{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BEX35MNIFHLHSOLA2WFPBIY6SF","short_pith_number":"pith:BEX35MNI","schema_version":"1.0","canonical_sha256":"092fbeb1a829d6793960d58af0a31e9154b1cd2d3418d001672438bce19b5aca","source":{"kind":"arxiv","id":"2605.04217","version":2},"attestation_state":"computed","paper":{"title":"Jordan-RoPE: Non-Semisimple Relative Positional Encoding via Complex Jordan Blocks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Non-semisimple Jordan blocks realize a distance-modulated phase basis for relative positional encoding","cross_cats":["cs.CL"],"primary_cat":"cs.LG","authors_text":"Yaobo Zhang","submitted_at":"2026-05-05T18:59:31Z","abstract_excerpt":"Relative positional encodings determine which functions of query-key lag can enter the primitive attention logit. RoPE supplies a rotary phase, while ALiBi supplies an additive distance bias. Motivated by group-theoretic views of linear translation-invariant positional encodings, we study a non-semisimple case in which a complex rotary eigenvalue and a nilpotent response live in the same defective Jordan block. The resulting relative operator generates oscillatory-polynomial features such as $e^{-\\gamma d}\\cos(\\omega d)$, $e^{-\\gamma d}\\sin(\\omega d)$, $d e^{-\\gamma d}\\cos(\\omega d)$, and $d e"},"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":"2605.04217","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-05T18:59:31Z","cross_cats_sorted":["cs.CL"],"title_canon_sha256":"f95c6c4b44010c361c59bce2d582e25ecb1ac8a84f776e1501a3fa1ff042c4a0","abstract_canon_sha256":"f51e2cdfb5841c530abdef5da65c817fc0687dfa7372cf02a1d52a49ce739ad5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:04.275204Z","signature_b64":"/UpYGkvXnXkYWktSollv+K3M5WvkGXhTqrBFtdk8WwVniMJedJIEw/5Hh097I4eFbCX6PyoYVbCDVL8Os9+vAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"092fbeb1a829d6793960d58af0a31e9154b1cd2d3418d001672438bce19b5aca","last_reissued_at":"2026-05-22T01:04:04.274254Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:04.274254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jordan-RoPE: Non-Semisimple Relative Positional Encoding via Complex Jordan Blocks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Non-semisimple Jordan blocks realize a distance-modulated phase basis for relative positional encoding","cross_cats":["cs.CL"],"primary_cat":"cs.LG","authors_text":"Yaobo Zhang","submitted_at":"2026-05-05T18:59:31Z","abstract_excerpt":"Relative positional encodings determine which functions of query-key lag can enter the primitive attention logit. RoPE supplies a rotary phase, while ALiBi supplies an additive distance bias. Motivated by group-theoretic views of linear translation-invariant positional encodings, we study a non-semisimple case in which a complex rotary eigenvalue and a nilpotent response live in the same defective Jordan block. The resulting relative operator generates oscillatory-polynomial features such as $e^{-\\gamma d}\\cos(\\omega d)$, $e^{-\\gamma d}\\sin(\\omega d)$, $d e^{-\\gamma d}\\cos(\\omega d)$, and $d e"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the construction realizes a distance-modulated phase basis d e^{iωd}, rather than merely adding a separate distance channel to RoPE.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the non-semisimple Jordan structure supplies an inductive bias that cannot be matched by simply combining existing RoPE and ALiBi channels or by other stabilized variants.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Jordan-RoPE realizes a non-semisimple relative positional operator that produces coupled oscillatory-polynomial features such as d e^{i omega d} for causal query-key lags.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-semisimple Jordan blocks realize a distance-modulated phase basis for relative positional encoding","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fc711af3fe77e3f5d8d18db2ddede5114ade7bebaddba6761f191cf3001abb36"},"source":{"id":"2605.04217","kind":"arxiv","version":2},"verdict":{"id":"45d65000-3658-495c-9334-7e7e5f7d554b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:06:24.228375Z","strongest_claim":"the construction realizes a distance-modulated phase basis d e^{iωd}, rather than merely adding a separate distance channel to RoPE.","one_line_summary":"Jordan-RoPE realizes a non-semisimple relative positional operator that produces coupled oscillatory-polynomial features such as d e^{i omega d} for causal query-key lags.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the non-semisimple Jordan structure supplies an inductive bias that cannot be matched by simply combining existing RoPE and ALiBi channels or by other stabilized variants.","pith_extraction_headline":"Non-semisimple Jordan blocks realize a distance-modulated phase basis for relative positional encoding"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04217/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T12:36:24.202863Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:21.071369Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:42:10.479550Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"edf6528cc2f93bc21de25d58173ff526ff19dc9ed8456313cceb427b27c84dfa"},"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":"2605.04217","created_at":"2026-05-22T01:04:04.274370+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.04217v2","created_at":"2026-05-22T01:04:04.274370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.04217","created_at":"2026-05-22T01:04:04.274370+00:00"},{"alias_kind":"pith_short_12","alias_value":"BEX35MNIFHLH","created_at":"2026-05-22T01:04:04.274370+00:00"},{"alias_kind":"pith_short_16","alias_value":"BEX35MNIFHLHSOLA","created_at":"2026-05-22T01:04:04.274370+00:00"},{"alias_kind":"pith_short_8","alias_value":"BEX35MNI","created_at":"2026-05-22T01:04:04.274370+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/BEX35MNIFHLHSOLA2WFPBIY6SF","json":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF.json","graph_json":"https://pith.science/api/pith-number/BEX35MNIFHLHSOLA2WFPBIY6SF/graph.json","events_json":"https://pith.science/api/pith-number/BEX35MNIFHLHSOLA2WFPBIY6SF/events.json","paper":"https://pith.science/paper/BEX35MNI"},"agent_actions":{"view_html":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF","download_json":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF.json","view_paper":"https://pith.science/paper/BEX35MNI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.04217&json=true","fetch_graph":"https://pith.science/api/pith-number/BEX35MNIFHLHSOLA2WFPBIY6SF/graph.json","fetch_events":"https://pith.science/api/pith-number/BEX35MNIFHLHSOLA2WFPBIY6SF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF/action/storage_attestation","attest_author":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF/action/author_attestation","sign_citation":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF/action/citation_signature","submit_replication":"https://pith.science/pith/BEX35MNIFHLHSOLA2WFPBIY6SF/action/replication_record"}},"created_at":"2026-05-22T01:04:04.274370+00:00","updated_at":"2026-05-22T01:04:04.274370+00:00"}