{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BZ7WVKG2WGK4RTW52GSPGRWKGG","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":"33ecd2d53a88730d5f4efdc5f04bf51b9db2b4551867a92d2ebbd45eb227cf3f","cross_cats_sorted":["cs.AI","cs.CL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-12T10:39:39Z","title_canon_sha256":"e20b4df8eb6d80255a5357a292d6ce2e666258f6da96b1e36f07d8bf51aa714d"},"schema_version":"1.0","source":{"id":"2606.19379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19379","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19379v1","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19379","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"BZ7WVKG2WGK4","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_16","alias_value":"BZ7WVKG2WGK4RTW5","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_8","alias_value":"BZ7WVKG2","created_at":"2026-06-19T16:12:23Z"}],"graph_snapshots":[{"event_id":"sha256:91040de66b71646b940f22adae4c632cd94052cbc4bbdd71b100680c576fc6d8","target":"graph","created_at":"2026-06-19T16:12:23Z","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/2606.19379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformer feed-forward networks (FFNs) are often treated as nonlinear stores of computation, yet how nonlinear a trained FFN block actually is has rarely been measured. We treat each FFN as a position-wise input-to-output map and split it into the exact least-squares linear approximation plus a residual. The held-out variance the closed-form linear map explains defines a block's linear recoverability (R^2_lin), an optimiser-free measure of its linearity.\n  Across all twelve blocks of GPT-2, Pythia-160m, and llama-160m, R^2_lin is highly heterogeneous and non-monotone with depth, ranging from","authors_text":"Stuart Whipp","cross_cats":["cs.AI","cs.CL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-12T10:39:39Z","title":"How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architectural"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19379","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":"sha256:6b15c0fc8bd8b5cb9d418cada777883348534c86b7c1fa93709bfb7a8eaa42bd","target":"record","created_at":"2026-06-19T16:12:23Z","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":"33ecd2d53a88730d5f4efdc5f04bf51b9db2b4551867a92d2ebbd45eb227cf3f","cross_cats_sorted":["cs.AI","cs.CL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-12T10:39:39Z","title_canon_sha256":"e20b4df8eb6d80255a5357a292d6ce2e666258f6da96b1e36f07d8bf51aa714d"},"schema_version":"1.0","source":{"id":"2606.19379","kind":"arxiv","version":1}},"canonical_sha256":"0e7f6aa8dab195c8ceddd1a4f346ca31bbced225246e905e05bcd1cb75b85731","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e7f6aa8dab195c8ceddd1a4f346ca31bbced225246e905e05bcd1cb75b85731","first_computed_at":"2026-06-19T16:12:23.632788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:23.632788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQhTyYYwEyI9vglm5sLEGXbT+k+nD42GPeH81Cm28JlHEcHg0inHEFYVz9m8eY4Lq++eaJ7l1e+wx13rBCvuCA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:23.633167Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b15c0fc8bd8b5cb9d418cada777883348534c86b7c1fa93709bfb7a8eaa42bd","sha256:91040de66b71646b940f22adae4c632cd94052cbc4bbdd71b100680c576fc6d8"],"state_sha256":"f297fbe964a1d669561618b50096fbb3aceac9ed2323f0578afa12611224ec49"}