{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TLQXP53K2KAPDTDGU24ANHPKUM","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":"f18251bacbdaa8fc21c232404871ea3103b31c447183a56bb41c118a1d36eb2e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T08:54:37Z","title_canon_sha256":"86018bf447e7672e87a4fd6cbd8f7afadc997d8359fe9e19d3f27e19631a9843"},"schema_version":"1.0","source":{"id":"2605.29619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29619","created_at":"2026-05-29T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29619v1","created_at":"2026-05-29T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29619","created_at":"2026-05-29T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"TLQXP53K2KAP","created_at":"2026-05-29T01:05:51Z"},{"alias_kind":"pith_short_16","alias_value":"TLQXP53K2KAPDTDG","created_at":"2026-05-29T01:05:51Z"},{"alias_kind":"pith_short_8","alias_value":"TLQXP53K","created_at":"2026-05-29T01:05:51Z"}],"graph_snapshots":[{"event_id":"sha256:5bf9397a07eccf2674fb14c650369ef4770e851f432fe55bdfc8259597630e33","target":"graph","created_at":"2026-05-29T01:05:51Z","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/2605.29619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we establish the existence of mass-conserving weak solutions to a nonlinear collision-induced breakage equation in which binary collisions may trigger particle breakup. The result is proved for a class of product-type collision kernels whose small-size behavior is controlled by a power-law function of the form $\\omega_0(x)\\le A_1\\,x^\\ell$, while no growth restriction is imposed on the large-size factor $\\omega_\\infty$. The qualitative behavior of the solutions depends crucially on the exponent $\\ell$ near the origin. Sublinear growth corresponding to $\\ell<\\tfrac12$ yields existe","authors_text":"Mashkoor Ali","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T08:54:37Z","title":"On a Class of Continuous Collision-Induced Breakage Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29619","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":"sha256:800cb4d9d25157955c5b9abc72b5e5775f9914630dac87b8b67835e703e1c6f9","target":"record","created_at":"2026-05-29T01:05:51Z","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":"f18251bacbdaa8fc21c232404871ea3103b31c447183a56bb41c118a1d36eb2e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T08:54:37Z","title_canon_sha256":"86018bf447e7672e87a4fd6cbd8f7afadc997d8359fe9e19d3f27e19631a9843"},"schema_version":"1.0","source":{"id":"2605.29619","kind":"arxiv","version":1}},"canonical_sha256":"9ae177f76ad280f1cc66a6b8069deaa3304eab9dad7053a2d14b2ce4e721f13a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ae177f76ad280f1cc66a6b8069deaa3304eab9dad7053a2d14b2ce4e721f13a","first_computed_at":"2026-05-29T01:05:51.329666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:51.329666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OdlI37TdbHmzMboz71pBCAO0JECSIBjzICqOWZ7aLeiebFHP8iEO6cqaAE/XIbB8/8/HTRYZ2PaLn8y6I5cbAw==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:51.330443Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:800cb4d9d25157955c5b9abc72b5e5775f9914630dac87b8b67835e703e1c6f9","sha256:5bf9397a07eccf2674fb14c650369ef4770e851f432fe55bdfc8259597630e33"],"state_sha256":"40399d56847612d81c8c236ad5f865287e31e637a38e0ca529211d5fe125dbd4"}