{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DODT5RVSF6LELYPNXHLUAWC4S7","short_pith_number":"pith:DODT5RVS","canonical_record":{"source":{"id":"1702.08514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-22T16:03:10Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"b08920df8010beb477f8792a3137baa9dd927c3fe2ccebb4572c26999a9178d8","abstract_canon_sha256":"a607ebecc5898dfe77ca9d836eed19da69c9dbb4ecc54bd7042ee03e5b5c95fc"},"schema_version":"1.0"},"canonical_sha256":"1b873ec6b22f9645e1edb9d740585c97cfa66b77f63bad7c4b81ac2553a8c166","source":{"kind":"arxiv","id":"1702.08514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08514","created_at":"2026-05-18T00:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08514v1","created_at":"2026-05-18T00:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08514","created_at":"2026-05-18T00:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"DODT5RVSF6LE","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DODT5RVSF6LELYPN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DODT5RVS","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DODT5RVSF6LELYPNXHLUAWC4S7","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-22T16:03:10Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"b08920df8010beb477f8792a3137baa9dd927c3fe2ccebb4572c26999a9178d8","abstract_canon_sha256":"a607ebecc5898dfe77ca9d836eed19da69c9dbb4ecc54bd7042ee03e5b5c95fc"},"schema_version":"1.0"},"canonical_sha256":"1b873ec6b22f9645e1edb9d740585c97cfa66b77f63bad7c4b81ac2553a8c166","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:48.525456Z","signature_b64":"NAV8GhdoyJYylOZm+aomGs97XPWOoFo0UI4eyXtJySY2LZ98scNDoTPmAarmBds8wyiNgbJBtItIgGulL4XVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b873ec6b22f9645e1edb9d740585c97cfa66b77f63bad7c4b81ac2553a8c166","last_reissued_at":"2026-05-18T00:49:48.524958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:48.524958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08514","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":"2026-05-18T00:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6mPGPB0NhPT2kiEge0tbJNQaf7ji4+6JBjEA/pjrRt7Pl6WCdU6rl1mXhX629LnllMP7LmRwOldm+xCGIuqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:56:52.235713Z"},"content_sha256":"cbdfb514d643c66b2d8f6130703bff1bc211855808ae328663cd9fea5eca4411","schema_version":"1.0","event_id":"sha256:cbdfb514d643c66b2d8f6130703bff1bc211855808ae328663cd9fea5eca4411"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DODT5RVSF6LELYPNXHLUAWC4S7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radial transonic shock solutions of Euler-Poisson system in convergent nozzles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.AP","authors_text":"Myoungjean Bae, Yong Park","submitted_at":"2017-02-22T16:03:10Z","abstract_excerpt":"Given constant data of density $\\rho_0$, velocity $-u_0{\\bf e}_r$, pressure $p_0$ and electric force $-E_0{\\bf e}_r$ for supersonic flow at the entrance, and constant pressure $p_{\\rm ex}$ for subsonic flow at the exit, we prove that Euler-Poisson system admits a unique transonic shock solution in a two dimensional convergent nozzle, provided that $u_0>0$, $E_0>0$, and that $E_0$ is sufficiently large depending on $(\\rho_0, u_0, p_0)$ and the length of the nozzle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08514","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":""},"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":"2026-05-18T00:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALxwBchNk0raOxdaK3u+RPhfHFmfTpINJ2W66FBKSr5lPONe1Gih0lpskxDXpY6YZURMooeaMadu56n4l9/bDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:56:52.236072Z"},"content_sha256":"bc86f0de68114aa398fa90e5b006047be422f3be870fb42d9408ea891caf2c2a","schema_version":"1.0","event_id":"sha256:bc86f0de68114aa398fa90e5b006047be422f3be870fb42d9408ea891caf2c2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DODT5RVSF6LELYPNXHLUAWC4S7/bundle.json","state_url":"https://pith.science/pith/DODT5RVSF6LELYPNXHLUAWC4S7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DODT5RVSF6LELYPNXHLUAWC4S7/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":"2026-07-05T11:56:52Z","links":{"resolver":"https://pith.science/pith/DODT5RVSF6LELYPNXHLUAWC4S7","bundle":"https://pith.science/pith/DODT5RVSF6LELYPNXHLUAWC4S7/bundle.json","state":"https://pith.science/pith/DODT5RVSF6LELYPNXHLUAWC4S7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DODT5RVSF6LELYPNXHLUAWC4S7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DODT5RVSF6LELYPNXHLUAWC4S7","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":"a607ebecc5898dfe77ca9d836eed19da69c9dbb4ecc54bd7042ee03e5b5c95fc","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-22T16:03:10Z","title_canon_sha256":"b08920df8010beb477f8792a3137baa9dd927c3fe2ccebb4572c26999a9178d8"},"schema_version":"1.0","source":{"id":"1702.08514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08514","created_at":"2026-05-18T00:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08514v1","created_at":"2026-05-18T00:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08514","created_at":"2026-05-18T00:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"DODT5RVSF6LE","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DODT5RVSF6LELYPN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DODT5RVS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:bc86f0de68114aa398fa90e5b006047be422f3be870fb42d9408ea891caf2c2a","target":"graph","created_at":"2026-05-18T00:49:48Z","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":"Given constant data of density $\\rho_0$, velocity $-u_0{\\bf e}_r$, pressure $p_0$ and electric force $-E_0{\\bf e}_r$ for supersonic flow at the entrance, and constant pressure $p_{\\rm ex}$ for subsonic flow at the exit, we prove that Euler-Poisson system admits a unique transonic shock solution in a two dimensional convergent nozzle, provided that $u_0>0$, $E_0>0$, and that $E_0$ is sufficiently large depending on $(\\rho_0, u_0, p_0)$ and the length of the nozzle.","authors_text":"Myoungjean Bae, Yong Park","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-22T16:03:10Z","title":"Radial transonic shock solutions of Euler-Poisson system in convergent nozzles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08514","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:cbdfb514d643c66b2d8f6130703bff1bc211855808ae328663cd9fea5eca4411","target":"record","created_at":"2026-05-18T00:49:48Z","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":"a607ebecc5898dfe77ca9d836eed19da69c9dbb4ecc54bd7042ee03e5b5c95fc","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-22T16:03:10Z","title_canon_sha256":"b08920df8010beb477f8792a3137baa9dd927c3fe2ccebb4572c26999a9178d8"},"schema_version":"1.0","source":{"id":"1702.08514","kind":"arxiv","version":1}},"canonical_sha256":"1b873ec6b22f9645e1edb9d740585c97cfa66b77f63bad7c4b81ac2553a8c166","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b873ec6b22f9645e1edb9d740585c97cfa66b77f63bad7c4b81ac2553a8c166","first_computed_at":"2026-05-18T00:49:48.524958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:48.524958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NAV8GhdoyJYylOZm+aomGs97XPWOoFo0UI4eyXtJySY2LZ98scNDoTPmAarmBds8wyiNgbJBtItIgGulL4XVAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:48.525456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbdfb514d643c66b2d8f6130703bff1bc211855808ae328663cd9fea5eca4411","sha256:bc86f0de68114aa398fa90e5b006047be422f3be870fb42d9408ea891caf2c2a"],"state_sha256":"51d7efc6ec565869c15d9e2af78f94f4556d3c5cb7c24b06331248c20f18392a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRrz8c0zMUMmwAtD1rxoSpygJ4t16IzrlhwUhjNB3R1vl0Da8DWXQBfz7PM2LopwnReCP+vWE+s2R5BXGpIQAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T11:56:52.237944Z","bundle_sha256":"ed3cadfd02b66cc04089bbab7206b056f75e319aa021b5f7aed6f675da5dff3d"}}