{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SLZHS7PQ3DTOTLTXLEQHPIM5DW","short_pith_number":"pith:SLZHS7PQ","schema_version":"1.0","canonical_sha256":"92f2797df0d8e6e9ae77592077a19d1d80bd4938dfc29cd552f629deab34fe11","source":{"kind":"arxiv","id":"2512.18965","version":2},"attestation_state":"computed","paper":{"title":"Lag Operator SSMs: A Geometric Framework for Structured State Space Modeling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kenji Doya, Noboru Murata, Sutashu Tomonaga","submitted_at":"2025-12-22T02:25:26Z","abstract_excerpt":"Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multistage process of continuous-time modeling and subsequent discretization, which can obscure intuition. We introduce a direct, first-principles framework for constructing discrete-time SSMs that is both flexible and modular. Our approach is based on a novel lag operator, which geometrically derives the discrete-time recurrence by measuring how the system's basis functions undergo what we "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2512.18965","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-12-22T02:25:26Z","cross_cats_sorted":[],"title_canon_sha256":"3440dbeea80f00497ece8eb9ad93541af23d75e98c77d37bd89e099a7794760b","abstract_canon_sha256":"9dba5472a5458116d57050d501648829b9f834aeaf10f97b87711c711b3bd137"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:21:44.180924Z","signature_b64":"8t6m+DB/I7Xp0/+orOD17CqYCW3ZaX6MPT4N8OOZg4wKiirVXWLep5HIm8bWlGTJFCplu3aVD+y7123/ScHDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92f2797df0d8e6e9ae77592077a19d1d80bd4938dfc29cd552f629deab34fe11","last_reissued_at":"2026-07-16T00:21:44.179986Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:21:44.179986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lag Operator SSMs: A Geometric Framework for Structured State Space Modeling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kenji Doya, Noboru Murata, Sutashu Tomonaga","submitted_at":"2025-12-22T02:25:26Z","abstract_excerpt":"Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multistage process of continuous-time modeling and subsequent discretization, which can obscure intuition. We introduce a direct, first-principles framework for constructing discrete-time SSMs that is both flexible and modular. Our approach is based on a novel lag operator, which geometrically derives the discrete-time recurrence by measuring how the system's basis functions undergo what we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.18965","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.18965/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2512.18965","created_at":"2026-07-16T00:21:44.180417+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.18965v2","created_at":"2026-07-16T00:21:44.180417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.18965","created_at":"2026-07-16T00:21:44.180417+00:00"},{"alias_kind":"pith_short_12","alias_value":"SLZHS7PQ3DTO","created_at":"2026-07-16T00:21:44.180417+00:00"},{"alias_kind":"pith_short_16","alias_value":"SLZHS7PQ3DTOTLTX","created_at":"2026-07-16T00:21:44.180417+00:00"},{"alias_kind":"pith_short_8","alias_value":"SLZHS7PQ","created_at":"2026-07-16T00:21:44.180417+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW","json":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW.json","graph_json":"https://pith.science/api/pith-number/SLZHS7PQ3DTOTLTXLEQHPIM5DW/graph.json","events_json":"https://pith.science/api/pith-number/SLZHS7PQ3DTOTLTXLEQHPIM5DW/events.json","paper":"https://pith.science/paper/SLZHS7PQ"},"agent_actions":{"view_html":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW","download_json":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW.json","view_paper":"https://pith.science/paper/SLZHS7PQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.18965&json=true","fetch_graph":"https://pith.science/api/pith-number/SLZHS7PQ3DTOTLTXLEQHPIM5DW/graph.json","fetch_events":"https://pith.science/api/pith-number/SLZHS7PQ3DTOTLTXLEQHPIM5DW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW/action/storage_attestation","attest_author":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW/action/author_attestation","sign_citation":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW/action/citation_signature","submit_replication":"https://pith.science/pith/SLZHS7PQ3DTOTLTXLEQHPIM5DW/action/replication_record"}},"created_at":"2026-07-16T00:21:44.180417+00:00","updated_at":"2026-07-16T00:21:44.180417+00:00"}