{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YDCK6IIUOVWIQFYOUSAIW3JR4A","short_pith_number":"pith:YDCK6IIU","canonical_record":{"source":{"id":"1109.4713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-09-22T07:20:41Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"421f3f8e0af43c2231fb95991c2c047e2830633581295b9d5cd696f9ac66003b","abstract_canon_sha256":"9a52f33d21dfba0526b571761590966bdff148898c02b0914da97833d8c1e660"},"schema_version":"1.0"},"canonical_sha256":"c0c4af2114756c88170ea4808b6d31e03bdaca77f63dec3e6dca9a56200dc90d","source":{"kind":"arxiv","id":"1109.4713","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4713","created_at":"2026-05-18T04:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4713v2","created_at":"2026-05-18T04:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4713","created_at":"2026-05-18T04:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"YDCK6IIUOVWI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YDCK6IIUOVWIQFYO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YDCK6IIU","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YDCK6IIUOVWIQFYOUSAIW3JR4A","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-09-22T07:20:41Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"421f3f8e0af43c2231fb95991c2c047e2830633581295b9d5cd696f9ac66003b","abstract_canon_sha256":"9a52f33d21dfba0526b571761590966bdff148898c02b0914da97833d8c1e660"},"schema_version":"1.0"},"canonical_sha256":"c0c4af2114756c88170ea4808b6d31e03bdaca77f63dec3e6dca9a56200dc90d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:32.030108Z","signature_b64":"kRqrpN1lGyOvKXfvm5E0Gj75R5WiFoqhmipk3m5QnPcHejIVNdtcCXIdsOEuAWct/x36632B+eWMPsVHKJxjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0c4af2114756c88170ea4808b6d31e03bdaca77f63dec3e6dca9a56200dc90d","last_reissued_at":"2026-05-18T04:07:32.029495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:32.029495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4713","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":"2026-05-18T04:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCiV2sTN4B4noYx52m+bo4hMeieH0jdG2riiKVNSv+htKnNhRNd8diq8KPV8w5eTMcPvr+CoeNwK+d6ofvamBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:38:28.288056Z"},"content_sha256":"15e3ec03933d5e6f73b72855771a6e12d278b57c009e89cae45f725462d2ad06","schema_version":"1.0","event_id":"sha256:15e3ec03933d5e6f73b72855771a6e12d278b57c009e89cae45f725462d2ad06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YDCK6IIUOVWIQFYOUSAIW3JR4A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact plane gravitational waves in the de Rham-Gabadadze-Tolley model of massive gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Morteza Mohseni","submitted_at":"2011-09-22T07:20:41Z","abstract_excerpt":"We show that the nonlinear massive gravity model of de Rham, Gabadadze, and Tolley admits exact plane gravitational wave solution whose waveform obeys the two-dimensional Helmholtz equation. The solution is valid for arbitrary values of the coefficients of the cubic and quartic terms. In the massless limit the solution reduces to the Aichelburg-Sexl metric in general relativity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4713","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":"2026-05-18T04:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6SrAus4BEnU0CKAIMUz2hnylGUGbRDTmmbK8LnXQ2CtfO/xn6YX4o837GOlL+LGGqx6BZ+0yHKBnP9vLcvANDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:38:28.288705Z"},"content_sha256":"d6888134612a6471f285634fe791c15fc7b45803ce019f46b67e70c4107fbf77","schema_version":"1.0","event_id":"sha256:d6888134612a6471f285634fe791c15fc7b45803ce019f46b67e70c4107fbf77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A/bundle.json","state_url":"https://pith.science/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A/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":"2026-05-31T18:38:28Z","links":{"resolver":"https://pith.science/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A","bundle":"https://pith.science/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A/bundle.json","state":"https://pith.science/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDCK6IIUOVWIQFYOUSAIW3JR4A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YDCK6IIUOVWIQFYOUSAIW3JR4A","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":"9a52f33d21dfba0526b571761590966bdff148898c02b0914da97833d8c1e660","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-09-22T07:20:41Z","title_canon_sha256":"421f3f8e0af43c2231fb95991c2c047e2830633581295b9d5cd696f9ac66003b"},"schema_version":"1.0","source":{"id":"1109.4713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4713","created_at":"2026-05-18T04:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4713v2","created_at":"2026-05-18T04:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4713","created_at":"2026-05-18T04:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"YDCK6IIUOVWI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YDCK6IIUOVWIQFYO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YDCK6IIU","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:d6888134612a6471f285634fe791c15fc7b45803ce019f46b67e70c4107fbf77","target":"graph","created_at":"2026-05-18T04:07:32Z","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":"We show that the nonlinear massive gravity model of de Rham, Gabadadze, and Tolley admits exact plane gravitational wave solution whose waveform obeys the two-dimensional Helmholtz equation. The solution is valid for arbitrary values of the coefficients of the cubic and quartic terms. In the massless limit the solution reduces to the Aichelburg-Sexl metric in general relativity.","authors_text":"Morteza Mohseni","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-09-22T07:20:41Z","title":"Exact plane gravitational waves in the de Rham-Gabadadze-Tolley model of massive gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4713","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":"sha256:15e3ec03933d5e6f73b72855771a6e12d278b57c009e89cae45f725462d2ad06","target":"record","created_at":"2026-05-18T04:07:32Z","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":"9a52f33d21dfba0526b571761590966bdff148898c02b0914da97833d8c1e660","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-09-22T07:20:41Z","title_canon_sha256":"421f3f8e0af43c2231fb95991c2c047e2830633581295b9d5cd696f9ac66003b"},"schema_version":"1.0","source":{"id":"1109.4713","kind":"arxiv","version":2}},"canonical_sha256":"c0c4af2114756c88170ea4808b6d31e03bdaca77f63dec3e6dca9a56200dc90d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0c4af2114756c88170ea4808b6d31e03bdaca77f63dec3e6dca9a56200dc90d","first_computed_at":"2026-05-18T04:07:32.029495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:32.029495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kRqrpN1lGyOvKXfvm5E0Gj75R5WiFoqhmipk3m5QnPcHejIVNdtcCXIdsOEuAWct/x36632B+eWMPsVHKJxjBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:32.030108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15e3ec03933d5e6f73b72855771a6e12d278b57c009e89cae45f725462d2ad06","sha256:d6888134612a6471f285634fe791c15fc7b45803ce019f46b67e70c4107fbf77"],"state_sha256":"77194dd3ab9ef2f8cc3dc84512ef9092db90e600b76191dd02c2a62e46bb04dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFH3/HgCAv1LSZyleGkii9guXzj/xV9pJd15meJWTF8rxOTj6IAetCMcMEnRQv12qzf5oTchX3i7y9H8+qsNAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:38:28.292530Z","bundle_sha256":"bf2d8cdbcd631a740856dac4a2acfc1dfe3dcb9b0c44d1a24c6ab258497dcb99"}}