{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:O73CVVVUXCZEBCUBEMKS7BPDYB","short_pith_number":"pith:O73CVVVU","canonical_record":{"source":{"id":"2608.11061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:29:01Z","cross_cats_sorted":[],"title_canon_sha256":"98a60f72dda21bc839ec268e26a8bb482295caa8aa497993aa63854fac3f05f7","abstract_canon_sha256":"a2d9c338981accccc916658e16c5378ec62549c46e64dd4181ed4c4132166d7a"},"schema_version":"1.0"},"canonical_sha256":"77f62ad6b4b8b2408a8123152f85e3c05bb3b7bda7635259e3a7be89f64e6ae6","source":{"kind":"arxiv","id":"2608.11061","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11061","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11061v1","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11061","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"O73CVVVUXCZE","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"pith_short_16","alias_value":"O73CVVVUXCZEBCUB","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"pith_short_8","alias_value":"O73CVVVU","created_at":"2026-08-12T01:24:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:O73CVVVUXCZEBCUBEMKS7BPDYB","target":"record","payload":{"canonical_record":{"source":{"id":"2608.11061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:29:01Z","cross_cats_sorted":[],"title_canon_sha256":"98a60f72dda21bc839ec268e26a8bb482295caa8aa497993aa63854fac3f05f7","abstract_canon_sha256":"a2d9c338981accccc916658e16c5378ec62549c46e64dd4181ed4c4132166d7a"},"schema_version":"1.0"},"canonical_sha256":"77f62ad6b4b8b2408a8123152f85e3c05bb3b7bda7635259e3a7be89f64e6ae6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:24:31.473802Z","signature_b64":"iA0XPlnlJQiI0e2qvpcGXntXJovDps0nDiTTakFgcNhUPtHmKsTo8hvkLJvhJTJYJR7fFmnUPEHir4agcgjkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77f62ad6b4b8b2408a8123152f85e3c05bb3b7bda7635259e3a7be89f64e6ae6","last_reissued_at":"2026-08-12T01:24:31.472152Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:24:31.472152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.11061","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":"2026-08-12T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ml0oWdlO4G7VVM5d3gYfk2/ez8shaCFxpb+x6g7pLHSZELTCAMKKPvnoLexYhAHcKfrdJfiFWt9FRlGnsqWHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T19:31:32.919473Z"},"content_sha256":"fa5b0372fdd849b2736c5f0ec083ba8ea69eac4baf4e4c5cff8d5fe1c08704ff","schema_version":"1.0","event_id":"sha256:fa5b0372fdd849b2736c5f0ec083ba8ea69eac4baf4e4c5cff8d5fe1c08704ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:O73CVVVUXCZEBCUBEMKS7BPDYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Batch Size or Negatives? A Selection Rule for Memory-Constrained Recommender Training","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alexey Zaytsev, Artyom Sabitov, Daniil Volkov","submitted_at":"2026-08-11T15:29:01Z","abstract_excerpt":"Large-scale neural recommender systems are typically trained with a softmax cross-entropy objective over the full item vocabulary. For a typical large number of possible items $K$, the final classification layer dominates memory, requiring $O(nK)$ logits and gradients to materialize for a batch of $n$ examples. Sampled softmax reduces this cost by restricting the objective to only $k \\ll K$ candidate negative items, resulting in an $O(nk)$ memory. However, for a fixed budget $B = n k$, it remains unclear whether one should prioritize larger batches or the inclusion of more negative items.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11061","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/2608.11061/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":"2026-08-12T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lb0ei2yJMPvgxhxAx8ro+idCgrjPRSjdpkSopp24/xXLYbnU2Q7K/HrxPNyWrnbClf9BwyB10TurAHSj+fhvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T19:31:32.919991Z"},"content_sha256":"21e8cf80cfec4ff60519281bdeee7fc0d3fe8a251ee7746cee7630c62f37f70c","schema_version":"1.0","event_id":"sha256:21e8cf80cfec4ff60519281bdeee7fc0d3fe8a251ee7746cee7630c62f37f70c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O73CVVVUXCZEBCUBEMKS7BPDYB/bundle.json","state_url":"https://pith.science/pith/O73CVVVUXCZEBCUBEMKS7BPDYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O73CVVVUXCZEBCUBEMKS7BPDYB/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":"2026-08-19T19:31:32Z","links":{"resolver":"https://pith.science/pith/O73CVVVUXCZEBCUBEMKS7BPDYB","bundle":"https://pith.science/pith/O73CVVVUXCZEBCUBEMKS7BPDYB/bundle.json","state":"https://pith.science/pith/O73CVVVUXCZEBCUBEMKS7BPDYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O73CVVVUXCZEBCUBEMKS7BPDYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:O73CVVVUXCZEBCUBEMKS7BPDYB","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":"a2d9c338981accccc916658e16c5378ec62549c46e64dd4181ed4c4132166d7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:29:01Z","title_canon_sha256":"98a60f72dda21bc839ec268e26a8bb482295caa8aa497993aa63854fac3f05f7"},"schema_version":"1.0","source":{"id":"2608.11061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11061","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11061v1","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11061","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"O73CVVVUXCZE","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"pith_short_16","alias_value":"O73CVVVUXCZEBCUB","created_at":"2026-08-12T01:24:31Z"},{"alias_kind":"pith_short_8","alias_value":"O73CVVVU","created_at":"2026-08-12T01:24:31Z"}],"graph_snapshots":[{"event_id":"sha256:21e8cf80cfec4ff60519281bdeee7fc0d3fe8a251ee7746cee7630c62f37f70c","target":"graph","created_at":"2026-08-12T01:24:31Z","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/2608.11061/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large-scale neural recommender systems are typically trained with a softmax cross-entropy objective over the full item vocabulary. For a typical large number of possible items $K$, the final classification layer dominates memory, requiring $O(nK)$ logits and gradients to materialize for a batch of $n$ examples. Sampled softmax reduces this cost by restricting the objective to only $k \\ll K$ candidate negative items, resulting in an $O(nk)$ memory. However, for a fixed budget $B = n k$, it remains unclear whether one should prioritize larger batches or the inclusion of more negative items.\n  We","authors_text":"Alexey Zaytsev, Artyom Sabitov, Daniil Volkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:29:01Z","title":"Batch Size or Negatives? A Selection Rule for Memory-Constrained Recommender Training"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11061","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:fa5b0372fdd849b2736c5f0ec083ba8ea69eac4baf4e4c5cff8d5fe1c08704ff","target":"record","created_at":"2026-08-12T01:24:31Z","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":"a2d9c338981accccc916658e16c5378ec62549c46e64dd4181ed4c4132166d7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:29:01Z","title_canon_sha256":"98a60f72dda21bc839ec268e26a8bb482295caa8aa497993aa63854fac3f05f7"},"schema_version":"1.0","source":{"id":"2608.11061","kind":"arxiv","version":1}},"canonical_sha256":"77f62ad6b4b8b2408a8123152f85e3c05bb3b7bda7635259e3a7be89f64e6ae6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77f62ad6b4b8b2408a8123152f85e3c05bb3b7bda7635259e3a7be89f64e6ae6","first_computed_at":"2026-08-12T01:24:31.472152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T01:24:31.472152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iA0XPlnlJQiI0e2qvpcGXntXJovDps0nDiTTakFgcNhUPtHmKsTo8hvkLJvhJTJYJR7fFmnUPEHir4agcgjkAw==","signature_status":"signed_v1","signed_at":"2026-08-12T01:24:31.473802Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.11061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa5b0372fdd849b2736c5f0ec083ba8ea69eac4baf4e4c5cff8d5fe1c08704ff","sha256:21e8cf80cfec4ff60519281bdeee7fc0d3fe8a251ee7746cee7630c62f37f70c"],"state_sha256":"6d9665760887dbde8ea5b528a2b0c3cf303c362109e63a8d25657c14ffdd7318"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sG2dJnFho9Pw1bK68TqHOmieCQc6QdqkLPl/QL6SKwrMLytz2NhwQ+p9ZpbH0sY24A5P6LeUD9B5zscaDUrSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T19:31:32.924622Z","bundle_sha256":"5f649e7cb642cbeb45926fc2ee1089f690637c0b5b5f3b13370cacccc848ea05"}}