{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WO34R44DI2FZDUCLDRZ22YVZ7E","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":"5892c1ad72e4bfba58586ec8cc450770ac4b3818a670264985e1b79b00972887","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T09:54:08Z","title_canon_sha256":"1072eaa7c138bd8bc3a6a72a33dd7cf1a23658099348780d13cebf9b7b131d57"},"schema_version":"1.0","source":{"id":"2606.05957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05957","created_at":"2026-06-05T01:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05957v1","created_at":"2026-06-05T01:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05957","created_at":"2026-06-05T01:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"WO34R44DI2FZ","created_at":"2026-06-05T01:15:28Z"},{"alias_kind":"pith_short_16","alias_value":"WO34R44DI2FZDUCL","created_at":"2026-06-05T01:15:28Z"},{"alias_kind":"pith_short_8","alias_value":"WO34R44D","created_at":"2026-06-05T01:15:28Z"}],"graph_snapshots":[{"event_id":"sha256:9c40af2e4a548509c053a120d0be0ab9bfa4f26ce44b5f1c7bb5ad88d69e395b","target":"graph","created_at":"2026-06-05T01:15:28Z","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/2606.05957/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Singular learning theory and information geometry have studied the same parameter spaces in mostly separate vocabularies: the former computes Bayesian invariants in resolved coordinates, the latter works in original coordinates under a non-degeneracy assumption that overparameterised models routinely violate. We bridge them through one primitive, the dead direction: a unit vector along which the Fisher metric degenerates, equivalently a tangent to the analytic singular set with a definite KL order, set by how fast the KL divergence vanishes. The two readings name the same vector; our central m","authors_text":"Tejas Pradeep Shirodkar","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T09:54:08Z","title":"Dead Directions: Geometric Singular Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05957","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:a1303da0f5aae136237e38c3dcbbcd5dd8eab89af54e9f6294763486c66b06e7","target":"record","created_at":"2026-06-05T01:15:28Z","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":"5892c1ad72e4bfba58586ec8cc450770ac4b3818a670264985e1b79b00972887","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-04T09:54:08Z","title_canon_sha256":"1072eaa7c138bd8bc3a6a72a33dd7cf1a23658099348780d13cebf9b7b131d57"},"schema_version":"1.0","source":{"id":"2606.05957","kind":"arxiv","version":1}},"canonical_sha256":"b3b7c8f383468b91d04b1c73ad62b9f91a393113ccedf09e9e31f817850c3173","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3b7c8f383468b91d04b1c73ad62b9f91a393113ccedf09e9e31f817850c3173","first_computed_at":"2026-06-05T01:15:28.762877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:28.762877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WT7eaTmMjfwmql6zJ5Cj4G/WBloCjP7h9pQ1yxwARXoeYaPnJdT9VXLJkXk4vfVEK1MZSfC1RKXhFDvbFKfWAA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:28.763327Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1303da0f5aae136237e38c3dcbbcd5dd8eab89af54e9f6294763486c66b06e7","sha256:9c40af2e4a548509c053a120d0be0ab9bfa4f26ce44b5f1c7bb5ad88d69e395b"],"state_sha256":"cbd078b54c9ddfa9937a77d13cff217423b5f48fa8a5f02c8fa82daf8e66a87b"}