{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OE3TS6XA6QLWM2B3SJKJEU34RC","short_pith_number":"pith:OE3TS6XA","canonical_record":{"source":{"id":"2602.05970","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-05T18:22:41Z","cross_cats_sorted":["cs.AI","math.DS","stat.ML"],"title_canon_sha256":"b38732c9fbf6a35fef1adf0ece91b4f7ac9f4a1526b3b341889ae264afcb028b","abstract_canon_sha256":"f70a44942fe3ea7f785c14b09abfb3ca90db3d9a17584c538d23582367d5d9c0"},"schema_version":"1.0"},"canonical_sha256":"7137397ae0f41766683b925492537c88a73b5ce1be221b34b6e4af8b72c84c59","source":{"kind":"arxiv","id":"2602.05970","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.05970","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"2602.05970v2","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.05970","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"OE3TS6XA6QLW","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"pith_short_16","alias_value":"OE3TS6XA6QLWM2B3","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"pith_short_8","alias_value":"OE3TS6XA","created_at":"2026-06-02T02:04:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OE3TS6XA6QLWM2B3SJKJEU34RC","target":"record","payload":{"canonical_record":{"source":{"id":"2602.05970","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-05T18:22:41Z","cross_cats_sorted":["cs.AI","math.DS","stat.ML"],"title_canon_sha256":"b38732c9fbf6a35fef1adf0ece91b4f7ac9f4a1526b3b341889ae264afcb028b","abstract_canon_sha256":"f70a44942fe3ea7f785c14b09abfb3ca90db3d9a17584c538d23582367d5d9c0"},"schema_version":"1.0"},"canonical_sha256":"7137397ae0f41766683b925492537c88a73b5ce1be221b34b6e4af8b72c84c59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:14.097334Z","signature_b64":"XAeByBV+RPc3RfSxhajiMnpeebpm3Q/9wC8Q/b17Tqc7lq3p/KSZTFkT/FWlp39dafYqvb/NkA7Kog864z2oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7137397ae0f41766683b925492537c88a73b5ce1be221b34b6e4af8b72c84c59","last_reissued_at":"2026-06-02T02:04:14.096864Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:14.096864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.05970","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/Z//+sqIqmhVAOTn7xhhvwDPh47kNpjUSmzhxwrr/Af0M35VH3l7vGYuUGkikU10nvPqEWJc3B2nKtnQ3lACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:10:33.556074Z"},"content_sha256":"75290dbe2fe25349a076dd16524cf43e87b560d0d337be16aea40d84812ac223","schema_version":"1.0","event_id":"sha256:75290dbe2fe25349a076dd16524cf43e87b560d0d337be16aea40d84812ac223"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OE3TS6XA6QLWM2B3SJKJEU34RC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse Depth Scaling From Most Layers Being Similar","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","math.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jeff Gore, Sara Kangaslahti, Yizhou Liu, Ziming Liu","submitted_at":"2026-02-05T18:22:41Z","abstract_excerpt":"Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error through ensemble averaging rather than compositional learning or discretizing smooth dynamics. This regime is inefficient yet robust and may arise from the architectural bias of residual networks and target functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.05970","kind":"arxiv","version":2},"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/2602.05970/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":"2026-06-02T02:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ueDtqtVyD2IV3ptDq2xg3XHixsMthLgmsa3J3jkdCRQ38o9qG24udfuO8rcSQzM1W4qM6E2CooxXBkM5fp4fAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:10:33.556800Z"},"content_sha256":"9ef5ad3935dde4c914982bbebcfb29a6f0e7fed4f05d8238ae941eceeb7d0181","schema_version":"1.0","event_id":"sha256:9ef5ad3935dde4c914982bbebcfb29a6f0e7fed4f05d8238ae941eceeb7d0181"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OE3TS6XA6QLWM2B3SJKJEU34RC/bundle.json","state_url":"https://pith.science/pith/OE3TS6XA6QLWM2B3SJKJEU34RC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OE3TS6XA6QLWM2B3SJKJEU34RC/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":"2026-06-07T14:10:33Z","links":{"resolver":"https://pith.science/pith/OE3TS6XA6QLWM2B3SJKJEU34RC","bundle":"https://pith.science/pith/OE3TS6XA6QLWM2B3SJKJEU34RC/bundle.json","state":"https://pith.science/pith/OE3TS6XA6QLWM2B3SJKJEU34RC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OE3TS6XA6QLWM2B3SJKJEU34RC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OE3TS6XA6QLWM2B3SJKJEU34RC","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":"f70a44942fe3ea7f785c14b09abfb3ca90db3d9a17584c538d23582367d5d9c0","cross_cats_sorted":["cs.AI","math.DS","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-05T18:22:41Z","title_canon_sha256":"b38732c9fbf6a35fef1adf0ece91b4f7ac9f4a1526b3b341889ae264afcb028b"},"schema_version":"1.0","source":{"id":"2602.05970","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.05970","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"2602.05970v2","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.05970","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"OE3TS6XA6QLW","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"pith_short_16","alias_value":"OE3TS6XA6QLWM2B3","created_at":"2026-06-02T02:04:14Z"},{"alias_kind":"pith_short_8","alias_value":"OE3TS6XA","created_at":"2026-06-02T02:04:14Z"}],"graph_snapshots":[{"event_id":"sha256:9ef5ad3935dde4c914982bbebcfb29a6f0e7fed4f05d8238ae941eceeb7d0181","target":"graph","created_at":"2026-06-02T02:04:14Z","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/2602.05970/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error through ensemble averaging rather than compositional learning or discretizing smooth dynamics. This regime is inefficient yet robust and may arise from the architectural bias of residual networks and target functions","authors_text":"Jeff Gore, Sara Kangaslahti, Yizhou Liu, Ziming Liu","cross_cats":["cs.AI","math.DS","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-05T18:22:41Z","title":"Inverse Depth Scaling From Most Layers Being Similar"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.05970","kind":"arxiv","version":2},"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":"sha256:75290dbe2fe25349a076dd16524cf43e87b560d0d337be16aea40d84812ac223","target":"record","created_at":"2026-06-02T02:04:14Z","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":"f70a44942fe3ea7f785c14b09abfb3ca90db3d9a17584c538d23582367d5d9c0","cross_cats_sorted":["cs.AI","math.DS","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-05T18:22:41Z","title_canon_sha256":"b38732c9fbf6a35fef1adf0ece91b4f7ac9f4a1526b3b341889ae264afcb028b"},"schema_version":"1.0","source":{"id":"2602.05970","kind":"arxiv","version":2}},"canonical_sha256":"7137397ae0f41766683b925492537c88a73b5ce1be221b34b6e4af8b72c84c59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7137397ae0f41766683b925492537c88a73b5ce1be221b34b6e4af8b72c84c59","first_computed_at":"2026-06-02T02:04:14.096864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:14.096864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XAeByBV+RPc3RfSxhajiMnpeebpm3Q/9wC8Q/b17Tqc7lq3p/KSZTFkT/FWlp39dafYqvb/NkA7Kog864z2oDQ==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:14.097334Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.05970","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75290dbe2fe25349a076dd16524cf43e87b560d0d337be16aea40d84812ac223","sha256:9ef5ad3935dde4c914982bbebcfb29a6f0e7fed4f05d8238ae941eceeb7d0181"],"state_sha256":"0bbd1c6a68d011e3a4e134bea33b627286ab783367c57f47a57234d52ba70e44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQDoq3cdYenO0k7Ig2eHFqpI5/uDyQbAEUmNxDAgiyjJZmwWEZ3CaprC3RZaDbU+VsDzc2tqYI7LJvflqXEcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:10:33.560804Z","bundle_sha256":"7254ba49b44859673388e178b32e57a31cb1ed6953ce82cedcd011118e95addf"}}