{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JRSHNXBJLOFTGJEX3JAUZQ5PLU","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":"384f88b4c1148e517411aca01e47b627022c0971bd24f8ae7c96d5e802f75a09","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T17:04:57Z","title_canon_sha256":"4f10a84cb9050462bf9b7a4c700634cd63225693b41c866b353690abe43112fd"},"schema_version":"1.0","source":{"id":"2606.09917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09917","created_at":"2026-06-10T00:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09917v1","created_at":"2026-06-10T00:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09917","created_at":"2026-06-10T00:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"JRSHNXBJLOFT","created_at":"2026-06-10T00:08:32Z"},{"alias_kind":"pith_short_16","alias_value":"JRSHNXBJLOFTGJEX","created_at":"2026-06-10T00:08:32Z"},{"alias_kind":"pith_short_8","alias_value":"JRSHNXBJ","created_at":"2026-06-10T00:08:32Z"}],"graph_snapshots":[{"event_id":"sha256:dd8906307c9d65ba592f2816e6f8ee4d4c0833b201ae899feb2170bbaa1a1f63","target":"graph","created_at":"2026-06-10T00:08:32Z","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/2606.09917/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables. Existing state-space models process time series by scanning tokenized temporal or spatial sequences, discarding the evolutionary geometric structure. We address this limitation by introducing manifold constraints into state-space modeling: treating the cross-variable correlation structure as a continuous trajectory on the symmetric positive definite manifold, whose Riemannian geometric features, tangent space linearity, and Frechet mean centrality act as a princi","authors_text":"Siu-Ming Yiu, Xingsheng Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T17:04:57Z","title":"SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09917","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":"sha256:4f614c616068f27289b5b11616b13cd8196fa5a79ba713b162a1670bc06b770e","target":"record","created_at":"2026-06-10T00:08:32Z","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":"384f88b4c1148e517411aca01e47b627022c0971bd24f8ae7c96d5e802f75a09","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T17:04:57Z","title_canon_sha256":"4f10a84cb9050462bf9b7a4c700634cd63225693b41c866b353690abe43112fd"},"schema_version":"1.0","source":{"id":"2606.09917","kind":"arxiv","version":1}},"canonical_sha256":"4c6476dc295b8b332497da414cc3af5d36c3044fd479375fc52d74fc6e5612d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c6476dc295b8b332497da414cc3af5d36c3044fd479375fc52d74fc6e5612d4","first_computed_at":"2026-06-10T00:08:32.904043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T00:08:32.904043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2kyZhcFqlcEPy3D+Yav24Y9sT1g2t/IEKj9a75QgHjn0mq/hcVq64AOOgLuNBrcuNHNim/uVEPPw5pLuoJNNCQ==","signature_status":"signed_v1","signed_at":"2026-06-10T00:08:32.904950Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f614c616068f27289b5b11616b13cd8196fa5a79ba713b162a1670bc06b770e","sha256:dd8906307c9d65ba592f2816e6f8ee4d4c0833b201ae899feb2170bbaa1a1f63"],"state_sha256":"f71f3796ca34372a94681c9d1065d4b3d2b0be7d0eefedfb087c384745d5a1a9"}