{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:C4XJ77Y2YKTWE7EPYLACWMREGY","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":"209840eb82209767eec760e1bf5722180382df66527ece3977a40387d489c211","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-03T12:06:28Z","title_canon_sha256":"1f8a2a614c17c5b6660eb8e5b6496f908dd2ba1f97c56bcce58db48ab047409b"},"schema_version":"1.0","source":{"id":"2606.04785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04785","created_at":"2026-06-04T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04785v1","created_at":"2026-06-04T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04785","created_at":"2026-06-04T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"C4XJ77Y2YKTW","created_at":"2026-06-04T01:09:29Z"},{"alias_kind":"pith_short_16","alias_value":"C4XJ77Y2YKTWE7EP","created_at":"2026-06-04T01:09:29Z"},{"alias_kind":"pith_short_8","alias_value":"C4XJ77Y2","created_at":"2026-06-04T01:09:29Z"}],"graph_snapshots":[{"event_id":"sha256:9e7f2bd4011f9b37c4a851ddf0dc3b7800e52095bfa5140e5c6ace5b94d79915","target":"graph","created_at":"2026-06-04T01:09:29Z","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/2606.04785/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study weak solutions of the one-dimensional pressureless Euler-Poisson-alignment system. When smooth solutions develop singularities, distributional weak solutions are not unique. We introduce an entropy-based selection principle via an associated scalar balance law with time-dependent flux and establish global well-posedness for its entropy solutions. The resulting entropic solution yields a uniquely selected weak solution of the Euler-Poisson-alignment system. In the attractive regime, it is compatible with sticky particle dynamics, while in the repulsive regime atomic states may disperse","authors_text":"Changhui Tan, Trevor M. Leslie","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-03T12:06:28Z","title":"Entropic solutions to the 1D pressureless Euler system with nonlocal interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04785","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":"sha256:898e9be50db27c9bc6985f8b8f6e86b3afb3d56adf092f3dd769a1ccbb751529","target":"record","created_at":"2026-06-04T01:09:29Z","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":"209840eb82209767eec760e1bf5722180382df66527ece3977a40387d489c211","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-03T12:06:28Z","title_canon_sha256":"1f8a2a614c17c5b6660eb8e5b6496f908dd2ba1f97c56bcce58db48ab047409b"},"schema_version":"1.0","source":{"id":"2606.04785","kind":"arxiv","version":1}},"canonical_sha256":"172e9fff1ac2a7627c8fc2c02b3224363d3cd33e161da7346273b868c27e73c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"172e9fff1ac2a7627c8fc2c02b3224363d3cd33e161da7346273b868c27e73c2","first_computed_at":"2026-06-04T01:09:29.834634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:29.834634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/x1wZnkS1UVq0oNLWrSAoOPoRxIJ1Vgl5CddrM52TTLUa+u3drY9sQQpMVoR+Kew/SqlBETFYCLqg4z+Teh8DQ==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:29.835208Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:898e9be50db27c9bc6985f8b8f6e86b3afb3d56adf092f3dd769a1ccbb751529","sha256:9e7f2bd4011f9b37c4a851ddf0dc3b7800e52095bfa5140e5c6ace5b94d79915"],"state_sha256":"4a6cac11293c568034b132ec5359ab058364f6dca1f98030043f425a87c3306a"}