{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:T3BUXEW6RRMSZ662QSNXGVXQGZ","short_pith_number":"pith:T3BUXEW6","canonical_record":{"source":{"id":"2312.13678","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-21T09:00:34Z","cross_cats_sorted":[],"title_canon_sha256":"5ed2d21d92a924d8766accb83df7daceb72ba408bbdcdee63797d87db25dd6ea","abstract_canon_sha256":"1587cea42808150476b9fbaf4c2f7fb7527cce9ae5a39050bb8ce16c713e4280"},"schema_version":"1.0"},"canonical_sha256":"9ec34b92de8c592cfbda849b7356f0365723073fbcb89c4570766d84ecb26d3c","source":{"kind":"arxiv","id":"2312.13678","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13678","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13678v2","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13678","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"pith_short_12","alias_value":"T3BUXEW6RRMS","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"pith_short_16","alias_value":"T3BUXEW6RRMSZ662","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"pith_short_8","alias_value":"T3BUXEW6","created_at":"2026-07-05T12:06:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:T3BUXEW6RRMSZ662QSNXGVXQGZ","target":"record","payload":{"canonical_record":{"source":{"id":"2312.13678","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-21T09:00:34Z","cross_cats_sorted":[],"title_canon_sha256":"5ed2d21d92a924d8766accb83df7daceb72ba408bbdcdee63797d87db25dd6ea","abstract_canon_sha256":"1587cea42808150476b9fbaf4c2f7fb7527cce9ae5a39050bb8ce16c713e4280"},"schema_version":"1.0"},"canonical_sha256":"9ec34b92de8c592cfbda849b7356f0365723073fbcb89c4570766d84ecb26d3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:58.075728Z","signature_b64":"Xih5jpF48D9IvTZ/VgfDGw9XzEJsEWImPTcdpMjtC6LT14B//CPvhDsuLnwbZanPl52+yLw0iiR1OE84H5/LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ec34b92de8c592cfbda849b7356f0365723073fbcb89c4570766d84ecb26d3c","last_reissued_at":"2026-07-05T12:06:58.075232Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:58.075232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.13678","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:06:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hkH+bMBXa55eYyVUL5gAe8XErpkyeR3g2BMg0FsJ8Wr1825BwHQ4iful1QDK16AhEdSsRFayN22I2UyJm5vBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T22:38:17.645079Z"},"content_sha256":"b4a0a43220cd8436825c514464b1718c180af0eb78238ac11c0c75429238eae8","schema_version":"1.0","event_id":"sha256:b4a0a43220cd8436825c514464b1718c180af0eb78238ac11c0c75429238eae8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:T3BUXEW6RRMSZ662QSNXGVXQGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hele-Shaw semi-flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Herbert Koch, Thomas Alazard","submitted_at":"2023-12-21T09:00:34Z","abstract_excerpt":"We prove that the Cauchy problem is well-posed in a strong sense and in a general setting. Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem within general fluid domains (enabling, for instance, changes in the topology of the fluid domain) and which satisfies several properties: We provide simple comparison arguments, establish a new stability estimate and derive several consequences, including monotonicity and continuity results for the solutions, along with many Lyapunov functionals. We establish an eventual analytic regularity result for any arbitrary in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13678","kind":"arxiv","version":2},"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/2312.13678/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":"2026-07-05T12:06:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IoGZYd0KFMdBfesf8hOlQlSaZ3/E04jwq52GEFTBz0zPpzuQsuTUAfiQjwHiYE8qLBEXKUxDO9AgdeEiNm08Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T22:38:17.645604Z"},"content_sha256":"927da34c0c855027e4862bd171b9dc621738b7ca03019bf0c43c7d5fccec59cf","schema_version":"1.0","event_id":"sha256:927da34c0c855027e4862bd171b9dc621738b7ca03019bf0c43c7d5fccec59cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ/bundle.json","state_url":"https://pith.science/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ/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":"2026-08-14T22:38:17Z","links":{"resolver":"https://pith.science/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ","bundle":"https://pith.science/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ/bundle.json","state":"https://pith.science/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3BUXEW6RRMSZ662QSNXGVXQGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:T3BUXEW6RRMSZ662QSNXGVXQGZ","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":"1587cea42808150476b9fbaf4c2f7fb7527cce9ae5a39050bb8ce16c713e4280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-21T09:00:34Z","title_canon_sha256":"5ed2d21d92a924d8766accb83df7daceb72ba408bbdcdee63797d87db25dd6ea"},"schema_version":"1.0","source":{"id":"2312.13678","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13678","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13678v2","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13678","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"pith_short_12","alias_value":"T3BUXEW6RRMS","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"pith_short_16","alias_value":"T3BUXEW6RRMSZ662","created_at":"2026-07-05T12:06:58Z"},{"alias_kind":"pith_short_8","alias_value":"T3BUXEW6","created_at":"2026-07-05T12:06:58Z"}],"graph_snapshots":[{"event_id":"sha256:927da34c0c855027e4862bd171b9dc621738b7ca03019bf0c43c7d5fccec59cf","target":"graph","created_at":"2026-07-05T12:06:58Z","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/2312.13678/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the Cauchy problem is well-posed in a strong sense and in a general setting. Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem within general fluid domains (enabling, for instance, changes in the topology of the fluid domain) and which satisfies several properties: We provide simple comparison arguments, establish a new stability estimate and derive several consequences, including monotonicity and continuity results for the solutions, along with many Lyapunov functionals. We establish an eventual analytic regularity result for any arbitrary in","authors_text":"Herbert Koch, Thomas Alazard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-21T09:00:34Z","title":"The Hele-Shaw semi-flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13678","kind":"arxiv","version":2},"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:b4a0a43220cd8436825c514464b1718c180af0eb78238ac11c0c75429238eae8","target":"record","created_at":"2026-07-05T12:06:58Z","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":"1587cea42808150476b9fbaf4c2f7fb7527cce9ae5a39050bb8ce16c713e4280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-21T09:00:34Z","title_canon_sha256":"5ed2d21d92a924d8766accb83df7daceb72ba408bbdcdee63797d87db25dd6ea"},"schema_version":"1.0","source":{"id":"2312.13678","kind":"arxiv","version":2}},"canonical_sha256":"9ec34b92de8c592cfbda849b7356f0365723073fbcb89c4570766d84ecb26d3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ec34b92de8c592cfbda849b7356f0365723073fbcb89c4570766d84ecb26d3c","first_computed_at":"2026-07-05T12:06:58.075232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:58.075232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xih5jpF48D9IvTZ/VgfDGw9XzEJsEWImPTcdpMjtC6LT14B//CPvhDsuLnwbZanPl52+yLw0iiR1OE84H5/LAA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:58.075728Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.13678","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4a0a43220cd8436825c514464b1718c180af0eb78238ac11c0c75429238eae8","sha256:927da34c0c855027e4862bd171b9dc621738b7ca03019bf0c43c7d5fccec59cf"],"state_sha256":"3efb132659ffbb2853a9a9b53cd7f413e64218d7f21a129d2a4535c3e45a91a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Upit/EkSiluyFBB+dQDnjeTRooTQczCKdnBiU+MdrwgiZhUSIv27XjejO0q0wHsCdh7W0SCzHseb+ILV0zqMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T22:38:17.649340Z","bundle_sha256":"6241fa39e9a409a7620802aac6adc6b4864b60ab7b79df7c2e6707335385fdd8"}}