{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZV2B27QTCYJ3F3WZ46R6OPO4UF","short_pith_number":"pith:ZV2B27QT","canonical_record":{"source":{"id":"2507.04206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-07-06T01:34:12Z","cross_cats_sorted":[],"title_canon_sha256":"9fda6e207e23cda839694caa9bb61a4e1f290592b9e5937b659ab615b94f7737","abstract_canon_sha256":"a57164e0f753bd05663881c75a2cfcf2ce9754057daa303d6147e0a36b6ac42e"},"schema_version":"1.0"},"canonical_sha256":"cd741d7e131613b2eed9e7a3e73ddca17e846d7f94e34e17deac8a7d522e4f48","source":{"kind":"arxiv","id":"2507.04206","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04206","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04206v1","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04206","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZV2B27QTCYJ3","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ZV2B27QTCYJ3F3WZ","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ZV2B27QT","created_at":"2026-07-05T11:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZV2B27QTCYJ3F3WZ46R6OPO4UF","target":"record","payload":{"canonical_record":{"source":{"id":"2507.04206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-07-06T01:34:12Z","cross_cats_sorted":[],"title_canon_sha256":"9fda6e207e23cda839694caa9bb61a4e1f290592b9e5937b659ab615b94f7737","abstract_canon_sha256":"a57164e0f753bd05663881c75a2cfcf2ce9754057daa303d6147e0a36b6ac42e"},"schema_version":"1.0"},"canonical_sha256":"cd741d7e131613b2eed9e7a3e73ddca17e846d7f94e34e17deac8a7d522e4f48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:43.674129Z","signature_b64":"aKnr6rn5e6daOYbYSNIjdz0XCXn6N52am182AL1PORidIa9Qz7mo/8S5cY1QOxUEKDLNlkY65haibMLc9lDtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd741d7e131613b2eed9e7a3e73ddca17e846d7f94e34e17deac8a7d522e4f48","last_reissued_at":"2026-07-05T11:32:43.673724Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:43.673724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.04206","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":"2026-07-05T11:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKAFlHvW7gwMgHKXRKajocDyHbPB+lmjzVPMI56l+OuPpjx7lHl2I9i53WgSl3ZKVgzGbnLuKgz39+qoaDViDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:14:21.344936Z"},"content_sha256":"86e3dea590011f42c755f26dc241bb67b3f3e009da1c67545e78cd81f9c2c190","schema_version":"1.0","event_id":"sha256:86e3dea590011f42c755f26dc241bb67b3f3e009da1c67545e78cd81f9c2c190"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZV2B27QTCYJ3F3WZ46R6OPO4UF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Sibei Liu, Zhijian Hu","submitted_at":"2025-07-06T01:34:12Z","abstract_excerpt":"Learning rate (LR) schedules in large language model (LLM) training often follow empirical templates: warm-up, constant plateau/stable phase, and decay (WSD). However, the mechanistic explanation for this strategy remains underexplored, and the choice of plateau height and decay schedule is largely heuristic. In this paper, we connect training dynamics to a thermodynamic analogy via the Mpemba effect - a phenomenon in which a hotter system cools faster than a colder one when quenched into the same bath. We analyze a class of \"valley-river\" loss landscapes, where sharp (valley) directions equil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04206","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/2507.04206/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":"2026-07-05T11:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2rtu6/arL1z+uZcKQlggYDMPO39oYDkEhA2Vhn6OfZLzeJVRIdSLzxlP62V5Nw8YYxr4BtXLIduBAZuezDEjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:14:21.346231Z"},"content_sha256":"8844a59ac68a22d4c253a7cdb7d7191667275fc141dce6754018ab1eb7d88ec1","schema_version":"1.0","event_id":"sha256:8844a59ac68a22d4c253a7cdb7d7191667275fc141dce6754018ab1eb7d88ec1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF/bundle.json","state_url":"https://pith.science/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF/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":"2026-08-17T14:14:21Z","links":{"resolver":"https://pith.science/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF","bundle":"https://pith.science/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF/bundle.json","state":"https://pith.science/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZV2B27QTCYJ3F3WZ46R6OPO4UF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZV2B27QTCYJ3F3WZ46R6OPO4UF","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":"a57164e0f753bd05663881c75a2cfcf2ce9754057daa303d6147e0a36b6ac42e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-07-06T01:34:12Z","title_canon_sha256":"9fda6e207e23cda839694caa9bb61a4e1f290592b9e5937b659ab615b94f7737"},"schema_version":"1.0","source":{"id":"2507.04206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04206","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04206v1","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04206","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZV2B27QTCYJ3","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ZV2B27QTCYJ3F3WZ","created_at":"2026-07-05T11:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ZV2B27QT","created_at":"2026-07-05T11:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:8844a59ac68a22d4c253a7cdb7d7191667275fc141dce6754018ab1eb7d88ec1","target":"graph","created_at":"2026-07-05T11:32:43Z","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/2507.04206/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Learning rate (LR) schedules in large language model (LLM) training often follow empirical templates: warm-up, constant plateau/stable phase, and decay (WSD). However, the mechanistic explanation for this strategy remains underexplored, and the choice of plateau height and decay schedule is largely heuristic. In this paper, we connect training dynamics to a thermodynamic analogy via the Mpemba effect - a phenomenon in which a hotter system cools faster than a colder one when quenched into the same bath. We analyze a class of \"valley-river\" loss landscapes, where sharp (valley) directions equil","authors_text":"Sibei Liu, Zhijian Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-07-06T01:34:12Z","title":"Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04206","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":"sha256:86e3dea590011f42c755f26dc241bb67b3f3e009da1c67545e78cd81f9c2c190","target":"record","created_at":"2026-07-05T11:32:43Z","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":"a57164e0f753bd05663881c75a2cfcf2ce9754057daa303d6147e0a36b6ac42e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-07-06T01:34:12Z","title_canon_sha256":"9fda6e207e23cda839694caa9bb61a4e1f290592b9e5937b659ab615b94f7737"},"schema_version":"1.0","source":{"id":"2507.04206","kind":"arxiv","version":1}},"canonical_sha256":"cd741d7e131613b2eed9e7a3e73ddca17e846d7f94e34e17deac8a7d522e4f48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd741d7e131613b2eed9e7a3e73ddca17e846d7f94e34e17deac8a7d522e4f48","first_computed_at":"2026-07-05T11:32:43.673724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:43.673724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKnr6rn5e6daOYbYSNIjdz0XCXn6N52am182AL1PORidIa9Qz7mo/8S5cY1QOxUEKDLNlkY65haibMLc9lDtCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:43.674129Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.04206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e3dea590011f42c755f26dc241bb67b3f3e009da1c67545e78cd81f9c2c190","sha256:8844a59ac68a22d4c253a7cdb7d7191667275fc141dce6754018ab1eb7d88ec1"],"state_sha256":"2b69130e3a0c66cadbb233f748b4263eae6b0ca882a5c916de9a3512bd2b3eae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i8ZWkXAEjb3tJi3R1LQXVw6KFJhgwTGRYGaeM7Gp80cIu6x+fRAO2fCxlFi3D4wIq9HZjnAj8eCfanptkZRpCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:14:21.374938Z","bundle_sha256":"ce782e2f5e7e222217bbc590673e277604f50647a694581f1f1a70a221d8af08"}}