{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:46YTQ6DX5HTW35DH7YTXRXA5N6","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":"7d95fd7dc6b1c4bae5ac281735e295b88f79783c254decb68d4739daa46de9af","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1996-12-12T15:15:26Z","title_canon_sha256":"df9b1768fe4d52a5f3d125c0eaaf2a52f50dce67d0095aa4a3435d864d02959e"},"schema_version":"1.0","source":{"id":"cond-mat/9612120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9612120","created_at":"2026-05-18T01:07:08Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9612120v2","created_at":"2026-05-18T01:07:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9612120","created_at":"2026-05-18T01:07:08Z"},{"alias_kind":"pith_short_12","alias_value":"46YTQ6DX5HTW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"46YTQ6DX5HTW35DH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"46YTQ6DX","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:e0292de7be22d8681bd5493c6a7a728069e686842ce2b6e899b8b1df8aa78410","target":"graph","created_at":"2026-05-18T01:07:08Z","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"},"paper":{"abstract_excerpt":"We consider the scaling solutions of Smoluchowski's equation of irreversible aggregation, for a non gelling collision kernel. The scaling mass distribution f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now, only be computed by numerical simulations. We develop here new general methods to obtain exact bounds and good approximations of $\\tau$. For the specific kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R is the particle radius), perturbative and nonperturbat","authors_text":"Clement Sire, Stephane Cueille","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1996-12-12T15:15:26Z","title":"Nontrivial Polydispersity Exponents in Aggregation Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9612120","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":"sha256:3849440b63b491c05144a5992ceda760d5c7f274b7534c3a8def44c0aaed160c","target":"record","created_at":"2026-05-18T01:07:08Z","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":"7d95fd7dc6b1c4bae5ac281735e295b88f79783c254decb68d4739daa46de9af","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1996-12-12T15:15:26Z","title_canon_sha256":"df9b1768fe4d52a5f3d125c0eaaf2a52f50dce67d0095aa4a3435d864d02959e"},"schema_version":"1.0","source":{"id":"cond-mat/9612120","kind":"arxiv","version":2}},"canonical_sha256":"e7b1387877e9e76df467fe2778dc1d6f8be1cac0c9b71f2b9c2843d3d3ca82d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7b1387877e9e76df467fe2778dc1d6f8be1cac0c9b71f2b9c2843d3d3ca82d6","first_computed_at":"2026-05-18T01:07:08.932758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:08.932758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"khHs2VofouxVfkD17pvdeZKqC2Q8mTZdWIjvsMP30HOiTOZE8QQKiNneBA5uXwHrk3I8/ADIMCIuV2K8L/bbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:08.933187Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9612120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3849440b63b491c05144a5992ceda760d5c7f274b7534c3a8def44c0aaed160c","sha256:e0292de7be22d8681bd5493c6a7a728069e686842ce2b6e899b8b1df8aa78410"],"state_sha256":"a77023ea83f9d74d8581f8a592fe7048ed2f9d35c6fab71c72b09f60b5307ae6"}