{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PYFJSEFJSBEOI4L47EQHASJXZQ","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":"7333754dafa342b624f394a064757e26b4168d741e5aa425c88f46598ab14a8d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.AI","submitted_at":"2024-03-22T15:44:59Z","title_canon_sha256":"438b3010214f02a571e20485f6a5b3affee7b5236200e2c941cc9aac3baa23ef"},"schema_version":"1.0","source":{"id":"2403.15297","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.15297","created_at":"2026-07-05T10:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"2403.15297v4","created_at":"2026-07-05T10:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.15297","created_at":"2026-07-05T10:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"PYFJSEFJSBEO","created_at":"2026-07-05T10:19:22Z"},{"alias_kind":"pith_short_16","alias_value":"PYFJSEFJSBEOI4L4","created_at":"2026-07-05T10:19:22Z"},{"alias_kind":"pith_short_8","alias_value":"PYFJSEFJ","created_at":"2026-07-05T10:19:22Z"}],"graph_snapshots":[{"event_id":"sha256:3f8d55825240f42048aa4795bd2798c867b3ef31b1f79c04558dc1c2202e54de","target":"graph","created_at":"2026-07-05T10:19:22Z","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/2403.15297/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The success of Large Language Models (LLMs), e.g., ChatGPT, is witnessed by their planetary popularity, their capability of human-like communication, and also by their steadily improved reasoning performance. However, it remains unclear whether LLMs reason. It is an open problem how traditional neural networks can be qualitatively extended to go beyond the statistic paradigm and achieve high-level cognition. Here, we present a novel qualitative extension by generalising computational building blocks from vectors to spheres. We propose Sphere Neural Networks (SphNNs) for human-like reasoning th","authors_text":"Mateja Jamnik, Pietro Li\\`o, Tiansi Dong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.AI","submitted_at":"2024-03-22T15:44:59Z","title":"Sphere Neural-Networks for Rational Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15297","kind":"arxiv","version":4},"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":"sha256:7c2a8d9ec0ffa44b22ba4c19364881a142ef3a377b42c45d09318bdcd8f9d952","target":"record","created_at":"2026-07-05T10:19:22Z","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":"7333754dafa342b624f394a064757e26b4168d741e5aa425c88f46598ab14a8d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.AI","submitted_at":"2024-03-22T15:44:59Z","title_canon_sha256":"438b3010214f02a571e20485f6a5b3affee7b5236200e2c941cc9aac3baa23ef"},"schema_version":"1.0","source":{"id":"2403.15297","kind":"arxiv","version":4}},"canonical_sha256":"7e0a9910a99048e4717cf920704937cc24bed0db5ead73162896fdc6cab726f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e0a9910a99048e4717cf920704937cc24bed0db5ead73162896fdc6cab726f2","first_computed_at":"2026-07-05T10:19:22.824589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:19:22.824589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KbWxkICx+Xh02IKci4FsB14LJWW/0SbEdaVdN34HtahE8q2pdE8JZlqKdaG914hCrxxC5SJcezWBHf219zieCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:19:22.825228Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.15297","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c2a8d9ec0ffa44b22ba4c19364881a142ef3a377b42c45d09318bdcd8f9d952","sha256:3f8d55825240f42048aa4795bd2798c867b3ef31b1f79c04558dc1c2202e54de"],"state_sha256":"c2b61bed6e8ccca55921b2ba1cf04d0b0917dba1570474fe223c73569b3f9592"}