{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5Q2EVXA4BWUQQST7DYBLQUSOUA","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":"902c2601f126159ad7aae3c0a7244811506ee7f9328b5a576a366199db9b0713","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T18:28:37Z","title_canon_sha256":"b746e0bbe2639cdf1da4bd16ec61e9073259dd41ee0325c06cadc07baf569a9a"},"schema_version":"1.0","source":{"id":"2606.19491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19491","created_at":"2026-06-19T16:12:27Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19491v1","created_at":"2026-06-19T16:12:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19491","created_at":"2026-06-19T16:12:27Z"},{"alias_kind":"pith_short_12","alias_value":"5Q2EVXA4BWUQ","created_at":"2026-06-19T16:12:27Z"},{"alias_kind":"pith_short_16","alias_value":"5Q2EVXA4BWUQQST7","created_at":"2026-06-19T16:12:27Z"},{"alias_kind":"pith_short_8","alias_value":"5Q2EVXA4","created_at":"2026-06-19T16:12:27Z"}],"graph_snapshots":[{"event_id":"sha256:ee18060858739d497d2c10f36d85e094274138d304f39c6279129fb01f942e31","target":"graph","created_at":"2026-06-19T16:12:27Z","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/2606.19491/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Pretrained transformers sit near singular minima of the loss, where the Fisher information metric degenerates along dead directions: directions in parameter space along which the directional Fisher vanishes. Locating such a direction normally needs a forward pass and an eigendecomposition of activations, or a sampling-based complexity estimate; none returns a direction computable from the network's parameters alone. We give one, for LayerNorm transformers. The inverse-scale direction $\\gamma^{-1}/\\|\\gamma^{-1}\\|$ of the LayerNorm affine is an exact algebraic kernel of the post-final-norm centr","authors_text":"P. J. Narayanan, Tejas Pradeep Shirodkar","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T18:28:37Z","title":"Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19491","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":"sha256:802a288bfd17c2accd28148bf61b5511ab0fdec8a1d62d8aed82d432c5b726e2","target":"record","created_at":"2026-06-19T16:12:27Z","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":"902c2601f126159ad7aae3c0a7244811506ee7f9328b5a576a366199db9b0713","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-17T18:28:37Z","title_canon_sha256":"b746e0bbe2639cdf1da4bd16ec61e9073259dd41ee0325c06cadc07baf569a9a"},"schema_version":"1.0","source":{"id":"2606.19491","kind":"arxiv","version":1}},"canonical_sha256":"ec344adc1c0da9084a7f1e02b8524ea00fe7ea2e92d8a0d7bcc4a83177af890b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec344adc1c0da9084a7f1e02b8524ea00fe7ea2e92d8a0d7bcc4a83177af890b","first_computed_at":"2026-06-19T16:12:27.170737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:27.170737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aobktxy9BynKUjdzUNVkPClazqkLGSkZQUospT2+eYgCpYI2tZ5KtcIs//YClLd+F7JrhpTbo1vKHeSzDH1AAw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:27.171077Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:802a288bfd17c2accd28148bf61b5511ab0fdec8a1d62d8aed82d432c5b726e2","sha256:ee18060858739d497d2c10f36d85e094274138d304f39c6279129fb01f942e31"],"state_sha256":"2b629262bbdea6823378c67ad5768ee8caff0e57691ecdd5b5a4eea6f5d29866"}