{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XZXKUSV6YW7GVCN2KU5DMF2Q7V","short_pith_number":"pith:XZXKUSV6","canonical_record":{"source":{"id":"2606.19831","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-18T06:25:18Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"696ab68c64b75c07c6ea234034044be3b67cc7aafd4e2bc811ed569b94ec1b58","abstract_canon_sha256":"d14919f7db589e3dc4bf3ead8f146c8db06a531f3f67985db1486f3b50cb8d6d"},"schema_version":"1.0"},"canonical_sha256":"be6eaa4abec5be6a89ba553a361750fd719c927cf66be6ed2829646bcf69f101","source":{"kind":"arxiv","id":"2606.19831","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19831","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19831v1","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19831","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"XZXKUSV6YW7G","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"pith_short_16","alias_value":"XZXKUSV6YW7GVCN2","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"pith_short_8","alias_value":"XZXKUSV6","created_at":"2026-06-19T16:12:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XZXKUSV6YW7GVCN2KU5DMF2Q7V","target":"record","payload":{"canonical_record":{"source":{"id":"2606.19831","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-18T06:25:18Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"696ab68c64b75c07c6ea234034044be3b67cc7aafd4e2bc811ed569b94ec1b58","abstract_canon_sha256":"d14919f7db589e3dc4bf3ead8f146c8db06a531f3f67985db1486f3b50cb8d6d"},"schema_version":"1.0"},"canonical_sha256":"be6eaa4abec5be6a89ba553a361750fd719c927cf66be6ed2829646bcf69f101","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:36.462778Z","signature_b64":"Yno+8WTMEWwZ+BsQhN2kC4+Q7sOrNgySpJajjSHFK/UZ6AS50//3U9Z9JxxcYIgCMJRRaccHgjl7KKMwPM/kAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6eaa4abec5be6a89ba553a361750fd719c927cf66be6ed2829646bcf69f101","last_reissued_at":"2026-06-19T16:12:36.462445Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:36.462445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.19831","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":"2026-06-19T16:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hMKBEzc4luBJFQnmwlZvUIbRsTP1wytNYJC42Z0jWR+++/4uilzGrNBSEQMPdhwQQEWdcXJBh5bc/7LZaUjkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:29:15.489494Z"},"content_sha256":"e942a32ab6a068798a89672fbd1fed398639718773ca18dcd18c6767309b622d","schema_version":"1.0","event_id":"sha256:e942a32ab6a068798a89672fbd1fed398639718773ca18dcd18c6767309b622d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XZXKUSV6YW7GVCN2KU5DMF2Q7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Leverage Is Not Reach: A Control-Window Law for Single-Neuron Steering in Language Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Hongliang Liu","submitted_at":"2026-06-18T06:25:18Z","abstract_excerpt":"Aligned language models gate behaviors such as refusal and language routing through sparse feed forward neurons, yet no theory predicts when a single neuron intervention controls a behavior coherently rather than collapsing the output. We develop a budget normalized control window framework for single neuron steering. A dose along one write direction reduces to one control coordinate: the alignment between the residual stream and the write, driven along a universal saturation curve in units of a coherence budget set by the residual norm divided by the write norm. Coherent control exists when a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19831","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/2606.19831/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":"2026-06-19T16:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3vYi2VpVFFA/qQlGzVrlQ8IqlOyDl4qnOUBIGtAWAOD3y3mWSRGjG0qoEx2McSuwvQwkGyQZ0Y41+/o97IHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:29:15.489864Z"},"content_sha256":"44054de6dcc83d27727ed32a4ae6839cc79b9f6de43635692d901fde716ee449","schema_version":"1.0","event_id":"sha256:44054de6dcc83d27727ed32a4ae6839cc79b9f6de43635692d901fde716ee449"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V/bundle.json","state_url":"https://pith.science/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V/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":"2026-06-29T19:29:15Z","links":{"resolver":"https://pith.science/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V","bundle":"https://pith.science/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V/bundle.json","state":"https://pith.science/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZXKUSV6YW7GVCN2KU5DMF2Q7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XZXKUSV6YW7GVCN2KU5DMF2Q7V","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":"d14919f7db589e3dc4bf3ead8f146c8db06a531f3f67985db1486f3b50cb8d6d","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-18T06:25:18Z","title_canon_sha256":"696ab68c64b75c07c6ea234034044be3b67cc7aafd4e2bc811ed569b94ec1b58"},"schema_version":"1.0","source":{"id":"2606.19831","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19831","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19831v1","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19831","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"XZXKUSV6YW7G","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"pith_short_16","alias_value":"XZXKUSV6YW7GVCN2","created_at":"2026-06-19T16:12:36Z"},{"alias_kind":"pith_short_8","alias_value":"XZXKUSV6","created_at":"2026-06-19T16:12:36Z"}],"graph_snapshots":[{"event_id":"sha256:44054de6dcc83d27727ed32a4ae6839cc79b9f6de43635692d901fde716ee449","target":"graph","created_at":"2026-06-19T16:12:36Z","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/2606.19831/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Aligned language models gate behaviors such as refusal and language routing through sparse feed forward neurons, yet no theory predicts when a single neuron intervention controls a behavior coherently rather than collapsing the output. We develop a budget normalized control window framework for single neuron steering. A dose along one write direction reduces to one control coordinate: the alignment between the residual stream and the write, driven along a universal saturation curve in units of a coherence budget set by the residual norm divided by the write norm. Coherent control exists when a","authors_text":"Hongliang Liu","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-18T06:25:18Z","title":"Leverage Is Not Reach: A Control-Window Law for Single-Neuron Steering in Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19831","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:e942a32ab6a068798a89672fbd1fed398639718773ca18dcd18c6767309b622d","target":"record","created_at":"2026-06-19T16:12:36Z","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":"d14919f7db589e3dc4bf3ead8f146c8db06a531f3f67985db1486f3b50cb8d6d","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-18T06:25:18Z","title_canon_sha256":"696ab68c64b75c07c6ea234034044be3b67cc7aafd4e2bc811ed569b94ec1b58"},"schema_version":"1.0","source":{"id":"2606.19831","kind":"arxiv","version":1}},"canonical_sha256":"be6eaa4abec5be6a89ba553a361750fd719c927cf66be6ed2829646bcf69f101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be6eaa4abec5be6a89ba553a361750fd719c927cf66be6ed2829646bcf69f101","first_computed_at":"2026-06-19T16:12:36.462445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:36.462445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yno+8WTMEWwZ+BsQhN2kC4+Q7sOrNgySpJajjSHFK/UZ6AS50//3U9Z9JxxcYIgCMJRRaccHgjl7KKMwPM/kAQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:36.462778Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e942a32ab6a068798a89672fbd1fed398639718773ca18dcd18c6767309b622d","sha256:44054de6dcc83d27727ed32a4ae6839cc79b9f6de43635692d901fde716ee449"],"state_sha256":"38dc0ae4b5543b18678a7fa811c7855bd0afa82b9bdfd49fd1b86cfc65a0f004"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIJnn2GZl1b+r8VKHkVv0kx5yHHiVwwSWepdCLVyV8n/Gavn4RHOaerr21qQzheOgPBHhNxTXmgjsHdNNWaLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:29:15.491803Z","bundle_sha256":"32d4eed3858226000928f41ebd76024d5a265b9caf7c9701dabb89a5837a5461"}}