{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:75Z3QHP46QRZ7LS3SAK45PUNXR","short_pith_number":"pith:75Z3QHP4","canonical_record":{"source":{"id":"1309.4768","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-18T11:01:38Z","cross_cats_sorted":[],"title_canon_sha256":"b530e5679e814dab4521e3834731e476344bfe2399788960b4058fd3fe12adda","abstract_canon_sha256":"e8cff20ac2ef69631641e94a678b9ef9976106b059fec3e889c238348f07a302"},"schema_version":"1.0"},"canonical_sha256":"ff73b81dfcf4239fae5b9015cebe8dbc5378bed720bf53dbffbef06b77cf7656","source":{"kind":"arxiv","id":"1309.4768","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4768","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4768v2","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4768","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"75Z3QHP46QRZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"75Z3QHP46QRZ7LS3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"75Z3QHP4","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:75Z3QHP46QRZ7LS3SAK45PUNXR","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4768","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-18T11:01:38Z","cross_cats_sorted":[],"title_canon_sha256":"b530e5679e814dab4521e3834731e476344bfe2399788960b4058fd3fe12adda","abstract_canon_sha256":"e8cff20ac2ef69631641e94a678b9ef9976106b059fec3e889c238348f07a302"},"schema_version":"1.0"},"canonical_sha256":"ff73b81dfcf4239fae5b9015cebe8dbc5378bed720bf53dbffbef06b77cf7656","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:11.497011Z","signature_b64":"bs7fgUfVEXnZCa4YlQWr0IerQPoPiE1K0t2Qgtd5noOQS7pypMnkjKOtO/v7c3+VY+CgIVpPIm1ZUUkPRyvhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff73b81dfcf4239fae5b9015cebe8dbc5378bed720bf53dbffbef06b77cf7656","last_reissued_at":"2026-05-18T02:56:11.496595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:11.496595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4768","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":"2026-05-18T02:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lSLw3Z7nq6AqqbxVjkxWcxvMt2bq9rDvcVPtMIlQsrOIlZ0SrygAjJ6AHp2uKenVMPnzcAwgYDRfA0pR0FvXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:55:33.157938Z"},"content_sha256":"3f88eca73321aec3df6c65820edfa6c2e2585ac7e533dd49fb76fd623ea7849e","schema_version":"1.0","event_id":"sha256:3f88eca73321aec3df6c65820edfa6c2e2585ac7e533dd49fb76fd623ea7849e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:75Z3QHP46QRZ7LS3SAK45PUNXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A scan of f(R) models admitting Rindler type acceleration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"M. Halilsoy, M. Kerachian, S. Habib Mazharimousavi","submitted_at":"2013-09-18T11:01:38Z","abstract_excerpt":"As a manifestation of large distance effect Grumiller modified Schwarzschild metric with an extraneous term reminiscent of Rindler acceleration. Such a term has the potential to explain the observed flat rotation curves in general relativity. The same idea has been extended herein to the larger arena of $f\\left( R\\right) $ theory. With particular emphasis on weak energy conditions (WECs) for a fluid we present various classes of $f\\left( R\\right) $ theories admitting a Rindler-type acceleration in the metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4768","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":"2026-05-18T02:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0SpGKk4+oyDaoZ3s535Wi+vi+dvYXhkb+SHPfa/XAaGLfabaB4S3UYXOEag3E7sHPDRyJgx0HsvZJRo2ssjZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:55:33.158286Z"},"content_sha256":"b46c19884e2058f5238a795ba0f2b4cf5a6cb756e6c23696206e9e6e1a556496","schema_version":"1.0","event_id":"sha256:b46c19884e2058f5238a795ba0f2b4cf5a6cb756e6c23696206e9e6e1a556496"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75Z3QHP46QRZ7LS3SAK45PUNXR/bundle.json","state_url":"https://pith.science/pith/75Z3QHP46QRZ7LS3SAK45PUNXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75Z3QHP46QRZ7LS3SAK45PUNXR/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":"2026-06-10T22:55:33Z","links":{"resolver":"https://pith.science/pith/75Z3QHP46QRZ7LS3SAK45PUNXR","bundle":"https://pith.science/pith/75Z3QHP46QRZ7LS3SAK45PUNXR/bundle.json","state":"https://pith.science/pith/75Z3QHP46QRZ7LS3SAK45PUNXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75Z3QHP46QRZ7LS3SAK45PUNXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:75Z3QHP46QRZ7LS3SAK45PUNXR","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":"e8cff20ac2ef69631641e94a678b9ef9976106b059fec3e889c238348f07a302","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-18T11:01:38Z","title_canon_sha256":"b530e5679e814dab4521e3834731e476344bfe2399788960b4058fd3fe12adda"},"schema_version":"1.0","source":{"id":"1309.4768","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4768","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4768v2","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4768","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"75Z3QHP46QRZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"75Z3QHP46QRZ7LS3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"75Z3QHP4","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:b46c19884e2058f5238a795ba0f2b4cf5a6cb756e6c23696206e9e6e1a556496","target":"graph","created_at":"2026-05-18T02:56:11Z","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"},"paper":{"abstract_excerpt":"As a manifestation of large distance effect Grumiller modified Schwarzschild metric with an extraneous term reminiscent of Rindler acceleration. Such a term has the potential to explain the observed flat rotation curves in general relativity. The same idea has been extended herein to the larger arena of $f\\left( R\\right) $ theory. With particular emphasis on weak energy conditions (WECs) for a fluid we present various classes of $f\\left( R\\right) $ theories admitting a Rindler-type acceleration in the metric.","authors_text":"M. Halilsoy, M. Kerachian, S. Habib Mazharimousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-18T11:01:38Z","title":"A scan of f(R) models admitting Rindler type acceleration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4768","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":"sha256:3f88eca73321aec3df6c65820edfa6c2e2585ac7e533dd49fb76fd623ea7849e","target":"record","created_at":"2026-05-18T02:56:11Z","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":"e8cff20ac2ef69631641e94a678b9ef9976106b059fec3e889c238348f07a302","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-18T11:01:38Z","title_canon_sha256":"b530e5679e814dab4521e3834731e476344bfe2399788960b4058fd3fe12adda"},"schema_version":"1.0","source":{"id":"1309.4768","kind":"arxiv","version":2}},"canonical_sha256":"ff73b81dfcf4239fae5b9015cebe8dbc5378bed720bf53dbffbef06b77cf7656","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff73b81dfcf4239fae5b9015cebe8dbc5378bed720bf53dbffbef06b77cf7656","first_computed_at":"2026-05-18T02:56:11.496595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:11.496595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bs7fgUfVEXnZCa4YlQWr0IerQPoPiE1K0t2Qgtd5noOQS7pypMnkjKOtO/v7c3+VY+CgIVpPIm1ZUUkPRyvhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:11.497011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4768","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f88eca73321aec3df6c65820edfa6c2e2585ac7e533dd49fb76fd623ea7849e","sha256:b46c19884e2058f5238a795ba0f2b4cf5a6cb756e6c23696206e9e6e1a556496"],"state_sha256":"e8ac723a06fd6a3fe29ce9cb5cc55fae32aecd0cb090b54af3ea925005e2dd04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ULpaoLNwVvCI8ih/MWkdwChkGVxUOuqWRvBlNAoM5RBbXdtdkFHnpx4eAPTrz25d1+7+CJGhxCvi4TYp8SsnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:55:33.160237Z","bundle_sha256":"269774f1b698e5bd7c53e2f11f32afd72fa6abfc32004008dc14c7d82eae7f74"}}