{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QERS5T3UX3VILFL2RRZUZ7ROD2","short_pith_number":"pith:QERS5T3U","schema_version":"1.0","canonical_sha256":"81232ecf74beea85957a8c734cfe2e1ebe540e1e31afebd95a0fea6feb7c85f6","source":{"kind":"arxiv","id":"2605.20635","version":1},"attestation_state":"computed","paper":{"title":"The General Theory of Localization Methods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Congwei Song","submitted_at":"2026-05-20T02:42:14Z","abstract_excerpt":"This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means -- key components that underpin the self-attention mechanism. To establish a rigorous theoretical foundation, the framework is formally defined through two essential pillars: the formulation of the local(-ized) model and the localization trick. We systematically investigate the connections between the localization method and a wide range of existing machine learning models/methods, including (but not limited to) kernel "},"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":"2605.20635","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T02:42:14Z","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"title_canon_sha256":"e3e7ffe44c9257eaa055d9cccf7fbf2ea513194a96d52e8865af6fc35600fb3e","abstract_canon_sha256":"d0e16367757a1f059bdabcb69edac7ac32eb70af9757dd19c96a8b9eb71b9175"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:45.973586Z","signature_b64":"AO1duWIpTo9F1Jmm1XWQdO+Ru+CyTiV7gWuHwwRS8M/VVjWqH5jCNDxEGCWGvzdtYmVzpK2YFOOqrjl9hnnADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81232ecf74beea85957a8c734cfe2e1ebe540e1e31afebd95a0fea6feb7c85f6","last_reissued_at":"2026-05-21T01:04:45.971429Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:45.971429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The General Theory of Localization Methods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Congwei Song","submitted_at":"2026-05-20T02:42:14Z","abstract_excerpt":"This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means -- key components that underpin the self-attention mechanism. To establish a rigorous theoretical foundation, the framework is formally defined through two essential pillars: the formulation of the local(-ized) model and the localization trick. We systematically investigate the connections between the localization method and a wide range of existing machine learning models/methods, including (but not limited to) kernel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20635","kind":"arxiv","version":1},"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/2605.20635/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":"2605.20635","created_at":"2026-05-21T01:04:45.971805+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20635v1","created_at":"2026-05-21T01:04:45.971805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20635","created_at":"2026-05-21T01:04:45.971805+00:00"},{"alias_kind":"pith_short_12","alias_value":"QERS5T3UX3VI","created_at":"2026-05-21T01:04:45.971805+00:00"},{"alias_kind":"pith_short_16","alias_value":"QERS5T3UX3VILFL2","created_at":"2026-05-21T01:04:45.971805+00:00"},{"alias_kind":"pith_short_8","alias_value":"QERS5T3U","created_at":"2026-05-21T01:04:45.971805+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/QERS5T3UX3VILFL2RRZUZ7ROD2","json":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2.json","graph_json":"https://pith.science/api/pith-number/QERS5T3UX3VILFL2RRZUZ7ROD2/graph.json","events_json":"https://pith.science/api/pith-number/QERS5T3UX3VILFL2RRZUZ7ROD2/events.json","paper":"https://pith.science/paper/QERS5T3U"},"agent_actions":{"view_html":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2","download_json":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2.json","view_paper":"https://pith.science/paper/QERS5T3U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20635&json=true","fetch_graph":"https://pith.science/api/pith-number/QERS5T3UX3VILFL2RRZUZ7ROD2/graph.json","fetch_events":"https://pith.science/api/pith-number/QERS5T3UX3VILFL2RRZUZ7ROD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2/action/storage_attestation","attest_author":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2/action/author_attestation","sign_citation":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2/action/citation_signature","submit_replication":"https://pith.science/pith/QERS5T3UX3VILFL2RRZUZ7ROD2/action/replication_record"}},"created_at":"2026-05-21T01:04:45.971805+00:00","updated_at":"2026-05-21T01:04:45.971805+00:00"}