{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6NP5W7HWDZZ7UIZRKIOJSTHQDS","short_pith_number":"pith:6NP5W7HW","canonical_record":{"source":{"id":"1209.2015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-07T14:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"850e50643a3402be14c88aadc99c8e40eedfb83de59fd9cf2258eed852078daa","abstract_canon_sha256":"ab202a6861f48274276de77b11fe7e4ffdd26aeb7f157eac581e6e3a10c455d2"},"schema_version":"1.0"},"canonical_sha256":"f35fdb7cf61e73fa2331521c994cf01c8fb43b716fca1a7a00b8624c87045d70","source":{"kind":"arxiv","id":"1209.2015","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2015","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2015v2","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2015","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"6NP5W7HWDZZ7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NP5W7HWDZZ7UIZR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NP5W7HW","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6NP5W7HWDZZ7UIZRKIOJSTHQDS","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-07T14:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"850e50643a3402be14c88aadc99c8e40eedfb83de59fd9cf2258eed852078daa","abstract_canon_sha256":"ab202a6861f48274276de77b11fe7e4ffdd26aeb7f157eac581e6e3a10c455d2"},"schema_version":"1.0"},"canonical_sha256":"f35fdb7cf61e73fa2331521c994cf01c8fb43b716fca1a7a00b8624c87045d70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:28.290148Z","signature_b64":"VB6HMsZmpf3f+ap+FTd4rILpFU0EufPyw6f8HzT++N7JOIRGaa9unmlBeSVmOUAWoDKwsfm0Jl/hpffPM+jbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f35fdb7cf61e73fa2331521c994cf01c8fb43b716fca1a7a00b8624c87045d70","last_reissued_at":"2026-05-18T00:59:28.289429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:28.289429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2015","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":"2026-05-18T00:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsJBdFyEPYTsX69A0D9Yx8o00xeOgtYmsA6gyfdQb/6WkCsbeHWE4Kho8eZXyGnDqqYZmO5nVPr3Q9hVp8JjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:47:18.725376Z"},"content_sha256":"8d59bdd9dbf6253491df4f4b9ac8e2099a29e356ae2978bc4645e5dd29df575b","schema_version":"1.0","event_id":"sha256:8d59bdd9dbf6253491df4f4b9ac8e2099a29e356ae2978bc4645e5dd29df575b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6NP5W7HWDZZ7UIZRKIOJSTHQDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Necessary conditions for having wormholes in f(R) gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"M. Halilsoy, S. Habib Mazharimousavi","submitted_at":"2012-09-07T14:06:25Z","abstract_excerpt":"For a generic $f(R)$ which admits a polynomial expansion of at least third order (i.e. $\\frac{d^{3}f}{dR^{3}}\\neq 0$) we find the near-throat wormhole solution. Necessary conditions for the existence of wormholes in such $f(R)$ theories are derived for both zero and non-zero matter sources. A particular choice of energy-momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC). For a range of parameters even the strong energy condition (SEC) is shown to be satisfied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2015","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":"2026-05-18T00:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJEG9o+8wAQHcEU19J4NbjTWP8AbWbKkLu6J/xiDTWjupA6vEocjE52LfUSwwTOV1ij+p59vg7oxpMo52jb+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:47:18.725726Z"},"content_sha256":"1c3c7cea50296219c673339f1fe5ccefaf7c99f9453d599f17fc7f889364314e","schema_version":"1.0","event_id":"sha256:1c3c7cea50296219c673339f1fe5ccefaf7c99f9453d599f17fc7f889364314e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS/bundle.json","state_url":"https://pith.science/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS/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":"2026-06-10T21:47:18Z","links":{"resolver":"https://pith.science/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS","bundle":"https://pith.science/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS/bundle.json","state":"https://pith.science/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NP5W7HWDZZ7UIZRKIOJSTHQDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6NP5W7HWDZZ7UIZRKIOJSTHQDS","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":"ab202a6861f48274276de77b11fe7e4ffdd26aeb7f157eac581e6e3a10c455d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-07T14:06:25Z","title_canon_sha256":"850e50643a3402be14c88aadc99c8e40eedfb83de59fd9cf2258eed852078daa"},"schema_version":"1.0","source":{"id":"1209.2015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2015","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2015v2","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2015","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"6NP5W7HWDZZ7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NP5W7HWDZZ7UIZR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NP5W7HW","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:1c3c7cea50296219c673339f1fe5ccefaf7c99f9453d599f17fc7f889364314e","target":"graph","created_at":"2026-05-18T00:59:28Z","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":"For a generic $f(R)$ which admits a polynomial expansion of at least third order (i.e. $\\frac{d^{3}f}{dR^{3}}\\neq 0$) we find the near-throat wormhole solution. Necessary conditions for the existence of wormholes in such $f(R)$ theories are derived for both zero and non-zero matter sources. A particular choice of energy-momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC). For a range of parameters even the strong energy condition (SEC) is shown to be satisfied.","authors_text":"M. Halilsoy, S. Habib Mazharimousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-07T14:06:25Z","title":"Necessary conditions for having wormholes in f(R) gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2015","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":"sha256:8d59bdd9dbf6253491df4f4b9ac8e2099a29e356ae2978bc4645e5dd29df575b","target":"record","created_at":"2026-05-18T00:59:28Z","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":"ab202a6861f48274276de77b11fe7e4ffdd26aeb7f157eac581e6e3a10c455d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-07T14:06:25Z","title_canon_sha256":"850e50643a3402be14c88aadc99c8e40eedfb83de59fd9cf2258eed852078daa"},"schema_version":"1.0","source":{"id":"1209.2015","kind":"arxiv","version":2}},"canonical_sha256":"f35fdb7cf61e73fa2331521c994cf01c8fb43b716fca1a7a00b8624c87045d70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f35fdb7cf61e73fa2331521c994cf01c8fb43b716fca1a7a00b8624c87045d70","first_computed_at":"2026-05-18T00:59:28.289429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:28.289429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VB6HMsZmpf3f+ap+FTd4rILpFU0EufPyw6f8HzT++N7JOIRGaa9unmlBeSVmOUAWoDKwsfm0Jl/hpffPM+jbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:28.290148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d59bdd9dbf6253491df4f4b9ac8e2099a29e356ae2978bc4645e5dd29df575b","sha256:1c3c7cea50296219c673339f1fe5ccefaf7c99f9453d599f17fc7f889364314e"],"state_sha256":"dca85e69ac5b42b53bb2509f8b9e621a21b23630cbfcabf13d4c5d7c7ef3f81a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TwgUmzZ27TZVEopeabUCt24iZIMOMWn5aOI8kogcke1UtDZYvnH9HN82+c3P/gKVpv9mrGtjLyxFfZiMDVX0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:47:18.727595Z","bundle_sha256":"adc0354f491c934fed52b6fe63bbfa87950c2939ad5c16258c1213d92befed9e"}}