{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SXOQSELWTAVPN7M3XWWRJANLX7","short_pith_number":"pith:SXOQSELW","canonical_record":{"source":{"id":"2606.13280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T12:34:47Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"098a1f5cb10326c3c0d0f2e2fd25c668ecb5b4fe33c10b04b02f55be9648bd22","abstract_canon_sha256":"2e7da3502870ced6e7b96d6f10ba8275dcb45b359a05d5f49eadaf342ccfea54"},"schema_version":"1.0"},"canonical_sha256":"95dd091176982af6fd9bbdad1481abbfe8d2048d38b98270d1c93ba096736013","source":{"kind":"arxiv","id":"2606.13280","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13280","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13280v1","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13280","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"SXOQSELWTAVP","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"pith_short_16","alias_value":"SXOQSELWTAVPN7M3","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"pith_short_8","alias_value":"SXOQSELW","created_at":"2026-06-12T01:09:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SXOQSELWTAVPN7M3XWWRJANLX7","target":"record","payload":{"canonical_record":{"source":{"id":"2606.13280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T12:34:47Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"098a1f5cb10326c3c0d0f2e2fd25c668ecb5b4fe33c10b04b02f55be9648bd22","abstract_canon_sha256":"2e7da3502870ced6e7b96d6f10ba8275dcb45b359a05d5f49eadaf342ccfea54"},"schema_version":"1.0"},"canonical_sha256":"95dd091176982af6fd9bbdad1481abbfe8d2048d38b98270d1c93ba096736013","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:50.299160Z","signature_b64":"DpjbaTeU0ZBHZBCLOwbjdWCmWWq4Uq7lX3QCSRqosQbiQ6OW14TQ5MqI1+MUl2kd2slG9PgMDYuXWCUFYXF1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95dd091176982af6fd9bbdad1481abbfe8d2048d38b98270d1c93ba096736013","last_reissued_at":"2026-06-12T01:09:50.298290Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:50.298290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.13280","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":"2026-06-12T01:09:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCBji5PUcvj9ntCJl2aw+00rU5fPDwy0Ad1GdghsWcSH/RJgMW1R5Z2TKoqlIhNcF6xrNHnFeVCWS8LdK9byBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T04:51:48.042681Z"},"content_sha256":"eb8386004f97198e5caa3c94f669e9a2b926b676d14429a0fe6f59cb34a5f431","schema_version":"1.0","event_id":"sha256:eb8386004f97198e5caa3c94f669e9a2b926b676d14429a0fe6f59cb34a5f431"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SXOQSELWTAVPN7M3XWWRJANLX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization Bounds for Transformer-Based Next-Token Prediction in a Language Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Insung Kong, Johannes Schmidt-Hieber, Niklas Dexheimer","submitted_at":"2026-06-11T12:34:47Z","abstract_excerpt":"A refined statistical understanding of LLM pre-training requires the analysis of the transformer architecture for data distributions that encapsulate key characteristics of text data. To address this, we propose a text data distribution based on an extension of the log-bilinear language model from the natural language processing literature. For this data generating process, we derive generalization bounds for deep transformer architectures, highlighting the dependence on the network architecture, the vocabulary size, the number of documents and the document length."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13280","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/2606.13280/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":"2026-06-12T01:09:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stAKyQYc8+XkKMhtxjjDRrs3Far4xjCUbYBzlLa+s49nSlJj+LnRtEh8MSTMzsisYj6bdIDB9eu9ukoN6jGQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T04:51:48.043488Z"},"content_sha256":"6f169a11eeafd9c59c6dffc69d218eb0b5c92d20e21a0d48d8340c7c40314c31","schema_version":"1.0","event_id":"sha256:6f169a11eeafd9c59c6dffc69d218eb0b5c92d20e21a0d48d8340c7c40314c31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXOQSELWTAVPN7M3XWWRJANLX7/bundle.json","state_url":"https://pith.science/pith/SXOQSELWTAVPN7M3XWWRJANLX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXOQSELWTAVPN7M3XWWRJANLX7/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":"2026-08-01T04:51:48Z","links":{"resolver":"https://pith.science/pith/SXOQSELWTAVPN7M3XWWRJANLX7","bundle":"https://pith.science/pith/SXOQSELWTAVPN7M3XWWRJANLX7/bundle.json","state":"https://pith.science/pith/SXOQSELWTAVPN7M3XWWRJANLX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXOQSELWTAVPN7M3XWWRJANLX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SXOQSELWTAVPN7M3XWWRJANLX7","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":"2e7da3502870ced6e7b96d6f10ba8275dcb45b359a05d5f49eadaf342ccfea54","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T12:34:47Z","title_canon_sha256":"098a1f5cb10326c3c0d0f2e2fd25c668ecb5b4fe33c10b04b02f55be9648bd22"},"schema_version":"1.0","source":{"id":"2606.13280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13280","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13280v1","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13280","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"SXOQSELWTAVP","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"pith_short_16","alias_value":"SXOQSELWTAVPN7M3","created_at":"2026-06-12T01:09:50Z"},{"alias_kind":"pith_short_8","alias_value":"SXOQSELW","created_at":"2026-06-12T01:09:50Z"}],"graph_snapshots":[{"event_id":"sha256:6f169a11eeafd9c59c6dffc69d218eb0b5c92d20e21a0d48d8340c7c40314c31","target":"graph","created_at":"2026-06-12T01:09:50Z","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/2606.13280/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A refined statistical understanding of LLM pre-training requires the analysis of the transformer architecture for data distributions that encapsulate key characteristics of text data. To address this, we propose a text data distribution based on an extension of the log-bilinear language model from the natural language processing literature. For this data generating process, we derive generalization bounds for deep transformer architectures, highlighting the dependence on the network architecture, the vocabulary size, the number of documents and the document length.","authors_text":"Insung Kong, Johannes Schmidt-Hieber, Niklas Dexheimer","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T12:34:47Z","title":"Generalization Bounds for Transformer-Based Next-Token Prediction in a Language Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13280","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:eb8386004f97198e5caa3c94f669e9a2b926b676d14429a0fe6f59cb34a5f431","target":"record","created_at":"2026-06-12T01:09:50Z","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":"2e7da3502870ced6e7b96d6f10ba8275dcb45b359a05d5f49eadaf342ccfea54","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-11T12:34:47Z","title_canon_sha256":"098a1f5cb10326c3c0d0f2e2fd25c668ecb5b4fe33c10b04b02f55be9648bd22"},"schema_version":"1.0","source":{"id":"2606.13280","kind":"arxiv","version":1}},"canonical_sha256":"95dd091176982af6fd9bbdad1481abbfe8d2048d38b98270d1c93ba096736013","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95dd091176982af6fd9bbdad1481abbfe8d2048d38b98270d1c93ba096736013","first_computed_at":"2026-06-12T01:09:50.298290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:50.298290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DpjbaTeU0ZBHZBCLOwbjdWCmWWq4Uq7lX3QCSRqosQbiQ6OW14TQ5MqI1+MUl2kd2slG9PgMDYuXWCUFYXF1Dg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:50.299160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb8386004f97198e5caa3c94f669e9a2b926b676d14429a0fe6f59cb34a5f431","sha256:6f169a11eeafd9c59c6dffc69d218eb0b5c92d20e21a0d48d8340c7c40314c31"],"state_sha256":"99c33638377aa735dc058f04a7e9490e42641440336cca1a6ff69edb9bfa3881"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"13F6X1D1FQQrRqyj+aQTTrtH6rZYEqmTbT3nGwpWTBbY9EgXKLaCgIfJERFx4Dtziz8K6qXXLGT197J4+WQTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T04:51:48.049109Z","bundle_sha256":"fe2c801d1077fb33306d5be9187fb6d9e5d15f5772956a627369b2bd630074f9"}}