{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:M6F7D7QHPWMVKHXGYQB2RWPYVX","short_pith_number":"pith:M6F7D7QH","canonical_record":{"source":{"id":"2607.26369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-29T01:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"7452d7321387ceae34dd57cc6c041a13d50d80ed9eb125766cf2ef226dc042c6","abstract_canon_sha256":"28eeb8b35da63d74895e9b4f78c01aa64952ec5ea6aea753ced5324b7618dba3"},"schema_version":"1.0"},"canonical_sha256":"678bf1fe077d99551ee6c403a8d9f8adc6939bfeb75ce201e7a9c5273f3a1d11","source":{"kind":"arxiv","id":"2607.26369","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26369","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26369v1","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26369","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"M6F7D7QHPWMV","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"M6F7D7QHPWMVKHXG","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"M6F7D7QH","created_at":"2026-07-30T01:18:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:M6F7D7QHPWMVKHXGYQB2RWPYVX","target":"record","payload":{"canonical_record":{"source":{"id":"2607.26369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-29T01:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"7452d7321387ceae34dd57cc6c041a13d50d80ed9eb125766cf2ef226dc042c6","abstract_canon_sha256":"28eeb8b35da63d74895e9b4f78c01aa64952ec5ea6aea753ced5324b7618dba3"},"schema_version":"1.0"},"canonical_sha256":"678bf1fe077d99551ee6c403a8d9f8adc6939bfeb75ce201e7a9c5273f3a1d11","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"678bf1fe077d99551ee6c403a8d9f8adc6939bfeb75ce201e7a9c5273f3a1d11","last_reissued_at":"2026-07-30T01:18:13.489408Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:18:13.489408Z"},"source_kind":"arxiv","source_id":"2607.26369","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-30T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9QiM+euNa4RPbL7jne6mBECFYwyztSLjUzQ6FoBzS4IxRGbckneDcidBVDsZqbqTl30KQ3n3b4+6ytRgR89NCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:05:43.517214Z"},"content_sha256":"f6fc574051f63c4cce7c630940b109ec13fbfcc3f474e91ae24964cf819b1edb","schema_version":"1.0","event_id":"sha256:f6fc574051f63c4cce7c630940b109ec13fbfcc3f474e91ae24964cf819b1edb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:M6F7D7QHPWMVKHXGYQB2RWPYVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"ClockRoPE: Random Fourier Rotations for Temporal Routine Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Joshua Ainslie, Krzysztof Choromanski, Qian Sun, Su-Lin Wu, Xiang Gao, Yiping Yuan, Yiwen Chen","submitted_at":"2026-07-29T01:07:27Z","abstract_excerpt":"Rotary Position Embedding (RoPE) has been widely adopted in transformer-based large language models. However, its log-linear frequency schedule, originally designed to produce long-term attention decay, limits its adoption in domains with more complex distance-correlation patterns, such as temporal periodicity in sequential recommendation. We investigate the expressiveness of general query/key rotations and find that any normalized continuous positive-definite attention modulation function can be approximated by random rotations induced by its own Fourier transform, which we term Random Fourie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26369","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/2607.26369/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-30T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJ1QQfxAydo0STdh8IKgh0D33wbUhuTKq1GjdII2TFxRme4myFsiKMjzNcQpeMo0xzd8slgxnU7U2+LvG6f/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:05:43.518006Z"},"content_sha256":"a0e1fe262d2fa3f3e2372c0be33f9c1a125adfd33fda04cca4ec8fc5a1e2900d","schema_version":"1.0","event_id":"sha256:a0e1fe262d2fa3f3e2372c0be33f9c1a125adfd33fda04cca4ec8fc5a1e2900d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX/bundle.json","state_url":"https://pith.science/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T01:05:43Z","links":{"resolver":"https://pith.science/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX","bundle":"https://pith.science/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX/bundle.json","state":"https://pith.science/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6F7D7QHPWMVKHXGYQB2RWPYVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M6F7D7QHPWMVKHXGYQB2RWPYVX","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":"28eeb8b35da63d74895e9b4f78c01aa64952ec5ea6aea753ced5324b7618dba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-29T01:07:27Z","title_canon_sha256":"7452d7321387ceae34dd57cc6c041a13d50d80ed9eb125766cf2ef226dc042c6"},"schema_version":"1.0","source":{"id":"2607.26369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26369","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26369v1","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26369","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"M6F7D7QHPWMV","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"M6F7D7QHPWMVKHXG","created_at":"2026-07-30T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"M6F7D7QH","created_at":"2026-07-30T01:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:a0e1fe262d2fa3f3e2372c0be33f9c1a125adfd33fda04cca4ec8fc5a1e2900d","target":"graph","created_at":"2026-07-30T01:18:13Z","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/2607.26369/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Rotary Position Embedding (RoPE) has been widely adopted in transformer-based large language models. However, its log-linear frequency schedule, originally designed to produce long-term attention decay, limits its adoption in domains with more complex distance-correlation patterns, such as temporal periodicity in sequential recommendation. We investigate the expressiveness of general query/key rotations and find that any normalized continuous positive-definite attention modulation function can be approximated by random rotations induced by its own Fourier transform, which we term Random Fourie","authors_text":"Joshua Ainslie, Krzysztof Choromanski, Qian Sun, Su-Lin Wu, Xiang Gao, Yiping Yuan, Yiwen Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-29T01:07:27Z","title":"ClockRoPE: Random Fourier Rotations for Temporal Routine Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26369","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:f6fc574051f63c4cce7c630940b109ec13fbfcc3f474e91ae24964cf819b1edb","target":"record","created_at":"2026-07-30T01:18:13Z","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":"28eeb8b35da63d74895e9b4f78c01aa64952ec5ea6aea753ced5324b7618dba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-29T01:07:27Z","title_canon_sha256":"7452d7321387ceae34dd57cc6c041a13d50d80ed9eb125766cf2ef226dc042c6"},"schema_version":"1.0","source":{"id":"2607.26369","kind":"arxiv","version":1}},"canonical_sha256":"678bf1fe077d99551ee6c403a8d9f8adc6939bfeb75ce201e7a9c5273f3a1d11","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"678bf1fe077d99551ee6c403a8d9f8adc6939bfeb75ce201e7a9c5273f3a1d11","first_computed_at":"2026-07-30T01:18:13.489408Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:18:13.489408Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.26369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6fc574051f63c4cce7c630940b109ec13fbfcc3f474e91ae24964cf819b1edb","sha256:a0e1fe262d2fa3f3e2372c0be33f9c1a125adfd33fda04cca4ec8fc5a1e2900d"],"state_sha256":"b680c6eefb54e7ff3a23853bc7c59ad3317ca253b53f00483abf61124d92a3b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6PF5arBkWhU0+Uxl/ulgb3F6Vb97Bd6q9efYzyVKLuEPoPBa9CYDa6BB6oXMU64fqoBGDdReR3pjZoc9+uoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T01:05:43.522180Z","bundle_sha256":"a3af79aed03882df0bd36c843522c335229436652d82363acd256bd8d32e9bf6"}}