{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NWOIUHOCYYZSYG5MCQAMYNNLBE","short_pith_number":"pith:NWOIUHOC","canonical_record":{"source":{"id":"2409.06953","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-11T02:29:53Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"7f5442eb10d536bfb17d35a0488fbf17559494c4a526fbcb8f1aa1e2602593ff","abstract_canon_sha256":"646d351bc06a9efda6db3b18274042baa7c902139d5a1ece67b583e9545f7c6d"},"schema_version":"1.0"},"canonical_sha256":"6d9c8a1dc2c6332c1bac1400cc35ab09113997801c6b22ca3183406a26ca695d","source":{"kind":"arxiv","id":"2409.06953","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.06953","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"2409.06953v4","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.06953","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"NWOIUHOCYYZS","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"pith_short_16","alias_value":"NWOIUHOCYYZSYG5M","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"pith_short_8","alias_value":"NWOIUHOC","created_at":"2026-07-05T11:01:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NWOIUHOCYYZSYG5MCQAMYNNLBE","target":"record","payload":{"canonical_record":{"source":{"id":"2409.06953","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-11T02:29:53Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"7f5442eb10d536bfb17d35a0488fbf17559494c4a526fbcb8f1aa1e2602593ff","abstract_canon_sha256":"646d351bc06a9efda6db3b18274042baa7c902139d5a1ece67b583e9545f7c6d"},"schema_version":"1.0"},"canonical_sha256":"6d9c8a1dc2c6332c1bac1400cc35ab09113997801c6b22ca3183406a26ca695d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:26.624888Z","signature_b64":"pcXdMZx2rN/leNxjEzzaYPq98zk1DG1gM8BmS9yDeaurcE1y89MdvooHNto7DcHDJBQBuJyEMZFMgUW2XqLmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d9c8a1dc2c6332c1bac1400cc35ab09113997801c6b22ca3183406a26ca695d","last_reissued_at":"2026-07-05T11:01:26.624408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:26.624408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.06953","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:01:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9geB1W4nM4PhqfGiWomn5OTU4A0zPdByRnXVBc/MUnVddubjkbMIKRf4Rj4MWu62bMSC0uwnD1p+cYoAprF7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:14:00.738833Z"},"content_sha256":"aa3614da5c1452015da9d208129a2c1e89078f2dc2b9e2183e248ffa2957fb67","schema_version":"1.0","event_id":"sha256:aa3614da5c1452015da9d208129a2c1e89078f2dc2b9e2183e248ffa2957fb67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NWOIUHOCYYZSYG5MCQAMYNNLBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neural Algorithmic Reasoning with Multiple Correct Solutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Danilo Numeroso, Dobrik Georgiev, Henry Fleischmann, John Poole, Pietro Li\\`o, Zeno Kujawa","submitted_at":"2024-09-11T02:29:53Z","abstract_excerpt":"Neural Algorithmic Reasoning (NAR) extends classical algorithms to higher dimensional data. However, canonical implementations of NAR train neural networks to return only a single solution, even when there are multiple correct solutions to a problem, such as single-source shortest paths. For some applications, it is desirable to recover more than one correct solution. To that end, we give the first method for NAR with multiple solutions. We demonstrate our method on two classical algorithms: Bellman-Ford (BF) and Depth-First Search (DFS), favouring deeper insight into two algorithms over a bro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.06953","kind":"arxiv","version":4},"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/2409.06953/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":"2026-07-05T11:01:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5rfdzTzMw+G5MN+wylXfB6639lQBhZgD0v+uh+/w5xdudR9HMK5UBAlfoT4RK+TLzW3rNegVkKTef53HaauCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:14:00.739216Z"},"content_sha256":"9ae2f4ebae2d4ab7b25a51f3602dffdaf6e86595bebc2b3e20ce149c622b119d","schema_version":"1.0","event_id":"sha256:9ae2f4ebae2d4ab7b25a51f3602dffdaf6e86595bebc2b3e20ce149c622b119d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE/bundle.json","state_url":"https://pith.science/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE/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":"2026-07-07T04:14:00Z","links":{"resolver":"https://pith.science/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE","bundle":"https://pith.science/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE/bundle.json","state":"https://pith.science/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWOIUHOCYYZSYG5MCQAMYNNLBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NWOIUHOCYYZSYG5MCQAMYNNLBE","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":"646d351bc06a9efda6db3b18274042baa7c902139d5a1ece67b583e9545f7c6d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-11T02:29:53Z","title_canon_sha256":"7f5442eb10d536bfb17d35a0488fbf17559494c4a526fbcb8f1aa1e2602593ff"},"schema_version":"1.0","source":{"id":"2409.06953","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.06953","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"2409.06953v4","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.06953","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"NWOIUHOCYYZS","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"pith_short_16","alias_value":"NWOIUHOCYYZSYG5M","created_at":"2026-07-05T11:01:26Z"},{"alias_kind":"pith_short_8","alias_value":"NWOIUHOC","created_at":"2026-07-05T11:01:26Z"}],"graph_snapshots":[{"event_id":"sha256:9ae2f4ebae2d4ab7b25a51f3602dffdaf6e86595bebc2b3e20ce149c622b119d","target":"graph","created_at":"2026-07-05T11:01:26Z","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/2409.06953/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural Algorithmic Reasoning (NAR) extends classical algorithms to higher dimensional data. However, canonical implementations of NAR train neural networks to return only a single solution, even when there are multiple correct solutions to a problem, such as single-source shortest paths. For some applications, it is desirable to recover more than one correct solution. To that end, we give the first method for NAR with multiple solutions. We demonstrate our method on two classical algorithms: Bellman-Ford (BF) and Depth-First Search (DFS), favouring deeper insight into two algorithms over a bro","authors_text":"Danilo Numeroso, Dobrik Georgiev, Henry Fleischmann, John Poole, Pietro Li\\`o, Zeno Kujawa","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-11T02:29:53Z","title":"Neural Algorithmic Reasoning with Multiple Correct Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.06953","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:aa3614da5c1452015da9d208129a2c1e89078f2dc2b9e2183e248ffa2957fb67","target":"record","created_at":"2026-07-05T11:01:26Z","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":"646d351bc06a9efda6db3b18274042baa7c902139d5a1ece67b583e9545f7c6d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-11T02:29:53Z","title_canon_sha256":"7f5442eb10d536bfb17d35a0488fbf17559494c4a526fbcb8f1aa1e2602593ff"},"schema_version":"1.0","source":{"id":"2409.06953","kind":"arxiv","version":4}},"canonical_sha256":"6d9c8a1dc2c6332c1bac1400cc35ab09113997801c6b22ca3183406a26ca695d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d9c8a1dc2c6332c1bac1400cc35ab09113997801c6b22ca3183406a26ca695d","first_computed_at":"2026-07-05T11:01:26.624408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:26.624408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pcXdMZx2rN/leNxjEzzaYPq98zk1DG1gM8BmS9yDeaurcE1y89MdvooHNto7DcHDJBQBuJyEMZFMgUW2XqLmBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:26.624888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.06953","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa3614da5c1452015da9d208129a2c1e89078f2dc2b9e2183e248ffa2957fb67","sha256:9ae2f4ebae2d4ab7b25a51f3602dffdaf6e86595bebc2b3e20ce149c622b119d"],"state_sha256":"df2d1a2df5ede162b199d33eb2b5ffcd2b9554a30a01f10380748fee7dc03d92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2DF93el2kENzLf4REuGVKS44rvChAfJGRBpmc5gY99a0sW+LW3HN3Z8m9N0qPPcE/iKFOrwoxjPAE7wAC+bCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T04:14:00.741135Z","bundle_sha256":"fb1fc7461d86bbb37fe8bf959d5fcc2a773693906802689de2547481e25ca355"}}