{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ADKXOZVRZJD247KFWBSYI2PMCV","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":"0d45be0b5628f30a954e0cec1b0ed75f4145e63940fe44e1e31e7f6ed35381c4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T22:16:37Z","title_canon_sha256":"8b37563942fcf8081bcc7f735ff28fa2dd92ff2c858ed8d81dcbab1c178fb267"},"schema_version":"1.0","source":{"id":"2607.25112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25112","created_at":"2026-07-29T00:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25112v1","created_at":"2026-07-29T00:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25112","created_at":"2026-07-29T00:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"ADKXOZVRZJD2","created_at":"2026-07-29T00:25:03Z"},{"alias_kind":"pith_short_16","alias_value":"ADKXOZVRZJD247KF","created_at":"2026-07-29T00:25:03Z"},{"alias_kind":"pith_short_8","alias_value":"ADKXOZVR","created_at":"2026-07-29T00:25:03Z"}],"graph_snapshots":[{"event_id":"sha256:6cc44c092b78828b0b635ad8b931e42b0fb54e7659e74a268b203e387395a6a0","target":"graph","created_at":"2026-07-29T00:25:03Z","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/2607.25112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a no-gelation mechanism that yields global solutions to the spatially homogeneous Boltzmann equation with mass exchange for Grad-cutoff hard potentials $B=E^\\gamma b(\\xi), 0<\\gamma<1$ and regularly varying mass-exchange rates. Without assuming any higher mass moment, we construct a convex superlinear weight assembled from dyadic hinges. Production of the weighted moment by collisions between large particles of comparable mass is absorbed by dissipation through collisions with a uniformly populated reservoir of bounded-mass particles. Regular variation makes the signed increments in ","authors_text":"Jian-Guo Liu, Siwei Luo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T22:16:37Z","title":"No Gelation and Global Existence for a Boltzmann Equation with Regularly Varying Mass-Exchange Rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25112","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":"sha256:6030d766933b3d71e36419d039b9d048efc292f32e2c05476867f368b57433a0","target":"record","created_at":"2026-07-29T00:25:03Z","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":"0d45be0b5628f30a954e0cec1b0ed75f4145e63940fe44e1e31e7f6ed35381c4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T22:16:37Z","title_canon_sha256":"8b37563942fcf8081bcc7f735ff28fa2dd92ff2c858ed8d81dcbab1c178fb267"},"schema_version":"1.0","source":{"id":"2607.25112","kind":"arxiv","version":1}},"canonical_sha256":"00d57766b1ca47ae7d45b0658469ec1558357451ec934881e536df83a5b5a7d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00d57766b1ca47ae7d45b0658469ec1558357451ec934881e536df83a5b5a7d7","first_computed_at":"2026-07-29T00:25:03.440780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T00:25:03.440780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hV/USNmfw8VsDPIqaU4zokIKtvDE/rlnX9TornQmh+sxOjgFZkjq2kSLNiBJBrwfEKClNE2OY8Oaf8vCAvs6DA==","signature_status":"signed_v1","signed_at":"2026-07-29T00:25:03.441628Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6030d766933b3d71e36419d039b9d048efc292f32e2c05476867f368b57433a0","sha256:6cc44c092b78828b0b635ad8b931e42b0fb54e7659e74a268b203e387395a6a0"],"state_sha256":"9367ed3a7cb8ce6d0bce2827079a9394ed57c0ced2300869455b79b2d1b027c2"}