{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BGFYEOMLT5OIVLTIR2YPK4N5CE","short_pith_number":"pith:BGFYEOML","canonical_record":{"source":{"id":"1205.5717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-25T15:07:33Z","cross_cats_sorted":["astro-ph.CO","gr-qc","quant-ph"],"title_canon_sha256":"f11523368a4909d42a175486c8c5918f1f04ea4f966d9ae868227fafb9cd67d0","abstract_canon_sha256":"6673f35c1f6bebe61d349f25c43f6b87916aeddc41efe039e48d346ef6bf9177"},"schema_version":"1.0"},"canonical_sha256":"098b82398b9f5c8aae688eb0f571bd11060e45e30f3637c6c02489e49bd5fedb","source":{"kind":"arxiv","id":"1205.5717","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5717","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5717v1","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5717","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"BGFYEOMLT5OI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BGFYEOMLT5OIVLTI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BGFYEOML","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BGFYEOMLT5OIVLTIR2YPK4N5CE","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-25T15:07:33Z","cross_cats_sorted":["astro-ph.CO","gr-qc","quant-ph"],"title_canon_sha256":"f11523368a4909d42a175486c8c5918f1f04ea4f966d9ae868227fafb9cd67d0","abstract_canon_sha256":"6673f35c1f6bebe61d349f25c43f6b87916aeddc41efe039e48d346ef6bf9177"},"schema_version":"1.0"},"canonical_sha256":"098b82398b9f5c8aae688eb0f571bd11060e45e30f3637c6c02489e49bd5fedb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:17.232258Z","signature_b64":"TIP0NUodfODaPmoyMWZqr41E1gK4Fbmnfv9iBX1PKegcv2J+qvwZMW0ugno+0Yu9EQFLhvmOQ7V3wuIKmCH2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"098b82398b9f5c8aae688eb0f571bd11060e45e30f3637c6c02489e49bd5fedb","last_reissued_at":"2026-05-18T01:57:17.231798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:17.231798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5717","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":"2026-05-18T01:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D02mT72uIqaxPGfLqYS+wnH0iSoMYNa0ZnovR+7mFtxDpVknl8VEemfACarG3oVkglMED4Hh2L4a7HXmRnmvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:19:09.527383Z"},"content_sha256":"db33028c51ed774ce5745b7a1abcc112d3dd427cd833d2e95a8ef1b17ab65796","schema_version":"1.0","event_id":"sha256:db33028c51ed774ce5745b7a1abcc112d3dd427cd833d2e95a8ef1b17ab65796"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BGFYEOMLT5OIVLTIR2YPK4N5CE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Astrophysical Evidence for the Non-Hermitian but $PT$-symmetric Hamiltonian of Conformal Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Philip D. Mannheim","submitted_at":"2012-05-25T15:07:33Z","abstract_excerpt":"In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but $PT$ symmetric on microscopic ones. In particular we show that the quantum-mechanical unitarity problem of the fourth-order derivative conformal gravity theory is resolved by recognizing that the scalar product appropriate to the theory is not the Dirac norm associated with a Hermitian Hamiltonian but is instead the norm associated with a non-Hermitian but $PT$-symmetric Hamiltonian. Moreover, the fourth-order theory Hamiltonia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5717","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":"2026-05-18T01:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bNib1/HD3nl2KMY1h7gdDXSYTwRxFbWehOMSr8AJUiy+RuW8B0cqsWuZsb5kVP4DPHbRNMpZiRyHJ3tpobtLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:19:09.527731Z"},"content_sha256":"98d01115fce31e913fa7aabe8bc82d360e0b2bcffa01ccfc128b0bd4977ee27b","schema_version":"1.0","event_id":"sha256:98d01115fce31e913fa7aabe8bc82d360e0b2bcffa01ccfc128b0bd4977ee27b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE/bundle.json","state_url":"https://pith.science/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE/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":"2026-06-05T02:19:09Z","links":{"resolver":"https://pith.science/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE","bundle":"https://pith.science/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE/bundle.json","state":"https://pith.science/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGFYEOMLT5OIVLTIR2YPK4N5CE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BGFYEOMLT5OIVLTIR2YPK4N5CE","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":"6673f35c1f6bebe61d349f25c43f6b87916aeddc41efe039e48d346ef6bf9177","cross_cats_sorted":["astro-ph.CO","gr-qc","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-25T15:07:33Z","title_canon_sha256":"f11523368a4909d42a175486c8c5918f1f04ea4f966d9ae868227fafb9cd67d0"},"schema_version":"1.0","source":{"id":"1205.5717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5717","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5717v1","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5717","created_at":"2026-05-18T01:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"BGFYEOMLT5OI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BGFYEOMLT5OIVLTI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BGFYEOML","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:98d01115fce31e913fa7aabe8bc82d360e0b2bcffa01ccfc128b0bd4977ee27b","target":"graph","created_at":"2026-05-18T01:57:17Z","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 review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but $PT$ symmetric on microscopic ones. In particular we show that the quantum-mechanical unitarity problem of the fourth-order derivative conformal gravity theory is resolved by recognizing that the scalar product appropriate to the theory is not the Dirac norm associated with a Hermitian Hamiltonian but is instead the norm associated with a non-Hermitian but $PT$-symmetric Hamiltonian. Moreover, the fourth-order theory Hamiltonia","authors_text":"Philip D. Mannheim","cross_cats":["astro-ph.CO","gr-qc","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-25T15:07:33Z","title":"Astrophysical Evidence for the Non-Hermitian but $PT$-symmetric Hamiltonian of Conformal Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5717","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:db33028c51ed774ce5745b7a1abcc112d3dd427cd833d2e95a8ef1b17ab65796","target":"record","created_at":"2026-05-18T01:57:17Z","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":"6673f35c1f6bebe61d349f25c43f6b87916aeddc41efe039e48d346ef6bf9177","cross_cats_sorted":["astro-ph.CO","gr-qc","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-25T15:07:33Z","title_canon_sha256":"f11523368a4909d42a175486c8c5918f1f04ea4f966d9ae868227fafb9cd67d0"},"schema_version":"1.0","source":{"id":"1205.5717","kind":"arxiv","version":1}},"canonical_sha256":"098b82398b9f5c8aae688eb0f571bd11060e45e30f3637c6c02489e49bd5fedb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"098b82398b9f5c8aae688eb0f571bd11060e45e30f3637c6c02489e49bd5fedb","first_computed_at":"2026-05-18T01:57:17.231798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:17.231798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TIP0NUodfODaPmoyMWZqr41E1gK4Fbmnfv9iBX1PKegcv2J+qvwZMW0ugno+0Yu9EQFLhvmOQ7V3wuIKmCH2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:17.232258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db33028c51ed774ce5745b7a1abcc112d3dd427cd833d2e95a8ef1b17ab65796","sha256:98d01115fce31e913fa7aabe8bc82d360e0b2bcffa01ccfc128b0bd4977ee27b"],"state_sha256":"dc7d2d282822ce7258802a44df3a8a2140aa789d8f69b9bdbd72f5d14c705685"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Htks4u4b6WxTiSxO5QAnV5N85bcSfrI4pNYoeUU1J5TGL2yYKmmi3AGU1vMq37jD7mbkGsqXPHjTSEY2Ko0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:19:09.529863Z","bundle_sha256":"9a16f1fa957d1997d2814191e4828134d275c832916300121e70abac5b2acd27"}}