{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F75BAPP6GPDQKTEQ7XSF77JJKR","short_pith_number":"pith:F75BAPP6","canonical_record":{"source":{"id":"1503.01826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-06T01:17:52Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"42828dc351aa0f9c957586074cb75b6cc021dd1462d2eaaafeab246f61e54bcb","abstract_canon_sha256":"874898419db79977a42f401a2e69568f8c3fe2e691b3a61e8d5855cdcc669fb3"},"schema_version":"1.0"},"canonical_sha256":"2ffa103dfe33c7054c90fde45ffd295442b6962199bfcd3293a5e5079f5b7c6d","source":{"kind":"arxiv","id":"1503.01826","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01826","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01826v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01826","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"F75BAPP6GPDQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F75BAPP6GPDQKTEQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F75BAPP6","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F75BAPP6GPDQKTEQ7XSF77JJKR","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-06T01:17:52Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"42828dc351aa0f9c957586074cb75b6cc021dd1462d2eaaafeab246f61e54bcb","abstract_canon_sha256":"874898419db79977a42f401a2e69568f8c3fe2e691b3a61e8d5855cdcc669fb3"},"schema_version":"1.0"},"canonical_sha256":"2ffa103dfe33c7054c90fde45ffd295442b6962199bfcd3293a5e5079f5b7c6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:27.460861Z","signature_b64":"Z+9C8/+4nBhHMPBWq9ltL8kZOCmZ7p0c5JF4dZGmg6Df2z4/fB4CM0rknHq2cJJxe8WBIOl7xpiH8TpcVziRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ffa103dfe33c7054c90fde45ffd295442b6962199bfcd3293a5e5079f5b7c6d","last_reissued_at":"2026-05-18T02:25:27.460504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:27.460504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01826","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":"2026-05-18T02:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtF9dg0GZcDiZE5HvErDweNqUURuekRz57Gz+YV1KazKvBKL/pJpENDZW0WLj+b8hJXjzdF3pIczwK+kt0ZTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:50:02.680468Z"},"content_sha256":"5a7e79eb8ddf9660357d5b45254e2016a88ad0c5099a99f52b6aa54d5d7b9509","schema_version":"1.0","event_id":"sha256:5a7e79eb8ddf9660357d5b45254e2016a88ad0c5099a99f52b6aa54d5d7b9509"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F75BAPP6GPDQKTEQ7XSF77JJKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Semiclassical Einstein Equation on Cosmological Spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"Daniel Siemssen","submitted_at":"2015-03-06T01:17:52Z","abstract_excerpt":"The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the stress-energy tensor and the semiclassical Einstein equation. Basic notions of differential geometry, topology, functional and microlocal analysis, causality and general relativity will be summarised, and the algebraic approach to QFT on curved spacetime will be reviewed. Apart from these foundations, the original research of the author and his collaborators will be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01826","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":"2026-05-18T02:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pdYC/xwHHnhALFrM472zHbtvNQkl+wgd3+Isfb/CxN3fVEQ1Mrfgl5h/QFaaBgcGlJBLJwTWRpseTQ/bQQbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:50:02.680820Z"},"content_sha256":"02edb6cfaafcd04614c9cdd4a2958d8a2287787bbaa820b0c7cf5c61ca9b69c5","schema_version":"1.0","event_id":"sha256:02edb6cfaafcd04614c9cdd4a2958d8a2287787bbaa820b0c7cf5c61ca9b69c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F75BAPP6GPDQKTEQ7XSF77JJKR/bundle.json","state_url":"https://pith.science/pith/F75BAPP6GPDQKTEQ7XSF77JJKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F75BAPP6GPDQKTEQ7XSF77JJKR/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":"2026-06-24T04:50:02Z","links":{"resolver":"https://pith.science/pith/F75BAPP6GPDQKTEQ7XSF77JJKR","bundle":"https://pith.science/pith/F75BAPP6GPDQKTEQ7XSF77JJKR/bundle.json","state":"https://pith.science/pith/F75BAPP6GPDQKTEQ7XSF77JJKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F75BAPP6GPDQKTEQ7XSF77JJKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F75BAPP6GPDQKTEQ7XSF77JJKR","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":"874898419db79977a42f401a2e69568f8c3fe2e691b3a61e8d5855cdcc669fb3","cross_cats_sorted":["gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-06T01:17:52Z","title_canon_sha256":"42828dc351aa0f9c957586074cb75b6cc021dd1462d2eaaafeab246f61e54bcb"},"schema_version":"1.0","source":{"id":"1503.01826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01826","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01826v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01826","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"F75BAPP6GPDQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F75BAPP6GPDQKTEQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F75BAPP6","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:02edb6cfaafcd04614c9cdd4a2958d8a2287787bbaa820b0c7cf5c61ca9b69c5","target":"graph","created_at":"2026-05-18T02:25:27Z","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":"The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the stress-energy tensor and the semiclassical Einstein equation. Basic notions of differential geometry, topology, functional and microlocal analysis, causality and general relativity will be summarised, and the algebraic approach to QFT on curved spacetime will be reviewed. Apart from these foundations, the original research of the author and his collaborators will be ","authors_text":"Daniel Siemssen","cross_cats":["gr-qc","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-06T01:17:52Z","title":"The Semiclassical Einstein Equation on Cosmological Spacetimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01826","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":"sha256:5a7e79eb8ddf9660357d5b45254e2016a88ad0c5099a99f52b6aa54d5d7b9509","target":"record","created_at":"2026-05-18T02:25:27Z","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":"874898419db79977a42f401a2e69568f8c3fe2e691b3a61e8d5855cdcc669fb3","cross_cats_sorted":["gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-06T01:17:52Z","title_canon_sha256":"42828dc351aa0f9c957586074cb75b6cc021dd1462d2eaaafeab246f61e54bcb"},"schema_version":"1.0","source":{"id":"1503.01826","kind":"arxiv","version":1}},"canonical_sha256":"2ffa103dfe33c7054c90fde45ffd295442b6962199bfcd3293a5e5079f5b7c6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ffa103dfe33c7054c90fde45ffd295442b6962199bfcd3293a5e5079f5b7c6d","first_computed_at":"2026-05-18T02:25:27.460504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:27.460504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z+9C8/+4nBhHMPBWq9ltL8kZOCmZ7p0c5JF4dZGmg6Df2z4/fB4CM0rknHq2cJJxe8WBIOl7xpiH8TpcVziRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:27.460861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a7e79eb8ddf9660357d5b45254e2016a88ad0c5099a99f52b6aa54d5d7b9509","sha256:02edb6cfaafcd04614c9cdd4a2958d8a2287787bbaa820b0c7cf5c61ca9b69c5"],"state_sha256":"20fde9a38f5dd76e29ea5b402aa6bbbea5192fcc2648df0bf300831b5bfcdefc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ygcj3DhjMxiqAA4n4uvUaCMdV2aEWU1ut4O0Pw8Ei2VooAzWlQFzhuUBrwaZNU+M4Wrkfko4J/MFh8q4RQ4lCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:50:02.682724Z","bundle_sha256":"b3b61cf9ea064fd6da745ab9edc4a182d9346b01a7c30673a79eefbb394c0035"}}