{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LE4UPOYXKVDZJ3TUQ5SUBBNC5Y","short_pith_number":"pith:LE4UPOYX","canonical_record":{"source":{"id":"2502.09292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T13:08:40Z","cross_cats_sorted":[],"title_canon_sha256":"6af9458b56acf938bf51cf7a33d93a6f73049aedf66e04f30e7b14ccb710dcbf","abstract_canon_sha256":"7ba7a21452c50f5ebb95e6db90bb661c65702a08230f09c18aafb016f2be4b98"},"schema_version":"1.0"},"canonical_sha256":"593947bb17554794ee7487654085a2ee2cff725079b00d517ab9b707e0ef44fa","source":{"kind":"arxiv","id":"2502.09292","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.09292","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"2502.09292v1","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09292","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"LE4UPOYXKVDZ","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"pith_short_16","alias_value":"LE4UPOYXKVDZJ3TU","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"pith_short_8","alias_value":"LE4UPOYX","created_at":"2026-07-05T10:13:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LE4UPOYXKVDZJ3TUQ5SUBBNC5Y","target":"record","payload":{"canonical_record":{"source":{"id":"2502.09292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T13:08:40Z","cross_cats_sorted":[],"title_canon_sha256":"6af9458b56acf938bf51cf7a33d93a6f73049aedf66e04f30e7b14ccb710dcbf","abstract_canon_sha256":"7ba7a21452c50f5ebb95e6db90bb661c65702a08230f09c18aafb016f2be4b98"},"schema_version":"1.0"},"canonical_sha256":"593947bb17554794ee7487654085a2ee2cff725079b00d517ab9b707e0ef44fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:54.949492Z","signature_b64":"yimAk0qbycqTKK8+Vj5ulwfc3uW5NBeXhw6kEKaWV1bKzdlK6soNynNIBKVS+k6ob3fjnht8RBahrwd3IVhfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"593947bb17554794ee7487654085a2ee2cff725079b00d517ab9b707e0ef44fa","last_reissued_at":"2026-07-05T10:13:54.949009Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:54.949009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.09292","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":"2026-07-05T10:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ah8JCUv2i+Qj86m26r9HSVecgGIDu49+HBy/BDs9bPhwbwOndyJ4FmfUssMHdF6sg0lqDIL0FAScCDFQHxjtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:40:01.457881Z"},"content_sha256":"808c2a4123b217cf7eeb8821a73ae1d81a98da78443e4e779c2257d015a1b42c","schema_version":"1.0","event_id":"sha256:808c2a4123b217cf7eeb8821a73ae1d81a98da78443e4e779c2257d015a1b42c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LE4UPOYXKVDZJ3TUQ5SUBBNC5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Failure of the least action admissibility principle in the context of the compressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Simon Markfelder, Valentin Pellhammer","submitted_at":"2025-02-13T13:08:40Z","abstract_excerpt":"Finding a proper solution concept for the multi-dimensional barotropic compressible Euler equations and related systems is still an unsolved problem. As revealed by convex integration, the classical notion of an admissible weak solutions (also known as weak entropy solutions) does not lead to uniqueness and allows for solutions which do not seem to be physical. For this reason, people have studied additional criteria in view of their ability to rule out the counterintuitive solutions generated by convex integration. Recently, in [H.~Gimperlein, M.~Grinfeld, R.~J.~Knops and M.~Slemrod: The leas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09292","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/2502.09292/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":"2026-07-05T10:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rZAMUNw95GmYhhVEGCQtR4DOSOXhNyKkEjEc8NGhhf2FrZBe3+saXkbdqNcPFDokycD/8v/hdeyHdQLqX/PIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:40:01.458263Z"},"content_sha256":"ab7ce23a187eac6988387ebe425a2e20d462e91dcdd3d549ffdc0826b2b6f07d","schema_version":"1.0","event_id":"sha256:ab7ce23a187eac6988387ebe425a2e20d462e91dcdd3d549ffdc0826b2b6f07d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y/bundle.json","state_url":"https://pith.science/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y/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":"2026-08-13T23:40:01Z","links":{"resolver":"https://pith.science/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y","bundle":"https://pith.science/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y/bundle.json","state":"https://pith.science/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LE4UPOYXKVDZJ3TUQ5SUBBNC5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LE4UPOYXKVDZJ3TUQ5SUBBNC5Y","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":"7ba7a21452c50f5ebb95e6db90bb661c65702a08230f09c18aafb016f2be4b98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T13:08:40Z","title_canon_sha256":"6af9458b56acf938bf51cf7a33d93a6f73049aedf66e04f30e7b14ccb710dcbf"},"schema_version":"1.0","source":{"id":"2502.09292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.09292","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"2502.09292v1","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09292","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"LE4UPOYXKVDZ","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"pith_short_16","alias_value":"LE4UPOYXKVDZJ3TU","created_at":"2026-07-05T10:13:54Z"},{"alias_kind":"pith_short_8","alias_value":"LE4UPOYX","created_at":"2026-07-05T10:13:54Z"}],"graph_snapshots":[{"event_id":"sha256:ab7ce23a187eac6988387ebe425a2e20d462e91dcdd3d549ffdc0826b2b6f07d","target":"graph","created_at":"2026-07-05T10:13:54Z","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/2502.09292/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Finding a proper solution concept for the multi-dimensional barotropic compressible Euler equations and related systems is still an unsolved problem. As revealed by convex integration, the classical notion of an admissible weak solutions (also known as weak entropy solutions) does not lead to uniqueness and allows for solutions which do not seem to be physical. For this reason, people have studied additional criteria in view of their ability to rule out the counterintuitive solutions generated by convex integration. Recently, in [H.~Gimperlein, M.~Grinfeld, R.~J.~Knops and M.~Slemrod: The leas","authors_text":"Simon Markfelder, Valentin Pellhammer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T13:08:40Z","title":"Failure of the least action admissibility principle in the context of the compressible Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09292","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":"sha256:808c2a4123b217cf7eeb8821a73ae1d81a98da78443e4e779c2257d015a1b42c","target":"record","created_at":"2026-07-05T10:13:54Z","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":"7ba7a21452c50f5ebb95e6db90bb661c65702a08230f09c18aafb016f2be4b98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T13:08:40Z","title_canon_sha256":"6af9458b56acf938bf51cf7a33d93a6f73049aedf66e04f30e7b14ccb710dcbf"},"schema_version":"1.0","source":{"id":"2502.09292","kind":"arxiv","version":1}},"canonical_sha256":"593947bb17554794ee7487654085a2ee2cff725079b00d517ab9b707e0ef44fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"593947bb17554794ee7487654085a2ee2cff725079b00d517ab9b707e0ef44fa","first_computed_at":"2026-07-05T10:13:54.949009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:54.949009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yimAk0qbycqTKK8+Vj5ulwfc3uW5NBeXhw6kEKaWV1bKzdlK6soNynNIBKVS+k6ob3fjnht8RBahrwd3IVhfBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:54.949492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.09292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:808c2a4123b217cf7eeb8821a73ae1d81a98da78443e4e779c2257d015a1b42c","sha256:ab7ce23a187eac6988387ebe425a2e20d462e91dcdd3d549ffdc0826b2b6f07d"],"state_sha256":"3d332b09239ead6d45a3632d30b31e9829f5b562ae2ac200c92ce59194f4ab04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+aOCNiJvHDSnaUOQviYp0tbkWXbis/c9ENtcZ6VQADXUoHth6j1YAOLsRys2emW0SqnuYAt1xilLsaaP3+fECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T23:40:01.466471Z","bundle_sha256":"36731e0fd6e5224a2e350d5974be0a4464e164b1d3502d9d69eb93f1523ad541"}}