{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XCRYW36QBRMMKBXSHDHHGVHUNP","short_pith_number":"pith:XCRYW36Q","canonical_record":{"source":{"id":"1012.5143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-23T04:47:22Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"0b6c47503de651ade6d192c4151bbde6789308a73f34e267e171c2d5e5138bd9","abstract_canon_sha256":"c6e56c1dfb3831d70214ff4f857f0a8f7294da2cb32e715554c89d49b9b2721f"},"schema_version":"1.0"},"canonical_sha256":"b8a38b6fd00c58c506f238ce7354f46bf14f4794dec9d1a2c502450fbe0497d2","source":{"kind":"arxiv","id":"1012.5143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5143","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5143v1","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5143","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"XCRYW36QBRMM","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XCRYW36QBRMMKBXS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XCRYW36Q","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XCRYW36QBRMMKBXSHDHHGVHUNP","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-23T04:47:22Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"0b6c47503de651ade6d192c4151bbde6789308a73f34e267e171c2d5e5138bd9","abstract_canon_sha256":"c6e56c1dfb3831d70214ff4f857f0a8f7294da2cb32e715554c89d49b9b2721f"},"schema_version":"1.0"},"canonical_sha256":"b8a38b6fd00c58c506f238ce7354f46bf14f4794dec9d1a2c502450fbe0497d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:35.716097Z","signature_b64":"+qdG0jrrdXLQVZe4eWWcMsLavZFkbgLyh0rkN8WsgLxaxoK0hYEtyhNyOX0n8ER7wP0J8Vk61AaisWbWu09iCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8a38b6fd00c58c506f238ce7354f46bf14f4794dec9d1a2c502450fbe0497d2","last_reissued_at":"2026-05-18T04:32:35.715548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:35.715548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5143","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":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/Q3rEQ+EiAUQOovheHpFJhkMjVONgb5Gwe0H2s2LDss7zGcV3usoyw3j5THsTNZZNKdIvIg7gHVtHMzp7iZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:33:26.136720Z"},"content_sha256":"bef1732c6aa4c605dbd334287af21f73eda76c2e0debd438382bd069e5c0c6d0","schema_version":"1.0","event_id":"sha256:bef1732c6aa4c605dbd334287af21f73eda76c2e0debd438382bd069e5c0c6d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XCRYW36QBRMMKBXSHDHHGVHUNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Manwai Yuen","submitted_at":"2010-12-23T04:47:22Z","abstract_excerpt":"In this paper, we continue to study the blowup problem of the $N$-dimensional compressible Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. In details, we extend the recent result of \"M.W. Yuen, \\textit{Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces}, Nonlinear Analysis Series A: Theory, Methods & Applications \\textbf{74} (2011), 1465--1470.\". We could further apply the integration method to obtain the more general results which the non-trivial classical solutions $(\\rho,V)$, with compact support in $[0,R]$, where $R>0$ is a positive constant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5143","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":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOv6T7rUGq30A69/V0T5sb+EHvE6mnblvW4jX7g5its3e3/tP1+LpRqt9f1jNaatVxwmezOOocZGtyuK+v2BAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:33:26.137083Z"},"content_sha256":"00a432c14419123056b975c52cf4b7c3b8347875f0f9a9002ecbec6513076472","schema_version":"1.0","event_id":"sha256:00a432c14419123056b975c52cf4b7c3b8347875f0f9a9002ecbec6513076472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCRYW36QBRMMKBXSHDHHGVHUNP/bundle.json","state_url":"https://pith.science/pith/XCRYW36QBRMMKBXSHDHHGVHUNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCRYW36QBRMMKBXSHDHHGVHUNP/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":"2026-05-28T12:33:26Z","links":{"resolver":"https://pith.science/pith/XCRYW36QBRMMKBXSHDHHGVHUNP","bundle":"https://pith.science/pith/XCRYW36QBRMMKBXSHDHHGVHUNP/bundle.json","state":"https://pith.science/pith/XCRYW36QBRMMKBXSHDHHGVHUNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCRYW36QBRMMKBXSHDHHGVHUNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XCRYW36QBRMMKBXSHDHHGVHUNP","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":"c6e56c1dfb3831d70214ff4f857f0a8f7294da2cb32e715554c89d49b9b2721f","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-23T04:47:22Z","title_canon_sha256":"0b6c47503de651ade6d192c4151bbde6789308a73f34e267e171c2d5e5138bd9"},"schema_version":"1.0","source":{"id":"1012.5143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5143","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5143v1","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5143","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"XCRYW36QBRMM","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XCRYW36QBRMMKBXS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XCRYW36Q","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:00a432c14419123056b975c52cf4b7c3b8347875f0f9a9002ecbec6513076472","target":"graph","created_at":"2026-05-18T04:32:35Z","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":"In this paper, we continue to study the blowup problem of the $N$-dimensional compressible Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. In details, we extend the recent result of \"M.W. Yuen, \\textit{Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces}, Nonlinear Analysis Series A: Theory, Methods & Applications \\textbf{74} (2011), 1465--1470.\". We could further apply the integration method to obtain the more general results which the non-trivial classical solutions $(\\rho,V)$, with compact support in $[0,R]$, where $R>0$ is a positive constant ","authors_text":"Manwai Yuen","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-23T04:47:22Z","title":"Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5143","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:bef1732c6aa4c605dbd334287af21f73eda76c2e0debd438382bd069e5c0c6d0","target":"record","created_at":"2026-05-18T04:32:35Z","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":"c6e56c1dfb3831d70214ff4f857f0a8f7294da2cb32e715554c89d49b9b2721f","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-23T04:47:22Z","title_canon_sha256":"0b6c47503de651ade6d192c4151bbde6789308a73f34e267e171c2d5e5138bd9"},"schema_version":"1.0","source":{"id":"1012.5143","kind":"arxiv","version":1}},"canonical_sha256":"b8a38b6fd00c58c506f238ce7354f46bf14f4794dec9d1a2c502450fbe0497d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8a38b6fd00c58c506f238ce7354f46bf14f4794dec9d1a2c502450fbe0497d2","first_computed_at":"2026-05-18T04:32:35.715548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:35.715548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+qdG0jrrdXLQVZe4eWWcMsLavZFkbgLyh0rkN8WsgLxaxoK0hYEtyhNyOX0n8ER7wP0J8Vk61AaisWbWu09iCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:35.716097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bef1732c6aa4c605dbd334287af21f73eda76c2e0debd438382bd069e5c0c6d0","sha256:00a432c14419123056b975c52cf4b7c3b8347875f0f9a9002ecbec6513076472"],"state_sha256":"c174df95144c2b3768f58395017bfed7ab59682603224e812a471eafbc588b1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+Mf5LJrsPW69sODSjVuxJ6lQxoLG9U2LS6QgUnPQy0PKxXa5cGvVP3qe1cyLyLeycqVgGAfJv/4sC42D1+3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:33:26.139330Z","bundle_sha256":"4a64001e456ba53de375a5a34399036c50254b9944a839826b766f18e2f1bd35"}}