{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SMERQVG2OCZ737UTRIAIOBW4AD","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":"ee28b85a7d7a1d0e8b17f3194dabe59178979fb9d7208c1ce3ee98e56817d5d9","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-09-05T16:20:48Z","title_canon_sha256":"4110cf7f09f30f48465b2da307970e7db75d347e1366425f728818b4acb3df72"},"schema_version":"1.0","source":{"id":"2509.05218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05218","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05218v2","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05218","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"SMERQVG2OCZ7","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"SMERQVG2OCZ737UT","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"SMERQVG2","created_at":"2026-07-05T12:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:1b24ede83c7a717f4eea383261d2415d1a2a2444b55b5bcb88ee47f66e060972","target":"graph","created_at":"2026-07-05T12:06:20Z","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/2509.05218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional representations, and relative approaches like Alibi exhibit performance degradation on extremely long contexts, the widely-used Rotary Positional Encoding (RoPE) introduces oscillatory attention patterns that hinder stable long-distance dependency modelling. We address these limitations through a geometric reformulation of positional encoding. Drawing inspiration from Lor","authors_text":"Chang Dai, Di Liang, Hongyu Shan, Mingyang Song","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-09-05T16:20:48Z","title":"HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05218","kind":"arxiv","version":2},"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:a5ad230c9612e470b15c79b46aae2269aa72337e63da7c39e597e4d417f52398","target":"record","created_at":"2026-07-05T12:06:20Z","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":"ee28b85a7d7a1d0e8b17f3194dabe59178979fb9d7208c1ce3ee98e56817d5d9","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-09-05T16:20:48Z","title_canon_sha256":"4110cf7f09f30f48465b2da307970e7db75d347e1366425f728818b4acb3df72"},"schema_version":"1.0","source":{"id":"2509.05218","kind":"arxiv","version":2}},"canonical_sha256":"93091854da70b3fdfe938a008706dc00d20924660e26a68456fd6dd79b9ffc86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93091854da70b3fdfe938a008706dc00d20924660e26a68456fd6dd79b9ffc86","first_computed_at":"2026-07-05T12:06:20.850651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:20.850651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RdH0dAeHb+jgOpL9VoslNOaO8JYFCNCdC4NrmspBqhjv14nROODmqsdBh5zetvqrroAr05i4VCloywW78BgYBA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:20.851137Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5ad230c9612e470b15c79b46aae2269aa72337e63da7c39e597e4d417f52398","sha256:1b24ede83c7a717f4eea383261d2415d1a2a2444b55b5bcb88ee47f66e060972"],"state_sha256":"92d31936360557ab42d5df71aa379b5a60ad1e0c7f22a4d026ec6ac558c9162f"}