{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6J63DAYRSIKU5MNMP53B6RUS5O","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":"a0022701580241e7dc5e3ced97712c9319211db87f550d0892abe22d0aa5b2aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-11T14:58:30Z","title_canon_sha256":"87219b05309deb06a0cae697603015ae653aa70be93730c85adfb8009216b03a"},"schema_version":"1.0","source":{"id":"2606.13433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13433","created_at":"2026-06-12T01:10:02Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13433v1","created_at":"2026-06-12T01:10:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13433","created_at":"2026-06-12T01:10:02Z"},{"alias_kind":"pith_short_12","alias_value":"6J63DAYRSIKU","created_at":"2026-06-12T01:10:02Z"},{"alias_kind":"pith_short_16","alias_value":"6J63DAYRSIKU5MNM","created_at":"2026-06-12T01:10:02Z"},{"alias_kind":"pith_short_8","alias_value":"6J63DAYR","created_at":"2026-06-12T01:10:02Z"}],"graph_snapshots":[{"event_id":"sha256:dcf7473c19b7b6c6a38c3c3778bfeb851fd0fd74a09a37f914ab96ed8172a11a","target":"graph","created_at":"2026-06-12T01:10:02Z","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/2606.13433/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a principled derivation of the Soft-Min-SNR weight of Crowson et al. (2024). The spread divergence of Zhang et al. (2018) convolves both compared distributions with a Gaussian kernel before taking the Kullback-Leibler (KL) divergence; applied to the per-sample local matched-Gaussian surrogate at each timestep, it yields the closed-form weight w(t,lambda) = sigma^2 / (sigma^2 + lambda). Three consequences follow. First, for variance-preserving schedules, w(t,lambda) equals a constant multiple of Soft-Min-SNR with gamma' = (1+lambda)/lambda, deriving a validated heuristic rather than int","authors_text":"Lei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-11T14:58:30Z","title":"Smoothed-KL Reweighting: A Principled Account and Matching Rule for SNR-Based Diffusion Training"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13433","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:eac6265e58d741729b4ffd501cd7d0165b2806f45620ff3298e7b70d7b00ea74","target":"record","created_at":"2026-06-12T01:10:02Z","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":"a0022701580241e7dc5e3ced97712c9319211db87f550d0892abe22d0aa5b2aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-11T14:58:30Z","title_canon_sha256":"87219b05309deb06a0cae697603015ae653aa70be93730c85adfb8009216b03a"},"schema_version":"1.0","source":{"id":"2606.13433","kind":"arxiv","version":1}},"canonical_sha256":"f27db1831192154eb1ac7f761f4692ebac30630a31675e8fa424068aa5eed6e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f27db1831192154eb1ac7f761f4692ebac30630a31675e8fa424068aa5eed6e2","first_computed_at":"2026-06-12T01:10:02.169688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:10:02.169688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QhSIQkyOaehzd2dtPv2F0lHCFBzZjh0Bz95e6UStLotvmH8BQEbcGzT0w8GX2weBdWkB8fyLye7WsHR+Vmb5CQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:10:02.170560Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eac6265e58d741729b4ffd501cd7d0165b2806f45620ff3298e7b70d7b00ea74","sha256:dcf7473c19b7b6c6a38c3c3778bfeb851fd0fd74a09a37f914ab96ed8172a11a"],"state_sha256":"3f5fddb5730e3c170ea61a3d560650e47aa7efd6e5cca933442422741cfc886d"}