{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZTJE7QHWJVW4BAFFPZPGWQ4X3D","short_pith_number":"pith:ZTJE7QHW","canonical_record":{"source":{"id":"2608.11690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:01:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"29b1c6b177562587c705ba17868c3629b5355449b0d62335d37a9398bcf4ba9e","abstract_canon_sha256":"0cb154489253747d2887b18d19b1403f91ecac3c22d380641ae3dfca46620699"},"schema_version":"1.0"},"canonical_sha256":"ccd24fc0f64d6dc080a57e5e6b4397d8d59ce31f3ffa3762c4952d28c0392bdc","source":{"kind":"arxiv","id":"2608.11690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11690","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11690v1","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11690","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZTJE7QHWJVW4","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZTJE7QHWJVW4BAFF","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZTJE7QHW","created_at":"2026-08-13T01:27:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZTJE7QHWJVW4BAFFPZPGWQ4X3D","target":"record","payload":{"canonical_record":{"source":{"id":"2608.11690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:01:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"29b1c6b177562587c705ba17868c3629b5355449b0d62335d37a9398bcf4ba9e","abstract_canon_sha256":"0cb154489253747d2887b18d19b1403f91ecac3c22d380641ae3dfca46620699"},"schema_version":"1.0"},"canonical_sha256":"ccd24fc0f64d6dc080a57e5e6b4397d8d59ce31f3ffa3762c4952d28c0392bdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T01:27:50.674644Z","signature_b64":"eoT3gB35BmSBsjKGHKkVc2ZWChOyKdCRX+aSV8w5V+kiTlLgFP4SmocBovFubCRziwvHY8TOxNBPIuYprmM3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccd24fc0f64d6dc080a57e5e6b4397d8d59ce31f3ffa3762c4952d28c0392bdc","last_reissued_at":"2026-08-13T01:27:50.671990Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T01:27:50.671990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.11690","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":"2026-08-13T01:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejJMjBboPOlTyPDUH0R8vNEUfDLBATHqjkhcdl3G5ShxiPCWxNiVAtuWtWbc+3H1smaRLDXrp4xmPgL7qVcBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:07:49.779864Z"},"content_sha256":"dccef6ac8d7a039d2b630b9e031353e3b2a1831829e69ce7847fe1e0c18ab591","schema_version":"1.0","event_id":"sha256:dccef6ac8d7a039d2b630b9e031353e3b2a1831829e69ce7847fe1e0c18ab591"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZTJE7QHWJVW4BAFFPZPGWQ4X3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Drift and Dependence: Layer-wise Information-Theoretic Bounds for Replay-Based Continual Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Tieliang Gong, Wen Wen, Yong-jin Liu, Zhongbo Zhang","submitted_at":"2026-08-12T06:01:49Z","abstract_excerpt":"Continual learning must absorb new tasks without erasing old ones, and replay---mixing a small buffer of past examples into current training---is among the most effective remedies for catastrophic forgetting. Yet its generalization behavior is shaped by two coupled effects that existing analyses fold into a single hypothesis-level quantity: finite memory replaces each past distribution with an empirical proxy, and repeated reuse couples the buffer, the current data, and the final hypothesis through a shared optimization trajectory. We develop a layer-wise information-theoretic framework that s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11690","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/2608.11690/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":"2026-08-13T01:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tcb0XkGi8Q4njKUbpEFcNoCp3wqTB2/YrqQScfYU9W8RqDuG1fTpZhg+96KZhQZ39RLe5DxkNK6U50kxfnK4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:07:49.784254Z"},"content_sha256":"2d3f6cb3a92a205541a9d600c7a08cb2bf9c288e7684e9866017e52a223a60c6","schema_version":"1.0","event_id":"sha256:2d3f6cb3a92a205541a9d600c7a08cb2bf9c288e7684e9866017e52a223a60c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D/bundle.json","state_url":"https://pith.science/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D/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":"2026-08-18T02:07:49Z","links":{"resolver":"https://pith.science/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D","bundle":"https://pith.science/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D/bundle.json","state":"https://pith.science/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTJE7QHWJVW4BAFFPZPGWQ4X3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZTJE7QHWJVW4BAFFPZPGWQ4X3D","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":"0cb154489253747d2887b18d19b1403f91ecac3c22d380641ae3dfca46620699","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:01:49Z","title_canon_sha256":"29b1c6b177562587c705ba17868c3629b5355449b0d62335d37a9398bcf4ba9e"},"schema_version":"1.0","source":{"id":"2608.11690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11690","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11690v1","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11690","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZTJE7QHWJVW4","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZTJE7QHWJVW4BAFF","created_at":"2026-08-13T01:27:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZTJE7QHW","created_at":"2026-08-13T01:27:50Z"}],"graph_snapshots":[{"event_id":"sha256:2d3f6cb3a92a205541a9d600c7a08cb2bf9c288e7684e9866017e52a223a60c6","target":"graph","created_at":"2026-08-13T01:27:50Z","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/2608.11690/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Continual learning must absorb new tasks without erasing old ones, and replay---mixing a small buffer of past examples into current training---is among the most effective remedies for catastrophic forgetting. Yet its generalization behavior is shaped by two coupled effects that existing analyses fold into a single hypothesis-level quantity: finite memory replaces each past distribution with an empirical proxy, and repeated reuse couples the buffer, the current data, and the final hypothesis through a shared optimization trajectory. We develop a layer-wise information-theoretic framework that s","authors_text":"Tieliang Gong, Wen Wen, Yong-jin Liu, Zhongbo Zhang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:01:49Z","title":"Drift and Dependence: Layer-wise Information-Theoretic Bounds for Replay-Based Continual Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11690","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:dccef6ac8d7a039d2b630b9e031353e3b2a1831829e69ce7847fe1e0c18ab591","target":"record","created_at":"2026-08-13T01:27:50Z","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":"0cb154489253747d2887b18d19b1403f91ecac3c22d380641ae3dfca46620699","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:01:49Z","title_canon_sha256":"29b1c6b177562587c705ba17868c3629b5355449b0d62335d37a9398bcf4ba9e"},"schema_version":"1.0","source":{"id":"2608.11690","kind":"arxiv","version":1}},"canonical_sha256":"ccd24fc0f64d6dc080a57e5e6b4397d8d59ce31f3ffa3762c4952d28c0392bdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccd24fc0f64d6dc080a57e5e6b4397d8d59ce31f3ffa3762c4952d28c0392bdc","first_computed_at":"2026-08-13T01:27:50.671990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-13T01:27:50.671990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eoT3gB35BmSBsjKGHKkVc2ZWChOyKdCRX+aSV8w5V+kiTlLgFP4SmocBovFubCRziwvHY8TOxNBPIuYprmM3Cg==","signature_status":"signed_v1","signed_at":"2026-08-13T01:27:50.674644Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.11690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dccef6ac8d7a039d2b630b9e031353e3b2a1831829e69ce7847fe1e0c18ab591","sha256:2d3f6cb3a92a205541a9d600c7a08cb2bf9c288e7684e9866017e52a223a60c6"],"state_sha256":"91e4efe75917f9396ee61ea57a47682cff6a32f81d109ed1da1dbfe589470090"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZTUEM7tsvmkWofoqtc3hXI9xRX6MtzqXPy6MvEbb5u2tzwgMqytMGcGx7sqg23H/J99qc5DhmpG/9nxHUdtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T02:07:49.796080Z","bundle_sha256":"f33a95f76e9168c5ec74e1ea5dd131743606f0de34e630f4add50e3d13e58d9d"}}