{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TEIOMHJTIAWZPAC2D57CFCFFGH","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":"b372839d2a82aa15f4353102729121b01c37f1d4d0a56b1c7fe98881c2c3946b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-12T19:21:23Z","title_canon_sha256":"aaf33bf90f03f84b493997633b106b7f4a97226a4afbb66ab912e25b746151bf"},"schema_version":"1.0","source":{"id":"2605.12671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12671","created_at":"2026-05-18T03:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12671v1","created_at":"2026-05-18T03:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12671","created_at":"2026-05-18T03:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"TEIOMHJTIAWZ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"TEIOMHJTIAWZPAC2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"TEIOMHJT","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:ed006d974bf34c723de53d0b623b88e540cd1739b8a7ad136bae0442211144f8","target":"graph","created_at":"2026-05-18T03:09:50Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the Overlap-Aware Sheaf Repulsion penalty successfully uncovers genuinely distinct mechanisms without introducing methodological artifacts, and that the theoretical analysis of high-dimensional superposition holds under the stated mild assumptions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"LLM tasks are supported by multiple distinct circuits rather than unique mechanisms, demonstrated via Overlap-Aware Sheaf Repulsion and the Distributive Dense Circuit Hypothesis."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete."}],"snapshot_sha256":"a4d99c565994cc02d05d3e383cc99a2c39351108ec19132fe7217e4ddc3f7310"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we present empirical and theoretical evidence against a central but largely implicit assumption in circuit and sheaf discovery (CSD), which we term the Functional Anisotropy Hypothesis: the idea that functions in large language models (LLMs) are localised to a unique or near-unique internal mechanism. We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete. To systematically uncover such competing mechanisms, we introduce Overlap-Aware Sheaf Repulsion, a method that augm","authors_text":"Bangwei Guo, Dimitris N. Metaxas, Gerald Penn, Jingcheng Niu, Jinman Zhao, Mingyu Jin, Xi Chen, Yutao Yue, Yutong Yin, Zhaoran Wang","cross_cats":[],"headline":"A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-12T19:21:23Z","title":"All Circuits Lead to Rome: Rethinking Functional Anisotropy in Circuit and Sheaf Discovery for LLMs"},"references":{"count":300,"internal_anchors":5,"resolved_work":300,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Abdelmalik, Philip and Peron, Emilie and Schnitzler, Johannes and Fontaine, Julie and Elfenkampera, Eva and Barbozaa, Philippe , year = 2018, journal =","work_id":"81d2a84a-3999-4193-8e69-e5c4d8ed287f","year":2018},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Proceedings of the 25th","work_id":"549a7fd5-5a79-41e6-9bf0-5ca64caef0ee","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"From Language as System to Language as Use:","work_id":"2dcc0e5c-426a-4a83-bbb0-d0f5f7d8d60f","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Ackema, Peter and Neeleman, Ad , year = 2004, publisher =","work_id":"49b766d9-0632-4342-afa8-450c88ca8334","year":2004},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Adger, David , year = 2003, publisher =","work_id":"db613369-147f-450d-9861-82a5137dbbcd","year":2003}],"snapshot_sha256":"be1972d0a73381e38ef6fe77fc85319f8053021e892feaf2c3196a26bdf58e28"},"source":{"id":"2605.12671","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T20:48:46.251781Z","id":"411f37ea-c6e1-4de5-a35b-913309568d81","model_set":{"reader":"grok-4.3"},"one_line_summary":"LLM tasks are supported by multiple distinct circuits rather than unique mechanisms, demonstrated via Overlap-Aware Sheaf Repulsion and the Distributive Dense Circuit Hypothesis.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete.","strongest_claim":"We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete.","weakest_assumption":"That the Overlap-Aware Sheaf Repulsion penalty successfully uncovers genuinely distinct mechanisms without introducing methodological artifacts, and that the theoretical analysis of high-dimensional superposition holds under the stated mild assumptions."}},"verdict_id":"411f37ea-c6e1-4de5-a35b-913309568d81"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f2586d371938286d03959f149e4e9a6eb52b5d0201bcc2c21e8b3ceeb8907720","target":"record","created_at":"2026-05-18T03:09:50Z","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":"b372839d2a82aa15f4353102729121b01c37f1d4d0a56b1c7fe98881c2c3946b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-12T19:21:23Z","title_canon_sha256":"aaf33bf90f03f84b493997633b106b7f4a97226a4afbb66ab912e25b746151bf"},"schema_version":"1.0","source":{"id":"2605.12671","kind":"arxiv","version":1}},"canonical_sha256":"9910e61d33402d97805a1f7e2288a531ce206f4307ac3f8348a0d04acbd89c17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9910e61d33402d97805a1f7e2288a531ce206f4307ac3f8348a0d04acbd89c17","first_computed_at":"2026-05-18T03:09:50.224482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:50.224482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FzqCGjsCcPAuznRQVlEF1/xsgDiHwmbjUtKonjmOQ1UjjPNWXMANX1Yf0fsnQdQKQGBahxiYFCyFpi8EnijWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:50.225183Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.12671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2586d371938286d03959f149e4e9a6eb52b5d0201bcc2c21e8b3ceeb8907720","sha256:ed006d974bf34c723de53d0b623b88e540cd1739b8a7ad136bae0442211144f8"],"state_sha256":"55af3a3a2f3a6854c41121de4c0cd62589a45e4439267cc76f6bc72b7f911f87"}