{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ELLASEOTYR4QH66OLLOQFIRAWH","short_pith_number":"pith:ELLASEOT","canonical_record":{"source":{"id":"2111.09457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-18T00:22:08Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d9ae015692f0ceec1b49081593cfcfb4f2f94692bae17dd6ba91f3cf0b358691","abstract_canon_sha256":"24a370dde3b24a92a7f63ed3aa408617d4bcba8553b23a5229bc6eb5372ef4fa"},"schema_version":"1.0"},"canonical_sha256":"22d60911d3c47903fbce5add02a220b1cadcef39b2ae2b8d05ac8c63a0652709","source":{"kind":"arxiv","id":"2111.09457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09457","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09457v1","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09457","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"pith_short_12","alias_value":"ELLASEOTYR4Q","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"pith_short_16","alias_value":"ELLASEOTYR4QH66O","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"pith_short_8","alias_value":"ELLASEOT","created_at":"2026-07-05T03:33:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ELLASEOTYR4QH66OLLOQFIRAWH","target":"record","payload":{"canonical_record":{"source":{"id":"2111.09457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-18T00:22:08Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d9ae015692f0ceec1b49081593cfcfb4f2f94692bae17dd6ba91f3cf0b358691","abstract_canon_sha256":"24a370dde3b24a92a7f63ed3aa408617d4bcba8553b23a5229bc6eb5372ef4fa"},"schema_version":"1.0"},"canonical_sha256":"22d60911d3c47903fbce5add02a220b1cadcef39b2ae2b8d05ac8c63a0652709","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:33:11.810672Z","signature_b64":"pxSNXGkKgHMG7Ztc9aCNncpmWbXqjQa/vYoiszCk8y55Xcu40fcT8ZK04LyAEWsN3VJdyjtGU1NUxloml1/2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22d60911d3c47903fbce5add02a220b1cadcef39b2ae2b8d05ac8c63a0652709","last_reissued_at":"2026-07-05T03:33:11.810154Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:33:11.810154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.09457","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":"2026-07-05T03:33:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5egzZqsnnRnICDovZrp9LTyfYFKvwrqVy+PboQEXlQ6dIvoSMf/fWeYMTdVhY8KCJv5gXXTRHmMbCEeMZxrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:07:34.163753Z"},"content_sha256":"3c813c7711b9e94b3df2572723c28c247ce8d037bc8d85e52b3cc72e79016785","schema_version":"1.0","event_id":"sha256:3c813c7711b9e94b3df2572723c28c247ce8d037bc8d85e52b3cc72e79016785"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ELLASEOTYR4QH66OLLOQFIRAWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ghost-free $F\\left( R,\\mathcal{G} \\right)$ Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Arkady A. Popov, S.D. Odintsov, S. Nojiri, V.K. Oikonomou","submitted_at":"2021-11-18T00:22:08Z","abstract_excerpt":"In this work we shall address the ghost issue of $F\\left( R,\\mathcal{G} \\right)$ gravity, which is known to be plagued with ghost degrees of freedom. These ghosts occur due to the presence of higher than two derivatives in the field equations, and can arise even when considering cosmological perturbations, where superluminal modes may arise in the theory. If we consider the quantum theory, the ghosts generate the negative norm states, which give the negative probabilities, and therefore the ghosts are physically inconsistent. Motivated by the importance of $F\\left( R,\\mathcal{G} \\right)$ gravi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09457","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.09457/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:33:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XggdsmolpWRIv5Wt/rnMhKkS3xrkBnhALlGF9B2luXmmRi52DuWDvQvA1mQPCy2GQ3GMQuK17HpyeHniLcD8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:07:34.164373Z"},"content_sha256":"80221ecba81ce5e359253acea44b7006a104c5a0dfffbabf98638fc6eda548be","schema_version":"1.0","event_id":"sha256:80221ecba81ce5e359253acea44b7006a104c5a0dfffbabf98638fc6eda548be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELLASEOTYR4QH66OLLOQFIRAWH/bundle.json","state_url":"https://pith.science/pith/ELLASEOTYR4QH66OLLOQFIRAWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELLASEOTYR4QH66OLLOQFIRAWH/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":"2026-08-05T13:07:34Z","links":{"resolver":"https://pith.science/pith/ELLASEOTYR4QH66OLLOQFIRAWH","bundle":"https://pith.science/pith/ELLASEOTYR4QH66OLLOQFIRAWH/bundle.json","state":"https://pith.science/pith/ELLASEOTYR4QH66OLLOQFIRAWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELLASEOTYR4QH66OLLOQFIRAWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ELLASEOTYR4QH66OLLOQFIRAWH","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":"24a370dde3b24a92a7f63ed3aa408617d4bcba8553b23a5229bc6eb5372ef4fa","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-18T00:22:08Z","title_canon_sha256":"d9ae015692f0ceec1b49081593cfcfb4f2f94692bae17dd6ba91f3cf0b358691"},"schema_version":"1.0","source":{"id":"2111.09457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09457","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09457v1","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09457","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"pith_short_12","alias_value":"ELLASEOTYR4Q","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"pith_short_16","alias_value":"ELLASEOTYR4QH66O","created_at":"2026-07-05T03:33:11Z"},{"alias_kind":"pith_short_8","alias_value":"ELLASEOT","created_at":"2026-07-05T03:33:11Z"}],"graph_snapshots":[{"event_id":"sha256:80221ecba81ce5e359253acea44b7006a104c5a0dfffbabf98638fc6eda548be","target":"graph","created_at":"2026-07-05T03:33:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.09457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we shall address the ghost issue of $F\\left( R,\\mathcal{G} \\right)$ gravity, which is known to be plagued with ghost degrees of freedom. These ghosts occur due to the presence of higher than two derivatives in the field equations, and can arise even when considering cosmological perturbations, where superluminal modes may arise in the theory. If we consider the quantum theory, the ghosts generate the negative norm states, which give the negative probabilities, and therefore the ghosts are physically inconsistent. Motivated by the importance of $F\\left( R,\\mathcal{G} \\right)$ gravi","authors_text":"Arkady A. Popov, S.D. Odintsov, S. Nojiri, V.K. Oikonomou","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-18T00:22:08Z","title":"Ghost-free $F\\left( R,\\mathcal{G} \\right)$ Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09457","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":"sha256:3c813c7711b9e94b3df2572723c28c247ce8d037bc8d85e52b3cc72e79016785","target":"record","created_at":"2026-07-05T03:33:11Z","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":"24a370dde3b24a92a7f63ed3aa408617d4bcba8553b23a5229bc6eb5372ef4fa","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-18T00:22:08Z","title_canon_sha256":"d9ae015692f0ceec1b49081593cfcfb4f2f94692bae17dd6ba91f3cf0b358691"},"schema_version":"1.0","source":{"id":"2111.09457","kind":"arxiv","version":1}},"canonical_sha256":"22d60911d3c47903fbce5add02a220b1cadcef39b2ae2b8d05ac8c63a0652709","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22d60911d3c47903fbce5add02a220b1cadcef39b2ae2b8d05ac8c63a0652709","first_computed_at":"2026-07-05T03:33:11.810154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:33:11.810154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pxSNXGkKgHMG7Ztc9aCNncpmWbXqjQa/vYoiszCk8y55Xcu40fcT8ZK04LyAEWsN3VJdyjtGU1NUxloml1/2Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:33:11.810672Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.09457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c813c7711b9e94b3df2572723c28c247ce8d037bc8d85e52b3cc72e79016785","sha256:80221ecba81ce5e359253acea44b7006a104c5a0dfffbabf98638fc6eda548be"],"state_sha256":"84cd0f252a33b8d65e2beb67a9afa700604a8fd49468e10c2af91ffda305e637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJH3lRDQkFU5K1MVc6YVdBuWlxICZECqNMHOk+jqTvzfHE1BZmY85dfaQ401fnaFXOmgPFQN4/lcF83NdccfCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T13:07:34.173533Z","bundle_sha256":"840e7a3061d955393ec116165b8185c7b10da6a0108b04d77af7c23c91642356"}}