{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FQLV235RQNYKTD2G3I6QCLDDC6","short_pith_number":"pith:FQLV235R","canonical_record":{"source":{"id":"2605.20988","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:23:03Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"6866da49403a13ea9bd3056d2516326cd1c3fbf7aa0d5a5be49b72855eab6730","abstract_canon_sha256":"cb92a056490ea9453c2cf6560745f699c4ce2b0ce891347a59b67ca7ad0466cb"},"schema_version":"1.0"},"canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","source":{"kind":"arxiv","id":"2605.20988","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20988","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20988v1","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20988","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"FQLV235RQNYK","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"FQLV235RQNYKTD2G","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"FQLV235R","created_at":"2026-05-21T01:05:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FQLV235RQNYKTD2G3I6QCLDDC6","target":"record","payload":{"canonical_record":{"source":{"id":"2605.20988","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:23:03Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"6866da49403a13ea9bd3056d2516326cd1c3fbf7aa0d5a5be49b72855eab6730","abstract_canon_sha256":"cb92a056490ea9453c2cf6560745f699c4ce2b0ce891347a59b67ca7ad0466cb"},"schema_version":"1.0"},"canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:31.236735Z","signature_b64":"uETBSLcEbAyRxhbJ3uJ2cH8/yG15PVCiGWjqIJxuaVAf44Ksigz2vfNA6keVgtmoNK1+RxF1bEbnAggHlwT0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","last_reissued_at":"2026-05-21T01:05:31.235933Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:31.235933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.20988","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":"2026-05-21T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edUu/pg2eas3K0VxV343uYd1+z2+ICaV2Eu1PM+ExtLkcH4k+vutKwQViFjoy0jhkRyHe6nDHWaN4v7wix0yCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:35:14.317023Z"},"content_sha256":"2312e120f10c28efd599630594bc90192d1f1875f8386df2bc28163a0c304144","schema_version":"1.0","event_id":"sha256:2312e120f10c28efd599630594bc90192d1f1875f8386df2bc28163a0c304144"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FQLV235RQNYKTD2G3I6QCLDDC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Sharper Picture of Generalization in Transformers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Paul Lintilhac, Sair Shaikh","submitted_at":"2026-05-20T10:23:03Z","abstract_excerpt":"We study transformers' generalization behavior on boolean domains from the perspective of the Fourier Spectra of their target functions. In contrast to prior work (Edelman et al., 2022; Trauger and Tewari, 2024), which derived generalization bounds from Rademacher complexity, we investigate the feasibility of obtaining generalization bounds via PAC-Bayes theory. We show that sparse spectra concentrated on low-degree components enable low-sharpness constructions with good generalization properties. Our idea is to show the existence of flat minima implementing any boolean function of sparsity no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20988","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/2605.20988/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":"2026-05-21T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8rsbmzQHioeVWzDfPssebQLqhWiWc8L1iJ+T5rth7SrBoah4PEQrIAGgsYGoeL7qTgCmzlz2wcvjygCIM7+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:35:14.317417Z"},"content_sha256":"0bd23c97d53255ba5b1675162e0ed1843f25b60581baa9ffb4fcdfd9336ef7da","schema_version":"1.0","event_id":"sha256:0bd23c97d53255ba5b1675162e0ed1843f25b60581baa9ffb4fcdfd9336ef7da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/bundle.json","state_url":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQLV235RQNYKTD2G3I6QCLDDC6/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":"2026-05-22T20:35:14Z","links":{"resolver":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6","bundle":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/bundle.json","state":"https://pith.science/pith/FQLV235RQNYKTD2G3I6QCLDDC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQLV235RQNYKTD2G3I6QCLDDC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FQLV235RQNYKTD2G3I6QCLDDC6","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":"cb92a056490ea9453c2cf6560745f699c4ce2b0ce891347a59b67ca7ad0466cb","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:23:03Z","title_canon_sha256":"6866da49403a13ea9bd3056d2516326cd1c3fbf7aa0d5a5be49b72855eab6730"},"schema_version":"1.0","source":{"id":"2605.20988","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20988","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20988v1","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20988","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"FQLV235RQNYK","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"FQLV235RQNYKTD2G","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"FQLV235R","created_at":"2026-05-21T01:05:31Z"}],"graph_snapshots":[{"event_id":"sha256:0bd23c97d53255ba5b1675162e0ed1843f25b60581baa9ffb4fcdfd9336ef7da","target":"graph","created_at":"2026-05-21T01:05:31Z","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/2605.20988/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study transformers' generalization behavior on boolean domains from the perspective of the Fourier Spectra of their target functions. In contrast to prior work (Edelman et al., 2022; Trauger and Tewari, 2024), which derived generalization bounds from Rademacher complexity, we investigate the feasibility of obtaining generalization bounds via PAC-Bayes theory. We show that sparse spectra concentrated on low-degree components enable low-sharpness constructions with good generalization properties. Our idea is to show the existence of flat minima implementing any boolean function of sparsity no","authors_text":"Paul Lintilhac, Sair Shaikh","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:23:03Z","title":"A Sharper Picture of Generalization in Transformers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20988","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":"sha256:2312e120f10c28efd599630594bc90192d1f1875f8386df2bc28163a0c304144","target":"record","created_at":"2026-05-21T01:05:31Z","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":"cb92a056490ea9453c2cf6560745f699c4ce2b0ce891347a59b67ca7ad0466cb","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:23:03Z","title_canon_sha256":"6866da49403a13ea9bd3056d2516326cd1c3fbf7aa0d5a5be49b72855eab6730"},"schema_version":"1.0","source":{"id":"2605.20988","kind":"arxiv","version":1}},"canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c175d6fb18370a98f46da3d012c63179dca4cd30a0c8f02106e1a782bd1d55d","first_computed_at":"2026-05-21T01:05:31.235933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:31.235933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uETBSLcEbAyRxhbJ3uJ2cH8/yG15PVCiGWjqIJxuaVAf44Ksigz2vfNA6keVgtmoNK1+RxF1bEbnAggHlwT0Cw==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:31.236735Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20988","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2312e120f10c28efd599630594bc90192d1f1875f8386df2bc28163a0c304144","sha256:0bd23c97d53255ba5b1675162e0ed1843f25b60581baa9ffb4fcdfd9336ef7da"],"state_sha256":"6775cd06c86637f38ac8db769711c701c72c00a7df9b8afdaa7b230c3d14450b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmD3xvHvqq67hh+n7EMNC7F63BVM+MQQD31X7pkz9dOLM5L1Eco74McPNbid3yfhLhjbJhdRNjJdbOs3aS6aCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T20:35:14.319522Z","bundle_sha256":"e7095e7f28e4a665b976fa75877b67290c74e9e5c90d47408966a42828f61c1b"}}