{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NIXHZLGX7UBNC4657K4MBN7EGL","short_pith_number":"pith:NIXHZLGX","canonical_record":{"source":{"id":"2403.11471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-18T04:43:19Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b8ec1d5bea6fbb8201c45cb6b75a01e2636ff428ce9d7dee2fc63df83badb5ac","abstract_canon_sha256":"737fe01f23e26ace95f9d2f18ae7e006493e326ac7ec8771808fee41e3b38ce4"},"schema_version":"1.0"},"canonical_sha256":"6a2e7cacd7fd02d173ddfab8c0b7e432f847d7d3329d224b27a69632828f69f5","source":{"kind":"arxiv","id":"2403.11471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.11471","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"2403.11471v1","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.11471","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"NIXHZLGX7UBN","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"pith_short_16","alias_value":"NIXHZLGX7UBNC465","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"pith_short_8","alias_value":"NIXHZLGX","created_at":"2026-07-05T07:57:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NIXHZLGX7UBNC4657K4MBN7EGL","target":"record","payload":{"canonical_record":{"source":{"id":"2403.11471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-18T04:43:19Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b8ec1d5bea6fbb8201c45cb6b75a01e2636ff428ce9d7dee2fc63df83badb5ac","abstract_canon_sha256":"737fe01f23e26ace95f9d2f18ae7e006493e326ac7ec8771808fee41e3b38ce4"},"schema_version":"1.0"},"canonical_sha256":"6a2e7cacd7fd02d173ddfab8c0b7e432f847d7d3329d224b27a69632828f69f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:57:16.994959Z","signature_b64":"aLrv8j1Ib8Sk4GWR1rMzNxvCtqciYKTsxBZnmwbRtFGrLUUDv6s8AFHk10lgzzGOB2EkeZ9lLQmyqqqg6/B4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a2e7cacd7fd02d173ddfab8c0b7e432f847d7d3329d224b27a69632828f69f5","last_reissued_at":"2026-07-05T07:57:16.994492Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:57:16.994492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.11471","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":"2026-07-05T07:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UURAR41MHcrjDHFc3G2GRdLGk9ECvQNK+pniYLd643dXAD4cEXevjU78NcAI2IK3i4H71Itr1jGX2ZaOrPb3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:22:25.720193Z"},"content_sha256":"0ffca97fad254404f901a434b25c87ab838436e17ebb41515288b144f0366012","schema_version":"1.0","event_id":"sha256:0ffca97fad254404f901a434b25c87ab838436e17ebb41515288b144f0366012"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NIXHZLGX7UBNC4657K4MBN7EGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-similar imploding solutions of the relativistic Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Feng Shao, Zhifei Zhang","submitted_at":"2024-03-18T04:43:19Z","abstract_excerpt":"Motivated by recent breakthrough on smooth imploding solutions of compressible Euler, we construct self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\\frac1\\ell\\varrho$ for \\textit{all} $\\ell>1$ in physical space dimension $d=2,3$ and for $\\ell>1$ close to 1 in higher dimensions. This work is a crucial step toward solving the long-standing problem: finite time blow-up of the supercritical defocusing nonlinear wave equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.11471","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/2403.11471/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":"2026-07-05T07:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFVOwNWd+w5u2Pv9F1s5D2vFMS+xr1x4Z79NS6TPXTYpT6G7xcTAoKc3QXsC+dXsZVV+WNLCLY0od7zVpzi/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:22:25.720712Z"},"content_sha256":"990924a3b48460e96e46a1cbe8464ff962b71190ecedcadab7f213a7d85128e7","schema_version":"1.0","event_id":"sha256:990924a3b48460e96e46a1cbe8464ff962b71190ecedcadab7f213a7d85128e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIXHZLGX7UBNC4657K4MBN7EGL/bundle.json","state_url":"https://pith.science/pith/NIXHZLGX7UBNC4657K4MBN7EGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIXHZLGX7UBNC4657K4MBN7EGL/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":"2026-08-11T10:22:25Z","links":{"resolver":"https://pith.science/pith/NIXHZLGX7UBNC4657K4MBN7EGL","bundle":"https://pith.science/pith/NIXHZLGX7UBNC4657K4MBN7EGL/bundle.json","state":"https://pith.science/pith/NIXHZLGX7UBNC4657K4MBN7EGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIXHZLGX7UBNC4657K4MBN7EGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NIXHZLGX7UBNC4657K4MBN7EGL","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":"737fe01f23e26ace95f9d2f18ae7e006493e326ac7ec8771808fee41e3b38ce4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-18T04:43:19Z","title_canon_sha256":"b8ec1d5bea6fbb8201c45cb6b75a01e2636ff428ce9d7dee2fc63df83badb5ac"},"schema_version":"1.0","source":{"id":"2403.11471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.11471","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"2403.11471v1","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.11471","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"NIXHZLGX7UBN","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"pith_short_16","alias_value":"NIXHZLGX7UBNC465","created_at":"2026-07-05T07:57:16Z"},{"alias_kind":"pith_short_8","alias_value":"NIXHZLGX","created_at":"2026-07-05T07:57:16Z"}],"graph_snapshots":[{"event_id":"sha256:990924a3b48460e96e46a1cbe8464ff962b71190ecedcadab7f213a7d85128e7","target":"graph","created_at":"2026-07-05T07:57:16Z","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/2403.11471/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by recent breakthrough on smooth imploding solutions of compressible Euler, we construct self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\\frac1\\ell\\varrho$ for \\textit{all} $\\ell>1$ in physical space dimension $d=2,3$ and for $\\ell>1$ close to 1 in higher dimensions. This work is a crucial step toward solving the long-standing problem: finite time blow-up of the supercritical defocusing nonlinear wave equation.","authors_text":"Dongyi Wei, Feng Shao, Zhifei Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-18T04:43:19Z","title":"Self-similar imploding solutions of the relativistic Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.11471","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":"sha256:0ffca97fad254404f901a434b25c87ab838436e17ebb41515288b144f0366012","target":"record","created_at":"2026-07-05T07:57:16Z","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":"737fe01f23e26ace95f9d2f18ae7e006493e326ac7ec8771808fee41e3b38ce4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-18T04:43:19Z","title_canon_sha256":"b8ec1d5bea6fbb8201c45cb6b75a01e2636ff428ce9d7dee2fc63df83badb5ac"},"schema_version":"1.0","source":{"id":"2403.11471","kind":"arxiv","version":1}},"canonical_sha256":"6a2e7cacd7fd02d173ddfab8c0b7e432f847d7d3329d224b27a69632828f69f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a2e7cacd7fd02d173ddfab8c0b7e432f847d7d3329d224b27a69632828f69f5","first_computed_at":"2026-07-05T07:57:16.994492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:57:16.994492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aLrv8j1Ib8Sk4GWR1rMzNxvCtqciYKTsxBZnmwbRtFGrLUUDv6s8AFHk10lgzzGOB2EkeZ9lLQmyqqqg6/B4Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:57:16.994959Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.11471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ffca97fad254404f901a434b25c87ab838436e17ebb41515288b144f0366012","sha256:990924a3b48460e96e46a1cbe8464ff962b71190ecedcadab7f213a7d85128e7"],"state_sha256":"386fcd1c1d0f1452defce48b93a0743fee3c4539283effb89dbbfe7a64387706"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clXk0/B/UMTLOJY4hZPzheq4oe8RuYnMKVrbLVCm1YhsZpirl1klUiufq8yy0qEahroYFTplwBw1lrHoUJ1MAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:22:25.725415Z","bundle_sha256":"5f98f7421ef95eeb8a16739d55f071b4e50a9b64603ca863cafee79a2c113079"}}