{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:I6EBB2GCPFIPCNX5YSUQSCCYU7","short_pith_number":"pith:I6EBB2GC","canonical_record":{"source":{"id":"0712.3504","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-12-20T17:21:27Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"8346ae26c6959dc4a5f00f7c12e240f17eaf6e778082d08d3e82fb60f001a6da","abstract_canon_sha256":"f45ec185672ae95067e6f3adc1f61190a69b1862eaf2d9f4cb37b895418cdced"},"schema_version":"1.0"},"canonical_sha256":"478810e8c27950f136fdc4a9090858a7e9dcbd18e12ac84b7c3a112dd4ad99c3","source":{"kind":"arxiv","id":"0712.3504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.3504","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"0712.3504v2","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.3504","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"I6EBB2GCPFIP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"I6EBB2GCPFIPCNX5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"I6EBB2GC","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:I6EBB2GCPFIPCNX5YSUQSCCYU7","target":"record","payload":{"canonical_record":{"source":{"id":"0712.3504","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-12-20T17:21:27Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"8346ae26c6959dc4a5f00f7c12e240f17eaf6e778082d08d3e82fb60f001a6da","abstract_canon_sha256":"f45ec185672ae95067e6f3adc1f61190a69b1862eaf2d9f4cb37b895418cdced"},"schema_version":"1.0"},"canonical_sha256":"478810e8c27950f136fdc4a9090858a7e9dcbd18e12ac84b7c3a112dd4ad99c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:52.334695Z","signature_b64":"PCBTGdeiwEDHSaq4P3Yc1w2wHaz1wbQ7ITPCzDjNe68uS3naMyrF/Olg0Ce7av4xgf9Ld4Ae9cjVLpYOKjaGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"478810e8c27950f136fdc4a9090858a7e9dcbd18e12ac84b7c3a112dd4ad99c3","last_reissued_at":"2026-05-18T03:06:52.334081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:52.334081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.3504","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":"2026-05-18T03:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHDMmX20ojnaO13hg0ZrEKey5zVZ+fB4CxB2i6lkOd3Zxnlxwya1IB6hXnH25O+HIY5/XOGzRQhYOOGw/620BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:47:16.923512Z"},"content_sha256":"6e88c8892328f88220fd2f91c76000c5f6252a4e1fae2d3be18fd6150fbd5b6c","schema_version":"1.0","event_id":"sha256:6e88c8892328f88220fd2f91c76000c5f6252a4e1fae2d3be18fd6150fbd5b6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:I6EBB2GCPFIPCNX5YSUQSCCYU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transformations of L\\'evy Processes","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Michael Sch\\\"urmann, Michael Skeide, Silvia Volkwardt","submitted_at":"2007-12-20T17:21:27Z","abstract_excerpt":"A L\\'evy process on a *-bialgebra is given by its generator, a conditionally positive hermitian linear functional vanishing at the unit element. A *-algebra homomorphism k from a *-bialgebra C to a *-bialgebra B with the property that k respects the counits maps generators on B to generators on C. A tranformation between the corrresponding two L\\'evy processes is given by forming infinitesimal convolution products.\n  This general result is applied to various situations, e.g., to a *-bialgebra and its associated primitive tensor *-bialgebra (called \"generator process\") as well as its associated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.3504","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":"2026-05-18T03:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwat9GhISiNhk63N8DDFsM/8bmWrnFyl3Mmdb9BSo2kdpc2/F/mSdIsCSMjzph2jgJH2pYu7J0ylfukRS9iFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:47:16.923857Z"},"content_sha256":"7bc91c5916803b7cbb90e4b2105c924896cb4614c8754930ada6febcd8a61cf8","schema_version":"1.0","event_id":"sha256:7bc91c5916803b7cbb90e4b2105c924896cb4614c8754930ada6febcd8a61cf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7/bundle.json","state_url":"https://pith.science/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7/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":"2026-06-22T16:47:16Z","links":{"resolver":"https://pith.science/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7","bundle":"https://pith.science/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7/bundle.json","state":"https://pith.science/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6EBB2GCPFIPCNX5YSUQSCCYU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:I6EBB2GCPFIPCNX5YSUQSCCYU7","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":"f45ec185672ae95067e6f3adc1f61190a69b1862eaf2d9f4cb37b895418cdced","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"math.PR","submitted_at":"2007-12-20T17:21:27Z","title_canon_sha256":"8346ae26c6959dc4a5f00f7c12e240f17eaf6e778082d08d3e82fb60f001a6da"},"schema_version":"1.0","source":{"id":"0712.3504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.3504","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"0712.3504v2","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.3504","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"I6EBB2GCPFIP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"I6EBB2GCPFIPCNX5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"I6EBB2GC","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7bc91c5916803b7cbb90e4b2105c924896cb4614c8754930ada6febcd8a61cf8","target":"graph","created_at":"2026-05-18T03:06:52Z","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":"A L\\'evy process on a *-bialgebra is given by its generator, a conditionally positive hermitian linear functional vanishing at the unit element. A *-algebra homomorphism k from a *-bialgebra C to a *-bialgebra B with the property that k respects the counits maps generators on B to generators on C. A tranformation between the corrresponding two L\\'evy processes is given by forming infinitesimal convolution products.\n  This general result is applied to various situations, e.g., to a *-bialgebra and its associated primitive tensor *-bialgebra (called \"generator process\") as well as its associated","authors_text":"Michael Sch\\\"urmann, Michael Skeide, Silvia Volkwardt","cross_cats":["math.OA"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-12-20T17:21:27Z","title":"Transformations of L\\'evy Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.3504","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":"sha256:6e88c8892328f88220fd2f91c76000c5f6252a4e1fae2d3be18fd6150fbd5b6c","target":"record","created_at":"2026-05-18T03:06:52Z","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":"f45ec185672ae95067e6f3adc1f61190a69b1862eaf2d9f4cb37b895418cdced","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"math.PR","submitted_at":"2007-12-20T17:21:27Z","title_canon_sha256":"8346ae26c6959dc4a5f00f7c12e240f17eaf6e778082d08d3e82fb60f001a6da"},"schema_version":"1.0","source":{"id":"0712.3504","kind":"arxiv","version":2}},"canonical_sha256":"478810e8c27950f136fdc4a9090858a7e9dcbd18e12ac84b7c3a112dd4ad99c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"478810e8c27950f136fdc4a9090858a7e9dcbd18e12ac84b7c3a112dd4ad99c3","first_computed_at":"2026-05-18T03:06:52.334081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:52.334081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PCBTGdeiwEDHSaq4P3Yc1w2wHaz1wbQ7ITPCzDjNe68uS3naMyrF/Olg0Ce7av4xgf9Ld4Ae9cjVLpYOKjaGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:52.334695Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.3504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e88c8892328f88220fd2f91c76000c5f6252a4e1fae2d3be18fd6150fbd5b6c","sha256:7bc91c5916803b7cbb90e4b2105c924896cb4614c8754930ada6febcd8a61cf8"],"state_sha256":"208d1864cf85158c8e8f1ce2b0b08e82b364c4f5704b9f00cf0480e306024d53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOxZ7QfgkekrouiOB1/TWeZgIEjpehmdJPOzCBKcOX/r8stwU5+xiCDBBMlVK6OmbHAmIcC3NmjXFXW1fDysAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:47:16.925783Z","bundle_sha256":"3019be275e4abebbc0c74d5bd3b12e3f73196bc5e59887e9ad993868a6a4f6fa"}}