{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HSG7NHHSYOOS6IF5C5CUVIEDAA","short_pith_number":"pith:HSG7NHHS","canonical_record":{"source":{"id":"1712.09878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-12-28T14:51:27Z","cross_cats_sorted":[],"title_canon_sha256":"ea2966ea39d0003d66da1e18e3393818f24fa89e0dba630aa6e31b3e64a53fec","abstract_canon_sha256":"b549575a8000d7a7802d833332b87e6a20354234356640be26e2ec27688c96da"},"schema_version":"1.0"},"canonical_sha256":"3c8df69cf2c39d2f20bd17454aa083001e8adaab62f3d0865d72bed54ce5b964","source":{"kind":"arxiv","id":"1712.09878","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09878","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09878v2","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09878","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"HSG7NHHSYOOS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HSG7NHHSYOOS6IF5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HSG7NHHS","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HSG7NHHSYOOS6IF5C5CUVIEDAA","target":"record","payload":{"canonical_record":{"source":{"id":"1712.09878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-12-28T14:51:27Z","cross_cats_sorted":[],"title_canon_sha256":"ea2966ea39d0003d66da1e18e3393818f24fa89e0dba630aa6e31b3e64a53fec","abstract_canon_sha256":"b549575a8000d7a7802d833332b87e6a20354234356640be26e2ec27688c96da"},"schema_version":"1.0"},"canonical_sha256":"3c8df69cf2c39d2f20bd17454aa083001e8adaab62f3d0865d72bed54ce5b964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:40.566523Z","signature_b64":"3ZJdvGnzJ3bIQElqEFI1t+B521FZLTb7tmQTQdMdHy+6vG4Pko+nphmlc0sqeKfsyyww6PfMx61NizzmCrA5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c8df69cf2c39d2f20bd17454aa083001e8adaab62f3d0865d72bed54ce5b964","last_reissued_at":"2026-05-18T00:14:40.565802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:40.565802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.09878","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":"2026-05-18T00:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wt7DDHym3RB7DJTU6QXDkijI8auUkcBDHj7IKydlV0quXBsbkzhF+GBUYf3fy5ezGDVateQI5Is6v5WxtDIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:16:38.371192Z"},"content_sha256":"5ab490f84df6ffe0ad5394e21b16c54ba003407d11c9eb0e5c99496ab38ce86e","schema_version":"1.0","event_id":"sha256:5ab490f84df6ffe0ad5394e21b16c54ba003407d11c9eb0e5c99496ab38ce86e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HSG7NHHSYOOS6IF5C5CUVIEDAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Adrian Herzog, Kristina Giesel","submitted_at":"2017-12-28T14:51:27Z","abstract_excerpt":"The theory of cosmological perturbations is a well elaborated field. To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up to the considered order in the perturbations. For linear cosmological perturbations one works with the so-called Bardeen potentials widely used in this context. However, there exists no common procedure to construct gauge invariant quantities also for higher order perturbations. Usually, one has to find new gauge invariant quantities independently for each o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09878","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":"2026-05-18T00:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WsK7Zp36xD5XE4Poy3LIjULAdtYjrKMLlFdrpUJWjUv07/QgluvqsdyQGJVkIFLJ/SG6EwidjXL6LQb0rTDwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:16:38.371923Z"},"content_sha256":"819494ca2160dc29fb83a16f33411aa074da9544303535a226bdfa5697c614f1","schema_version":"1.0","event_id":"sha256:819494ca2160dc29fb83a16f33411aa074da9544303535a226bdfa5697c614f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA/bundle.json","state_url":"https://pith.science/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA/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":"2026-06-09T07:16:38Z","links":{"resolver":"https://pith.science/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA","bundle":"https://pith.science/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA/bundle.json","state":"https://pith.science/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSG7NHHSYOOS6IF5C5CUVIEDAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HSG7NHHSYOOS6IF5C5CUVIEDAA","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":"b549575a8000d7a7802d833332b87e6a20354234356640be26e2ec27688c96da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-12-28T14:51:27Z","title_canon_sha256":"ea2966ea39d0003d66da1e18e3393818f24fa89e0dba630aa6e31b3e64a53fec"},"schema_version":"1.0","source":{"id":"1712.09878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09878","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09878v2","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09878","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"HSG7NHHSYOOS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HSG7NHHSYOOS6IF5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HSG7NHHS","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:819494ca2160dc29fb83a16f33411aa074da9544303535a226bdfa5697c614f1","target":"graph","created_at":"2026-05-18T00:14:40Z","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 theory of cosmological perturbations is a well elaborated field. To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up to the considered order in the perturbations. For linear cosmological perturbations one works with the so-called Bardeen potentials widely used in this context. However, there exists no common procedure to construct gauge invariant quantities also for higher order perturbations. Usually, one has to find new gauge invariant quantities independently for each o","authors_text":"Adrian Herzog, Kristina Giesel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-12-28T14:51:27Z","title":"Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09878","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":"sha256:5ab490f84df6ffe0ad5394e21b16c54ba003407d11c9eb0e5c99496ab38ce86e","target":"record","created_at":"2026-05-18T00:14:40Z","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":"b549575a8000d7a7802d833332b87e6a20354234356640be26e2ec27688c96da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-12-28T14:51:27Z","title_canon_sha256":"ea2966ea39d0003d66da1e18e3393818f24fa89e0dba630aa6e31b3e64a53fec"},"schema_version":"1.0","source":{"id":"1712.09878","kind":"arxiv","version":2}},"canonical_sha256":"3c8df69cf2c39d2f20bd17454aa083001e8adaab62f3d0865d72bed54ce5b964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c8df69cf2c39d2f20bd17454aa083001e8adaab62f3d0865d72bed54ce5b964","first_computed_at":"2026-05-18T00:14:40.565802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:40.565802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ZJdvGnzJ3bIQElqEFI1t+B521FZLTb7tmQTQdMdHy+6vG4Pko+nphmlc0sqeKfsyyww6PfMx61NizzmCrA5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:40.566523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab490f84df6ffe0ad5394e21b16c54ba003407d11c9eb0e5c99496ab38ce86e","sha256:819494ca2160dc29fb83a16f33411aa074da9544303535a226bdfa5697c614f1"],"state_sha256":"761606b5d357c05ecb2bf0b28062330bb96630aad57adc4d31f1388e7cdf8730"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kCYSG/OILgoJKnmxjf0n0Cp9lzSIBsG7SnVW9VvWhgpsG9k1p/WeYuqyWPz5z33BiWcaH7AMpKdt1xtat/aVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:16:38.375635Z","bundle_sha256":"cd01691bd3f412d28c31c05342b974fbe3de15324061fac3901ba98e325240c3"}}