{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YCQVTFUF6VKKK4IEGZ42M7NJW6","short_pith_number":"pith:YCQVTFUF","schema_version":"1.0","canonical_sha256":"c0a1599685f554a571043679a67da9b7a8405b5d6e586990275089bf5f1fc797","source":{"kind":"arxiv","id":"2606.07713","version":1},"attestation_state":"computed","paper":{"title":"Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI","cs.PF"],"primary_cat":"cs.LG","authors_text":"Gaetan Hains, Lenore Mullin","submitted_at":"2026-06-05T14:44:49Z","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"},"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":"2606.07713","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-05T14:44:49Z","cross_cats_sorted":["cs.AI","cs.PF"],"title_canon_sha256":"2a938638e74ced5b3fc71f20c7421e411ef85b6be452f0b89927bcadf74b1dcd","abstract_canon_sha256":"e4e6a0e997c713f6bfc29a76bfb20fe0b4282028d21200e48adcdaf7a108aab5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:50.059132Z","signature_b64":"JgcIBvmiy4349pMEB8sP9mtkc7IIrrBs8psOgRpfE5q0+6+myXGGJUOl7i0Oi3fTSK6gRAfieuaVOS3xqyXrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0a1599685f554a571043679a67da9b7a8405b5d6e586990275089bf5f1fc797","last_reissued_at":"2026-06-09T01:04:50.058649Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:50.058649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI","cs.PF"],"primary_cat":"cs.LG","authors_text":"Gaetan Hains, Lenore Mullin","submitted_at":"2026-06-05T14:44:49Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07713","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/2606.07713/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":"2606.07713","created_at":"2026-06-09T01:04:50.058705+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.07713v1","created_at":"2026-06-09T01:04:50.058705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07713","created_at":"2026-06-09T01:04:50.058705+00:00"},{"alias_kind":"pith_short_12","alias_value":"YCQVTFUF6VKK","created_at":"2026-06-09T01:04:50.058705+00:00"},{"alias_kind":"pith_short_16","alias_value":"YCQVTFUF6VKKK4IE","created_at":"2026-06-09T01:04:50.058705+00:00"},{"alias_kind":"pith_short_8","alias_value":"YCQVTFUF","created_at":"2026-06-09T01:04:50.058705+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/YCQVTFUF6VKKK4IEGZ42M7NJW6","json":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6.json","graph_json":"https://pith.science/api/pith-number/YCQVTFUF6VKKK4IEGZ42M7NJW6/graph.json","events_json":"https://pith.science/api/pith-number/YCQVTFUF6VKKK4IEGZ42M7NJW6/events.json","paper":"https://pith.science/paper/YCQVTFUF"},"agent_actions":{"view_html":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6","download_json":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6.json","view_paper":"https://pith.science/paper/YCQVTFUF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.07713&json=true","fetch_graph":"https://pith.science/api/pith-number/YCQVTFUF6VKKK4IEGZ42M7NJW6/graph.json","fetch_events":"https://pith.science/api/pith-number/YCQVTFUF6VKKK4IEGZ42M7NJW6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6/action/storage_attestation","attest_author":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6/action/author_attestation","sign_citation":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6/action/citation_signature","submit_replication":"https://pith.science/pith/YCQVTFUF6VKKK4IEGZ42M7NJW6/action/replication_record"}},"created_at":"2026-06-09T01:04:50.058705+00:00","updated_at":"2026-06-09T01:04:50.058705+00:00"}