{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KFXT6OSRX7KZLEWZPKBQUTYK4Q","short_pith_number":"pith:KFXT6OSR","canonical_record":{"source":{"id":"1612.08361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-26T10:43:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"df23061abefbc1f0de570464729fa796194549b9614f386ee1c18654c639dd02","abstract_canon_sha256":"8e44205cf46b1fbfced339680fad9983b48e2865915cc1090734a23b4bc9ca99"},"schema_version":"1.0"},"canonical_sha256":"516f3f3a51bfd59592d97a830a4f0ae4256f8bc924548e3b5ecc1ae37e3021bc","source":{"kind":"arxiv","id":"1612.08361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08361","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08361v2","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08361","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"KFXT6OSRX7KZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KFXT6OSRX7KZLEWZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KFXT6OSR","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KFXT6OSRX7KZLEWZPKBQUTYK4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-26T10:43:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"df23061abefbc1f0de570464729fa796194549b9614f386ee1c18654c639dd02","abstract_canon_sha256":"8e44205cf46b1fbfced339680fad9983b48e2865915cc1090734a23b4bc9ca99"},"schema_version":"1.0"},"canonical_sha256":"516f3f3a51bfd59592d97a830a4f0ae4256f8bc924548e3b5ecc1ae37e3021bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:13.514448Z","signature_b64":"tWCgvUJNULL0aROXuckMuDgUByekiIjy8oNPLnVHYiY4gQaST55R2+3+I8B0MAoj7bdgqZS5+Q9XCKdF7/MrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"516f3f3a51bfd59592d97a830a4f0ae4256f8bc924548e3b5ecc1ae37e3021bc","last_reissued_at":"2026-05-18T00:31:13.513837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:13.513837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08361","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":"2026-05-18T00:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/YkfeYMv9VzPr534vIegylGfSxG4xtLZ0jS1c/3Qu9HmBOi6r0ALbm88Aj3FuvAUQFn885a5JKS+RY+dbXvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:14:43.527963Z"},"content_sha256":"21dbac2d443adb62a865d14d50506b221d0f3344754399d740ecce3f4dc3d11a","schema_version":"1.0","event_id":"sha256:21dbac2d443adb62a865d14d50506b221d0f3344754399d740ecce3f4dc3d11a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KFXT6OSRX7KZLEWZPKBQUTYK4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The linear stability of the post-Newtonian triangular equilibrium in the three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Kei Yamada, Takuya Tsuchiya","submitted_at":"2016-12-26T10:43:34Z","abstract_excerpt":"Continuing work initiated in an earlier publication [Yamada, Tsuchiya, and Asada, Phys. Rev. D 91, 124016 (2015)], we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein-Infeld-Hoffman form of equations of motion for $N$-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e. we take account of perturbations orthogonal to the orbital plane, as well as perturbati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08361","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":"2026-05-18T00:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SigbLYDuCQjz8nj/SqsLM+LFKyQrggsWVj140tTg+p1h3IF2mnLaEIGr32HyjsJCBZk7zbSY339LVpv+s37fBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:14:43.528631Z"},"content_sha256":"6933fe4b7cecb8990ace073545134c929463527f5719aa2de33144c1cb4eed8e","schema_version":"1.0","event_id":"sha256:6933fe4b7cecb8990ace073545134c929463527f5719aa2de33144c1cb4eed8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q/bundle.json","state_url":"https://pith.science/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q/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":"2026-05-23T03:14:43Z","links":{"resolver":"https://pith.science/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q","bundle":"https://pith.science/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q/bundle.json","state":"https://pith.science/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFXT6OSRX7KZLEWZPKBQUTYK4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KFXT6OSRX7KZLEWZPKBQUTYK4Q","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":"8e44205cf46b1fbfced339680fad9983b48e2865915cc1090734a23b4bc9ca99","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-26T10:43:34Z","title_canon_sha256":"df23061abefbc1f0de570464729fa796194549b9614f386ee1c18654c639dd02"},"schema_version":"1.0","source":{"id":"1612.08361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08361","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08361v2","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08361","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"KFXT6OSRX7KZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KFXT6OSRX7KZLEWZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KFXT6OSR","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:6933fe4b7cecb8990ace073545134c929463527f5719aa2de33144c1cb4eed8e","target":"graph","created_at":"2026-05-18T00:31:13Z","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":"Continuing work initiated in an earlier publication [Yamada, Tsuchiya, and Asada, Phys. Rev. D 91, 124016 (2015)], we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein-Infeld-Hoffman form of equations of motion for $N$-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e. we take account of perturbations orthogonal to the orbital plane, as well as perturbati","authors_text":"Kei Yamada, Takuya Tsuchiya","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-26T10:43:34Z","title":"The linear stability of the post-Newtonian triangular equilibrium in the three-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08361","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":"sha256:21dbac2d443adb62a865d14d50506b221d0f3344754399d740ecce3f4dc3d11a","target":"record","created_at":"2026-05-18T00:31:13Z","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":"8e44205cf46b1fbfced339680fad9983b48e2865915cc1090734a23b4bc9ca99","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-12-26T10:43:34Z","title_canon_sha256":"df23061abefbc1f0de570464729fa796194549b9614f386ee1c18654c639dd02"},"schema_version":"1.0","source":{"id":"1612.08361","kind":"arxiv","version":2}},"canonical_sha256":"516f3f3a51bfd59592d97a830a4f0ae4256f8bc924548e3b5ecc1ae37e3021bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"516f3f3a51bfd59592d97a830a4f0ae4256f8bc924548e3b5ecc1ae37e3021bc","first_computed_at":"2026-05-18T00:31:13.513837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:13.513837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tWCgvUJNULL0aROXuckMuDgUByekiIjy8oNPLnVHYiY4gQaST55R2+3+I8B0MAoj7bdgqZS5+Q9XCKdF7/MrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:13.514448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21dbac2d443adb62a865d14d50506b221d0f3344754399d740ecce3f4dc3d11a","sha256:6933fe4b7cecb8990ace073545134c929463527f5719aa2de33144c1cb4eed8e"],"state_sha256":"f431ef20fd5bf68f3bd2826ce548a1a9b05666a85d367da9d47a2bf14701a0bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLJQZhtxx35iDO7W6w98wXnLpPL1hMz+/vHgztFMtc4NIF7KFunfQLDAmalocds8YlDup2w1THr2zVgPEGdVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:14:43.532139Z","bundle_sha256":"7cb3134cfc53fc825d204fb65b777771490028fa232da9ce4f0027858c21c2ff"}}