02526d4757669a792203fbba5e5aa7d2abb75684d712dd2024d20cf1496a977b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02526d4757669a792203fbba5e5aa7d2abb75684d712dd2024d20cf1496a977b","first_computed_at":"2026-05-18T01:19:20.511515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:20.511515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"htqy3tH0a8QBZUJQeKPszXx6g/3dDqz9A8YnTk3PTOv9VFs7anQOJ94GQbvyyN/sQe4fp7qNCyRCTAk+clsyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:20.512035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2b09501d12548650843b64347166a9b8be1e49f3c7931299b1a05f6c907992b","sha256:a60e4b3abd38d91486003d07c82efa9da4a1971d8c000f113a829ea9c4fb3200"],"state_sha256":"e3319ba96b8a70eb1cc1bbf06b28511f1a5e7f3f14679283e4c0a19fc241dfc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ior2lvCzWR1ROzgbuyjWv2vIq8nDoSDCEZWtf8FA+2zBfoHAQbRXy8XaH8say3YWb/v3XKzWVBBxxY1wNfukAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:06:59.400336Z","bundle_sha256":"2bc3189cf05aaca17f1e053e3c5849a5301a6c1d034858ae2ceb378f0b970db0"}}