{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FE7MWSXTYF2ZQGCG6CINKKYHZN","short_pith_number":"pith:FE7MWSXT","canonical_record":{"source":{"id":"1603.00569","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T03:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"368690047bed65608aff51a477e60d68e1ccbb2c700a86e64a483d15c362b2bb","abstract_canon_sha256":"cd92503106084a8d2e6f1ce5d9cd20cf79aa7fb7ba1e6e746d0e62820d58d05a"},"schema_version":"1.0"},"canonical_sha256":"293ecb4af3c175981846f090d52b07cb6d6a0b49a65872d1636d1116477c1179","source":{"kind":"arxiv","id":"1603.00569","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00569","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00569v5","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00569","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"FE7MWSXTYF2Z","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FE7MWSXTYF2ZQGCG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FE7MWSXT","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FE7MWSXTYF2ZQGCG6CINKKYHZN","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00569","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T03:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"368690047bed65608aff51a477e60d68e1ccbb2c700a86e64a483d15c362b2bb","abstract_canon_sha256":"cd92503106084a8d2e6f1ce5d9cd20cf79aa7fb7ba1e6e746d0e62820d58d05a"},"schema_version":"1.0"},"canonical_sha256":"293ecb4af3c175981846f090d52b07cb6d6a0b49a65872d1636d1116477c1179","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:25.791019Z","signature_b64":"Z4gxFWi4LA7EYC1Pdgrsf72YjnqPJvfPSjqOjJWjjXhCnWpKV8/GDFcdv6h6YGLgvNfnqQ3pgcZUTHWwNirHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"293ecb4af3c175981846f090d52b07cb6d6a0b49a65872d1636d1116477c1179","last_reissued_at":"2026-05-18T00:59:25.790411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:25.790411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00569","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o6hnfr8dx63h2bO5CtTmLu7QrGRGtDZwaCrNZ+7N3s6aCIx5KG3jQX2J5Sicf5PxKrtSx8dVUnuIUVaGwG2jBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:01:02.153393Z"},"content_sha256":"e1d2a18e407440e2a6fd75e95499778d09a8ea8d72dfa6822be08e200fdd3971","schema_version":"1.0","event_id":"sha256:e1d2a18e407440e2a6fd75e95499778d09a8ea8d72dfa6822be08e200fdd3971"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FE7MWSXTYF2ZQGCG6CINKKYHZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Application of the Nash-Moser Theorem to the Vacuum Boundary Problem of Gaseous Stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tetu Makino","submitted_at":"2016-03-02T03:55:22Z","abstract_excerpt":"We have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler-Poisson equations in the non-relativistic theory or by the Einstein-Euler equations in the relativistic theory. The problems are to construct solutions whose first approximations are small time-periodic solutions to the linearized problem at an equilibrium and to construct solutions to the Cauchy problem near an equilibrium. These problems can be solved when $1/(\\gamma-1)$ is an integer, where $\\gamma$ is the adiabatic exponent of the gas near the vacuum, by the formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00569","kind":"arxiv","version":5},"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":"2026-05-18T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITaLqVMuUElAPVQDeGLyKn4miVhUeab5lORp1cx7GZ/N1GvOkjdz7I7/gaRW+YOuYFR1OEvYyupgf+Fnc/Y+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:01:02.153741Z"},"content_sha256":"dee4ef8f3b0ebb78f179e7901291ea109e8ac42589390ea168458f814b4d9f6d","schema_version":"1.0","event_id":"sha256:dee4ef8f3b0ebb78f179e7901291ea109e8ac42589390ea168458f814b4d9f6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN/bundle.json","state_url":"https://pith.science/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN/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":"2026-06-05T10:01:02Z","links":{"resolver":"https://pith.science/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN","bundle":"https://pith.science/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN/bundle.json","state":"https://pith.science/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FE7MWSXTYF2ZQGCG6CINKKYHZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FE7MWSXTYF2ZQGCG6CINKKYHZN","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":"cd92503106084a8d2e6f1ce5d9cd20cf79aa7fb7ba1e6e746d0e62820d58d05a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T03:55:22Z","title_canon_sha256":"368690047bed65608aff51a477e60d68e1ccbb2c700a86e64a483d15c362b2bb"},"schema_version":"1.0","source":{"id":"1603.00569","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00569","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00569v5","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00569","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"FE7MWSXTYF2Z","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FE7MWSXTYF2ZQGCG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FE7MWSXT","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:dee4ef8f3b0ebb78f179e7901291ea109e8ac42589390ea168458f814b4d9f6d","target":"graph","created_at":"2026-05-18T00:59:25Z","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 have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler-Poisson equations in the non-relativistic theory or by the Einstein-Euler equations in the relativistic theory. The problems are to construct solutions whose first approximations are small time-periodic solutions to the linearized problem at an equilibrium and to construct solutions to the Cauchy problem near an equilibrium. These problems can be solved when $1/(\\gamma-1)$ is an integer, where $\\gamma$ is the adiabatic exponent of the gas near the vacuum, by the formu","authors_text":"Tetu Makino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T03:55:22Z","title":"An Application of the Nash-Moser Theorem to the Vacuum Boundary Problem of Gaseous Stars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00569","kind":"arxiv","version":5},"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:e1d2a18e407440e2a6fd75e95499778d09a8ea8d72dfa6822be08e200fdd3971","target":"record","created_at":"2026-05-18T00:59:25Z","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":"cd92503106084a8d2e6f1ce5d9cd20cf79aa7fb7ba1e6e746d0e62820d58d05a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T03:55:22Z","title_canon_sha256":"368690047bed65608aff51a477e60d68e1ccbb2c700a86e64a483d15c362b2bb"},"schema_version":"1.0","source":{"id":"1603.00569","kind":"arxiv","version":5}},"canonical_sha256":"293ecb4af3c175981846f090d52b07cb6d6a0b49a65872d1636d1116477c1179","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"293ecb4af3c175981846f090d52b07cb6d6a0b49a65872d1636d1116477c1179","first_computed_at":"2026-05-18T00:59:25.790411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:25.790411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z4gxFWi4LA7EYC1Pdgrsf72YjnqPJvfPSjqOjJWjjXhCnWpKV8/GDFcdv6h6YGLgvNfnqQ3pgcZUTHWwNirHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:25.791019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00569","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1d2a18e407440e2a6fd75e95499778d09a8ea8d72dfa6822be08e200fdd3971","sha256:dee4ef8f3b0ebb78f179e7901291ea109e8ac42589390ea168458f814b4d9f6d"],"state_sha256":"d90df8904934849562485053ae2b525e5e4f0ce1012b4d8a191959caaab33ca0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pblxCHM6wQQUA+SsFMz5QfyVsjlObi2Zj/xNU6iheoXmyGLmGzciavzd7aqwSghZg3Db4pCIzkXyTWzw3X4iDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:01:02.155657Z","bundle_sha256":"626361f9e3b10ce91705bb309a04faba2999e5b8462fac763593da43a5ab9000"}}