{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RS27RAQCDOUVMAO45HBROE42XN","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":"32b3aff62f43882b8acd8d182882ad45dc8595dc1ebb332e07cdbd5d1a1c2c19","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-23T18:02:46Z","title_canon_sha256":"53be9028d3fa434bd46c5cc6f6064a03bfbf92b1245205ba372db5e5892ac6ef"},"schema_version":"1.0","source":{"id":"2505.18266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.18266","created_at":"2026-07-05T11:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2505.18266v1","created_at":"2026-07-05T11:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18266","created_at":"2026-07-05T11:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"RS27RAQCDOUV","created_at":"2026-07-05T11:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"RS27RAQCDOUVMAO4","created_at":"2026-07-05T11:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"RS27RAQC","created_at":"2026-07-05T11:08:43Z"}],"graph_snapshots":[{"event_id":"sha256:f9ea85e331e9bd959493c6daff349652d2ef196b1e67be673b327f288e86022e","target":"graph","created_at":"2026-07-05T11:08:43Z","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/2505.18266/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a testable universality hypothesis, asserting that seemingly disparate neural network solutions observed in the simple task of modular addition are unified under a common abstract algorithm. While prior work interpreted variations in neuron-level representations as evidence for distinct algorithms, we demonstrate - through multi-level analyses spanning neurons, neuron clusters, and entire networks - that multilayer perceptrons and transformers universally implement the abstract algorithm we call the approximate Chinese Remainder Theorem. Crucially, we introduce approximate cosets an","authors_text":"Doina Precup, Gabriela Moisescu-Pareja, Gavin McCracken, Jonathan Love, Vincent Letourneau","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-23T18:02:46Z","title":"Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18266","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":"sha256:3f0d74c059dfd78d6b7a913246af80f808196e7f01d767584dd075ac35e4018e","target":"record","created_at":"2026-07-05T11:08:43Z","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":"32b3aff62f43882b8acd8d182882ad45dc8595dc1ebb332e07cdbd5d1a1c2c19","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-23T18:02:46Z","title_canon_sha256":"53be9028d3fa434bd46c5cc6f6064a03bfbf92b1245205ba372db5e5892ac6ef"},"schema_version":"1.0","source":{"id":"2505.18266","kind":"arxiv","version":1}},"canonical_sha256":"8cb5f882021ba95601dce9c317139abb4cd2ea99946908704b70b4a3950f2213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cb5f882021ba95601dce9c317139abb4cd2ea99946908704b70b4a3950f2213","first_computed_at":"2026-07-05T11:08:43.811482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:08:43.811482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GA/6lfP6C/R+DJzDQNNiRZiAS/PhuPh9GDYkA6RHF/aCalKHqFFyroXk6q6AaVm9Za3lCIDCPaB91MMw183MBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:08:43.811921Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.18266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f0d74c059dfd78d6b7a913246af80f808196e7f01d767584dd075ac35e4018e","sha256:f9ea85e331e9bd959493c6daff349652d2ef196b1e67be673b327f288e86022e"],"state_sha256":"31309e9b4b4b4fbf173075f41db2e585b4778332e072bbda6cfdf60e27ed8aa8"}