{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LL36BD2EEDYMC4NVXLGAM5AURB","short_pith_number":"pith:LL36BD2E","canonical_record":{"source":{"id":"2501.06444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-11T05:54:10Z","cross_cats_sorted":["cs.AI","cs.CC"],"title_canon_sha256":"50b53312b26e604784183f3261d3cd5b1de2ae4db14b55db3a5e8b32057871ab","abstract_canon_sha256":"a5e67b8555ce6cf762ec84b1e12c1840169a8adf047c9129f72bd0b534d4549c"},"schema_version":"1.0"},"canonical_sha256":"5af7e08f4420f0c171b5bacc06741488552ac46882fc8a09a5760100c72a8c36","source":{"kind":"arxiv","id":"2501.06444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.06444","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"arxiv_version","alias_value":"2501.06444v1","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06444","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"pith_short_12","alias_value":"LL36BD2EEDYM","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"pith_short_16","alias_value":"LL36BD2EEDYMC4NV","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"pith_short_8","alias_value":"LL36BD2E","created_at":"2026-07-05T10:00:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LL36BD2EEDYMC4NVXLGAM5AURB","target":"record","payload":{"canonical_record":{"source":{"id":"2501.06444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-11T05:54:10Z","cross_cats_sorted":["cs.AI","cs.CC"],"title_canon_sha256":"50b53312b26e604784183f3261d3cd5b1de2ae4db14b55db3a5e8b32057871ab","abstract_canon_sha256":"a5e67b8555ce6cf762ec84b1e12c1840169a8adf047c9129f72bd0b534d4549c"},"schema_version":"1.0"},"canonical_sha256":"5af7e08f4420f0c171b5bacc06741488552ac46882fc8a09a5760100c72a8c36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:03.458440Z","signature_b64":"rBcqDQC89bMzrJCxu+6IOZFvRjWiB6U3+vVwLpwSXsU8/Bdm0826wGiIOUC5AvQeq/cxuI0ytkgNQEJHeJjkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5af7e08f4420f0c171b5bacc06741488552ac46882fc8a09a5760100c72a8c36","last_reissued_at":"2026-07-05T10:00:03.457941Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:03.457941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.06444","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":"2026-07-05T10:00:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJwUWLCaJ53yuYtUb/0FzjPOHS0/4qgCzgf8O8NYC9WpawMEMv3Pa4XH/hZRQ6tgkWLJXWHm+J0KizxSSDCtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:58:24.734864Z"},"content_sha256":"f8304c9e394ac2f0a85b0a1b3dbf592b30b62b385f9a6c748df6803869fc635a","schema_version":"1.0","event_id":"sha256:f8304c9e394ac2f0a85b0a1b3dbf592b30b62b385f9a6c748df6803869fc635a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LL36BD2EEDYMC4NVXLGAM5AURB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Computational Capability of Graph Neural Networks: A Circuit Complexity Bound Perspective","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.CC"],"primary_cat":"cs.LG","authors_text":"Jiahao Zhang, Wei Wang, Xiaoyu Li, Yingyu Liang, Zhao Song, Zhenmei Shi","submitted_at":"2025-01-11T05:54:10Z","abstract_excerpt":"Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have achieved significant empirical success, their theoretical limitations remain an active area of research. Existing studies primarily focus on characterizing GNN expressiveness through Weisfeiler-Lehman (WL) graph isomorphism tests. In this paper, we take a fundamentally different approach by exploring the computational limitations of GNNs through the lens of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06444","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/2501.06444/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":"2026-07-05T10:00:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lT2zyaTbYyi/gAQEQawXtR2hqDFUsG9h56Uzx9LzHAnae01PFFl2bWIBEsPPCbEX30J03QhYWrFjVMS4LelVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:58:24.735379Z"},"content_sha256":"290355befb7bc0ad685af75ba72bebea3b1e52944f39b0cb1ba017e7ceb23544","schema_version":"1.0","event_id":"sha256:290355befb7bc0ad685af75ba72bebea3b1e52944f39b0cb1ba017e7ceb23544"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL36BD2EEDYMC4NVXLGAM5AURB/bundle.json","state_url":"https://pith.science/pith/LL36BD2EEDYMC4NVXLGAM5AURB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL36BD2EEDYMC4NVXLGAM5AURB/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":"2026-08-08T18:58:24Z","links":{"resolver":"https://pith.science/pith/LL36BD2EEDYMC4NVXLGAM5AURB","bundle":"https://pith.science/pith/LL36BD2EEDYMC4NVXLGAM5AURB/bundle.json","state":"https://pith.science/pith/LL36BD2EEDYMC4NVXLGAM5AURB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL36BD2EEDYMC4NVXLGAM5AURB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LL36BD2EEDYMC4NVXLGAM5AURB","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":"a5e67b8555ce6cf762ec84b1e12c1840169a8adf047c9129f72bd0b534d4549c","cross_cats_sorted":["cs.AI","cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-11T05:54:10Z","title_canon_sha256":"50b53312b26e604784183f3261d3cd5b1de2ae4db14b55db3a5e8b32057871ab"},"schema_version":"1.0","source":{"id":"2501.06444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.06444","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"arxiv_version","alias_value":"2501.06444v1","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06444","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"pith_short_12","alias_value":"LL36BD2EEDYM","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"pith_short_16","alias_value":"LL36BD2EEDYMC4NV","created_at":"2026-07-05T10:00:03Z"},{"alias_kind":"pith_short_8","alias_value":"LL36BD2E","created_at":"2026-07-05T10:00:03Z"}],"graph_snapshots":[{"event_id":"sha256:290355befb7bc0ad685af75ba72bebea3b1e52944f39b0cb1ba017e7ceb23544","target":"graph","created_at":"2026-07-05T10:00:03Z","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/2501.06444/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have achieved significant empirical success, their theoretical limitations remain an active area of research. Existing studies primarily focus on characterizing GNN expressiveness through Weisfeiler-Lehman (WL) graph isomorphism tests. In this paper, we take a fundamentally different approach by exploring the computational limitations of GNNs through the lens of c","authors_text":"Jiahao Zhang, Wei Wang, Xiaoyu Li, Yingyu Liang, Zhao Song, Zhenmei Shi","cross_cats":["cs.AI","cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-11T05:54:10Z","title":"On the Computational Capability of Graph Neural Networks: A Circuit Complexity Bound Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06444","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:f8304c9e394ac2f0a85b0a1b3dbf592b30b62b385f9a6c748df6803869fc635a","target":"record","created_at":"2026-07-05T10:00:03Z","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":"a5e67b8555ce6cf762ec84b1e12c1840169a8adf047c9129f72bd0b534d4549c","cross_cats_sorted":["cs.AI","cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-11T05:54:10Z","title_canon_sha256":"50b53312b26e604784183f3261d3cd5b1de2ae4db14b55db3a5e8b32057871ab"},"schema_version":"1.0","source":{"id":"2501.06444","kind":"arxiv","version":1}},"canonical_sha256":"5af7e08f4420f0c171b5bacc06741488552ac46882fc8a09a5760100c72a8c36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5af7e08f4420f0c171b5bacc06741488552ac46882fc8a09a5760100c72a8c36","first_computed_at":"2026-07-05T10:00:03.457941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:00:03.457941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rBcqDQC89bMzrJCxu+6IOZFvRjWiB6U3+vVwLpwSXsU8/Bdm0826wGiIOUC5AvQeq/cxuI0ytkgNQEJHeJjkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:00:03.458440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.06444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8304c9e394ac2f0a85b0a1b3dbf592b30b62b385f9a6c748df6803869fc635a","sha256:290355befb7bc0ad685af75ba72bebea3b1e52944f39b0cb1ba017e7ceb23544"],"state_sha256":"946963f2aeebcb497d242362690920b14a7a4ea52698c691e7945042a8e96a25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KlHyA0BBbNm9ToAqfML7DH0EGgjAKoswYePB3MZDulVsJQzS9SXxI+eB3ccUlP/CDM3i4n4ho+Hz8NXAsWZzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:58:24.740375Z","bundle_sha256":"c1e2c926a8a8b0c7b9e2c8fac74054d60e3f756f01c02123c0b0cbb45192a690"}}