{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YCQVTFUF6VKKK4IEGZ42M7NJW6","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":"e4e6a0e997c713f6bfc29a76bfb20fe0b4282028d21200e48adcdaf7a108aab5","cross_cats_sorted":["cs.AI","cs.PF"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-05T14:44:49Z","title_canon_sha256":"2a938638e74ced5b3fc71f20c7421e411ef85b6be452f0b89927bcadf74b1dcd"},"schema_version":"1.0","source":{"id":"2606.07713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07713","created_at":"2026-06-09T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07713v1","created_at":"2026-06-09T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07713","created_at":"2026-06-09T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"YCQVTFUF6VKK","created_at":"2026-06-09T01:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCQVTFUF6VKKK4IE","created_at":"2026-06-09T01:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCQVTFUF","created_at":"2026-06-09T01:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:6430cd33219cb5d1af683ad35d1f71e8f731e2260d56ab29319c537cf3fdf1a8","target":"graph","created_at":"2026-06-09T01:04:50Z","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/2606.07713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The attention mechanism is the dominant computational bottleneck in modern transformer-based AI. Its standard implementation incurs quadratic memory traffic in the sequence length~$n$, and DRAM accesses cost 100--1000$\\times$ more energy than arithmetic operations on contemporary hardware, so any analysis focused solely on FLOP counts fundamentally mischaracterises the bottleneck.\n  We present a Mathematics of Arrays (MoA) reformulation of scaled dot-product attention and its numerically stable softmax, deriving a Denotational Normal Form (DNF) that eliminates all intermediate arrays -- includ","authors_text":"Gaetan Hains, Lenore Mullin","cross_cats":["cs.AI","cs.PF"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-05T14:44:49Z","title":"Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07713","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:bea158b1fa763aa54a8135bd7589c7ec68508dbd1e4112f94d1f72fb068d56a7","target":"record","created_at":"2026-06-09T01:04:50Z","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":"e4e6a0e997c713f6bfc29a76bfb20fe0b4282028d21200e48adcdaf7a108aab5","cross_cats_sorted":["cs.AI","cs.PF"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-05T14:44:49Z","title_canon_sha256":"2a938638e74ced5b3fc71f20c7421e411ef85b6be452f0b89927bcadf74b1dcd"},"schema_version":"1.0","source":{"id":"2606.07713","kind":"arxiv","version":1}},"canonical_sha256":"c0a1599685f554a571043679a67da9b7a8405b5d6e586990275089bf5f1fc797","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a1599685f554a571043679a67da9b7a8405b5d6e586990275089bf5f1fc797","first_computed_at":"2026-06-09T01:04:50.058649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:04:50.058649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JgcIBvmiy4349pMEB8sP9mtkc7IIrrBs8psOgRpfE5q0+6+myXGGJUOl7i0Oi3fTSK6gRAfieuaVOS3xqyXrDw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:04:50.059132Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bea158b1fa763aa54a8135bd7589c7ec68508dbd1e4112f94d1f72fb068d56a7","sha256:6430cd33219cb5d1af683ad35d1f71e8f731e2260d56ab29319c537cf3fdf1a8"],"state_sha256":"3e5287e69948d61b4d60c77cc4a6cb1d9e6281c63711b7a801e3a6f1381e4bdc"}