{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:D6KHVIPVYWITJMBJMY7BTZYVCA","short_pith_number":"pith:D6KHVIPV","canonical_record":{"source":{"id":"2601.19442","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-27T10:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"d64626cbd8aff6ae97f3740a53845083b16f2d81b55ab3d9521ad91d618bb3eb","abstract_canon_sha256":"914e856b8e596148c3d3abd0182d367df90e75e5c59cef78f0a4939236d0569e"},"schema_version":"1.0"},"canonical_sha256":"1f947aa1f5c59134b029663e19e715103b64824e2274af160a4da9a2b2b8d3fe","source":{"kind":"arxiv","id":"2601.19442","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.19442","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"2601.19442v2","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.19442","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"D6KHVIPVYWIT","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"pith_short_16","alias_value":"D6KHVIPVYWITJMBJ","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"pith_short_8","alias_value":"D6KHVIPV","created_at":"2026-07-13T01:17:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:D6KHVIPVYWITJMBJMY7BTZYVCA","target":"record","payload":{"canonical_record":{"source":{"id":"2601.19442","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-27T10:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"d64626cbd8aff6ae97f3740a53845083b16f2d81b55ab3d9521ad91d618bb3eb","abstract_canon_sha256":"914e856b8e596148c3d3abd0182d367df90e75e5c59cef78f0a4939236d0569e"},"schema_version":"1.0"},"canonical_sha256":"1f947aa1f5c59134b029663e19e715103b64824e2274af160a4da9a2b2b8d3fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:17:55.660487Z","signature_b64":"CC7uZztyTVwwAJ/epKQdolsvS9HL6+V0Q0gkAWGkbsVHxpzvDPf8D5F2AGO1zhADluK7sW1BJUvlY/xShcSgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f947aa1f5c59134b029663e19e715103b64824e2274af160a4da9a2b2b8d3fe","last_reissued_at":"2026-07-13T01:17:55.659214Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:17:55.659214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.19442","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":"2026-07-13T01:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"008gPqA5Sk1LfWLkdlTpEDn2AJCSIJ3+iFZACmhvgg92oxolYG5AMMzWjBX4lbbckC6iBF9Li5EaQVmzzzttCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T20:12:52.175872Z"},"content_sha256":"81a866f241ad86469ab6ab7595159eac593e2ba014d1bc1963f5e1be2e7d202c","schema_version":"1.0","event_id":"sha256:81a866f241ad86469ab6ab7595159eac593e2ba014d1bc1963f5e1be2e7d202c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:D6KHVIPVYWITJMBJMY7BTZYVCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dissipative Solutions to a Compressible Non-Newtonian Korteweg System with Density-Dependent Viscous Stress Tensor","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Lacave, Didier Bresch, Maja Szlenk","submitted_at":"2026-01-27T10:26:05Z","abstract_excerpt":"The main objective of this paper is to prove that if capillarity effect is taken into account then there exist dissipative solutions to a system describing viscoplastic compressible flows with density dependent viscosities in a periodic domain $\\T^d$ with $d=2,3$. We calculate the relative entropy inequality and in consequence show existence of dissipative solutions and the weak-strong uniqueness for this system. Our result extends the recent result concerning the link between Euler--Korteweg and Navier--Stokes--Korteweg systems for Newtonian flows (when the viscosity depends on the density) ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19442","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/2601.19442/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":"2026-07-13T01:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"px2bZiXr4UIvHo3ySC42+rb3S0isTkYiwi0JtmpsFn79HYMs77H65QuxIGisD4PKvUSHDcGFNH2ekjE0lD+eAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T20:12:52.176367Z"},"content_sha256":"9856625243840ecdb4d075f71f2232797acdb948dfc5ceaaeedb75906931f6b7","schema_version":"1.0","event_id":"sha256:9856625243840ecdb4d075f71f2232797acdb948dfc5ceaaeedb75906931f6b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6KHVIPVYWITJMBJMY7BTZYVCA/bundle.json","state_url":"https://pith.science/pith/D6KHVIPVYWITJMBJMY7BTZYVCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6KHVIPVYWITJMBJMY7BTZYVCA/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":"2026-08-14T20:12:52Z","links":{"resolver":"https://pith.science/pith/D6KHVIPVYWITJMBJMY7BTZYVCA","bundle":"https://pith.science/pith/D6KHVIPVYWITJMBJMY7BTZYVCA/bundle.json","state":"https://pith.science/pith/D6KHVIPVYWITJMBJMY7BTZYVCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6KHVIPVYWITJMBJMY7BTZYVCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D6KHVIPVYWITJMBJMY7BTZYVCA","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":"914e856b8e596148c3d3abd0182d367df90e75e5c59cef78f0a4939236d0569e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-27T10:26:05Z","title_canon_sha256":"d64626cbd8aff6ae97f3740a53845083b16f2d81b55ab3d9521ad91d618bb3eb"},"schema_version":"1.0","source":{"id":"2601.19442","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.19442","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"2601.19442v2","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.19442","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"D6KHVIPVYWIT","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"pith_short_16","alias_value":"D6KHVIPVYWITJMBJ","created_at":"2026-07-13T01:17:55Z"},{"alias_kind":"pith_short_8","alias_value":"D6KHVIPV","created_at":"2026-07-13T01:17:55Z"}],"graph_snapshots":[{"event_id":"sha256:9856625243840ecdb4d075f71f2232797acdb948dfc5ceaaeedb75906931f6b7","target":"graph","created_at":"2026-07-13T01:17:55Z","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/2601.19442/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main objective of this paper is to prove that if capillarity effect is taken into account then there exist dissipative solutions to a system describing viscoplastic compressible flows with density dependent viscosities in a periodic domain $\\T^d$ with $d=2,3$. We calculate the relative entropy inequality and in consequence show existence of dissipative solutions and the weak-strong uniqueness for this system. Our result extends the recent result concerning the link between Euler--Korteweg and Navier--Stokes--Korteweg systems for Newtonian flows (when the viscosity depends on the density) [","authors_text":"Christophe Lacave, Didier Bresch, Maja Szlenk","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-27T10:26:05Z","title":"Dissipative Solutions to a Compressible Non-Newtonian Korteweg System with Density-Dependent Viscous Stress Tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19442","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":"sha256:81a866f241ad86469ab6ab7595159eac593e2ba014d1bc1963f5e1be2e7d202c","target":"record","created_at":"2026-07-13T01:17:55Z","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":"914e856b8e596148c3d3abd0182d367df90e75e5c59cef78f0a4939236d0569e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-27T10:26:05Z","title_canon_sha256":"d64626cbd8aff6ae97f3740a53845083b16f2d81b55ab3d9521ad91d618bb3eb"},"schema_version":"1.0","source":{"id":"2601.19442","kind":"arxiv","version":2}},"canonical_sha256":"1f947aa1f5c59134b029663e19e715103b64824e2274af160a4da9a2b2b8d3fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f947aa1f5c59134b029663e19e715103b64824e2274af160a4da9a2b2b8d3fe","first_computed_at":"2026-07-13T01:17:55.659214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:17:55.659214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CC7uZztyTVwwAJ/epKQdolsvS9HL6+V0Q0gkAWGkbsVHxpzvDPf8D5F2AGO1zhADluK7sW1BJUvlY/xShcSgBA==","signature_status":"signed_v1","signed_at":"2026-07-13T01:17:55.660487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.19442","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81a866f241ad86469ab6ab7595159eac593e2ba014d1bc1963f5e1be2e7d202c","sha256:9856625243840ecdb4d075f71f2232797acdb948dfc5ceaaeedb75906931f6b7"],"state_sha256":"3228af5ffd32acd8d736a2dfc7d4696d38f8d760238aa482ee4aed7d6d4365d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kWf5K9D4PY0HsUcbzLOOdEu6NAHCxlCtLHSrakCTOVYsILW3WUFoqY5MrNXI2VYy4H4fcCl+GZ4w0b6R0AbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T20:12:52.180601Z","bundle_sha256":"a19bd3dd311b1c3244a50b03e6373cc193483a5741eacc201c4f48ac55026c28"}}