{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JERPIQCYXKBGNOBJRNGZLSNNAR","short_pith_number":"pith:JERPIQCY","canonical_record":{"source":{"id":"1908.03120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T15:33:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"858660979d697e9c18fb5a53443e7a4c87e69196a48ba7be0fe17b011b9a509f","abstract_canon_sha256":"ca33f202f68a575af5c6877905ddf2277c5a231a78787f33c3036d38db1251cf"},"schema_version":"1.0"},"canonical_sha256":"4922f44058ba8266b8298b4d95c9ad046ce3de1f988a423906c34f91fac51e8d","source":{"kind":"arxiv","id":"1908.03120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03120","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03120v1","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03120","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"JERPIQCYXKBG","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"pith_short_16","alias_value":"JERPIQCYXKBGNOBJ","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"pith_short_8","alias_value":"JERPIQCY","created_at":"2026-07-04T23:52:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JERPIQCYXKBGNOBJRNGZLSNNAR","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T15:33:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"858660979d697e9c18fb5a53443e7a4c87e69196a48ba7be0fe17b011b9a509f","abstract_canon_sha256":"ca33f202f68a575af5c6877905ddf2277c5a231a78787f33c3036d38db1251cf"},"schema_version":"1.0"},"canonical_sha256":"4922f44058ba8266b8298b4d95c9ad046ce3de1f988a423906c34f91fac51e8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:26.252411Z","signature_b64":"C5B5YIE62/P6gJGtsHJ7SqP/yTDq31wc+M9FxxGcbg4SaXBgErD9mM+rPjB9Wo7E9pi5hfiNOP7+Bn+7TBOOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4922f44058ba8266b8298b4d95c9ad046ce3de1f988a423906c34f91fac51e8d","last_reissued_at":"2026-07-04T23:52:26.251971Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:26.251971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03120","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+IwAj4eUC3rEYgCLshDMl/Gk6lPh5th0Aje7Ozg/WjJKtuA8HBLTk+SXGAnqtbM0f213SRZiRPRuvD1eBICAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:50:12.560892Z"},"content_sha256":"523328d81ea36e1fac2b5e4a69463fe5ce0d564a8a315f4c56c75088eb8fe7c6","schema_version":"1.0","event_id":"sha256:523328d81ea36e1fac2b5e4a69463fe5ce0d564a8a315f4c56c75088eb8fe7c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JERPIQCYXKBGNOBJRNGZLSNNAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of a time periodic solution for the compressible Euler equation with a time periodic outer force","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Naoki Tsuge","submitted_at":"2019-08-08T15:33:29Z","abstract_excerpt":"We are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time periodic solution. Although this is a fundamental problem for other equations, it has not been received much attention for the system of conservation laws until now."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03120","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03120/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxTbwvO/1JJWkHBvuPa5p+KqZj3v7nygNAH52hlBBR2Hgs5lwaD6272R8sKJw78+uNawKr3aVnxvUzENz31FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:50:12.561392Z"},"content_sha256":"648c7c205634740359e6565403070711a6e416cb83cab5ce342874a503198fd1","schema_version":"1.0","event_id":"sha256:648c7c205634740359e6565403070711a6e416cb83cab5ce342874a503198fd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JERPIQCYXKBGNOBJRNGZLSNNAR/bundle.json","state_url":"https://pith.science/pith/JERPIQCYXKBGNOBJRNGZLSNNAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JERPIQCYXKBGNOBJRNGZLSNNAR/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":"2026-08-16T18:50:12Z","links":{"resolver":"https://pith.science/pith/JERPIQCYXKBGNOBJRNGZLSNNAR","bundle":"https://pith.science/pith/JERPIQCYXKBGNOBJRNGZLSNNAR/bundle.json","state":"https://pith.science/pith/JERPIQCYXKBGNOBJRNGZLSNNAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JERPIQCYXKBGNOBJRNGZLSNNAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JERPIQCYXKBGNOBJRNGZLSNNAR","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":"ca33f202f68a575af5c6877905ddf2277c5a231a78787f33c3036d38db1251cf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T15:33:29Z","title_canon_sha256":"858660979d697e9c18fb5a53443e7a4c87e69196a48ba7be0fe17b011b9a509f"},"schema_version":"1.0","source":{"id":"1908.03120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03120","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03120v1","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03120","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"JERPIQCYXKBG","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"pith_short_16","alias_value":"JERPIQCYXKBGNOBJ","created_at":"2026-07-04T23:52:26Z"},{"alias_kind":"pith_short_8","alias_value":"JERPIQCY","created_at":"2026-07-04T23:52:26Z"}],"graph_snapshots":[{"event_id":"sha256:648c7c205634740359e6565403070711a6e416cb83cab5ce342874a503198fd1","target":"graph","created_at":"2026-07-04T23:52:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.03120/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time periodic solution. Although this is a fundamental problem for other equations, it has not been received much attention for the system of conservation laws until now.","authors_text":"Naoki Tsuge","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T15:33:29Z","title":"Existence of a time periodic solution for the compressible Euler equation with a time periodic outer force"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03120","kind":"arxiv","version":1},"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":"sha256:523328d81ea36e1fac2b5e4a69463fe5ce0d564a8a315f4c56c75088eb8fe7c6","target":"record","created_at":"2026-07-04T23:52:26Z","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":"ca33f202f68a575af5c6877905ddf2277c5a231a78787f33c3036d38db1251cf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T15:33:29Z","title_canon_sha256":"858660979d697e9c18fb5a53443e7a4c87e69196a48ba7be0fe17b011b9a509f"},"schema_version":"1.0","source":{"id":"1908.03120","kind":"arxiv","version":1}},"canonical_sha256":"4922f44058ba8266b8298b4d95c9ad046ce3de1f988a423906c34f91fac51e8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4922f44058ba8266b8298b4d95c9ad046ce3de1f988a423906c34f91fac51e8d","first_computed_at":"2026-07-04T23:52:26.251971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:26.251971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5B5YIE62/P6gJGtsHJ7SqP/yTDq31wc+M9FxxGcbg4SaXBgErD9mM+rPjB9Wo7E9pi5hfiNOP7+Bn+7TBOOCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:26.252411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:523328d81ea36e1fac2b5e4a69463fe5ce0d564a8a315f4c56c75088eb8fe7c6","sha256:648c7c205634740359e6565403070711a6e416cb83cab5ce342874a503198fd1"],"state_sha256":"7fb2892c3f80100ab855a94eb16bad7c42d324799cb6327dbfb86723738e3f2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLSsPMd7PHBqQdQYqAlVLe9qSvUq6l4sQeC+jNgt84GDAUUz4H8O8IQiQzL7NslHKpaX2PY0oNCISxA9Nk+sDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:50:12.566118Z","bundle_sha256":"eeea5948ee798f13c37a8009b2018f75dc84ea4ad0b887b3ff9d28290331e959"}}