{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HWBTGIBZUO5NKDPJFVPCRYWXNH","short_pith_number":"pith:HWBTGIBZ","canonical_record":{"source":{"id":"2410.16935","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-22T12:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"5a5897cc428b4b0dcec5cf5b47c65f40f5e3574386560248132d34b8940783f4","abstract_canon_sha256":"35a93bc67be5ac0037c365b5f9e4efdd8661cc48c638d763fc00460de1657588"},"schema_version":"1.0"},"canonical_sha256":"3d83332039a3bad50de92d5e28e2d769c391062b65ba9fefbbe1155339248f51","source":{"kind":"arxiv","id":"2410.16935","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.16935","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"2410.16935v2","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.16935","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"HWBTGIBZUO5N","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"pith_short_16","alias_value":"HWBTGIBZUO5NKDPJ","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"pith_short_8","alias_value":"HWBTGIBZ","created_at":"2026-07-05T10:25:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HWBTGIBZUO5NKDPJFVPCRYWXNH","target":"record","payload":{"canonical_record":{"source":{"id":"2410.16935","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-22T12:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"5a5897cc428b4b0dcec5cf5b47c65f40f5e3574386560248132d34b8940783f4","abstract_canon_sha256":"35a93bc67be5ac0037c365b5f9e4efdd8661cc48c638d763fc00460de1657588"},"schema_version":"1.0"},"canonical_sha256":"3d83332039a3bad50de92d5e28e2d769c391062b65ba9fefbbe1155339248f51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:12.431342Z","signature_b64":"FEw/kdnZNb0vGEgVbW+Tcq4p5vSucA9pssH8EObXVDAeNaI0605ZrXcxkkQi/UdcxTPXGjKssyY4xenXg34tCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d83332039a3bad50de92d5e28e2d769c391062b65ba9fefbbe1155339248f51","last_reissued_at":"2026-07-05T10:25:12.430828Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:12.430828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.16935","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rUVZ45EhBdrgLNmT55xcAL3C7b1GqcOkeNkSNLR6CdvJa85cqFRXgmqEyp5OtCrUYXMQ1e4VoZ4MzFeU/C3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:52:04.163195Z"},"content_sha256":"ee3b4ae226f721c5bb69b72607499a1dfc967d0e53c1ef3e6459882a9b2e0ccf","schema_version":"1.0","event_id":"sha256:ee3b4ae226f721c5bb69b72607499a1dfc967d0e53c1ef3e6459882a9b2e0ccf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HWBTGIBZUO5NKDPJFVPCRYWXNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Dominik Fuchsgruber, Simon Geisler, Stephan G\\\"unnemann, Tim Po\\v{s}tuvan","submitted_at":"2024-10-22T12:12:43Z","abstract_excerpt":"Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the diameter of a pipe. Topological methods model edge signals with inherent direction by representing them relative to a so-called orientation assigned to each edge. These approaches can neither model undirected edge signals nor distinguish if an edge itself is directed or undirected. We address these shortcomings by (i) revising the notion of orientation equivar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16935","kind":"arxiv","version":2},"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/2410.16935/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":"2026-07-05T10:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QX+c2AHTWBr1IGFPUyFAlj1QCA4L0au5se/1PF71OvobtxKoDidpH1Ak6XhMU5oJ66DlNxG/94V4ew05XxJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:52:04.163582Z"},"content_sha256":"3ce5be375b976177f1ddb6ca75b477ce967f24955675eff1a95174a5e464b601","schema_version":"1.0","event_id":"sha256:3ce5be375b976177f1ddb6ca75b477ce967f24955675eff1a95174a5e464b601"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH/bundle.json","state_url":"https://pith.science/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH/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":"2026-07-06T14:52:04Z","links":{"resolver":"https://pith.science/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH","bundle":"https://pith.science/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH/bundle.json","state":"https://pith.science/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWBTGIBZUO5NKDPJFVPCRYWXNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HWBTGIBZUO5NKDPJFVPCRYWXNH","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":"35a93bc67be5ac0037c365b5f9e4efdd8661cc48c638d763fc00460de1657588","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-22T12:12:43Z","title_canon_sha256":"5a5897cc428b4b0dcec5cf5b47c65f40f5e3574386560248132d34b8940783f4"},"schema_version":"1.0","source":{"id":"2410.16935","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.16935","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"2410.16935v2","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.16935","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"HWBTGIBZUO5N","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"pith_short_16","alias_value":"HWBTGIBZUO5NKDPJ","created_at":"2026-07-05T10:25:12Z"},{"alias_kind":"pith_short_8","alias_value":"HWBTGIBZ","created_at":"2026-07-05T10:25:12Z"}],"graph_snapshots":[{"event_id":"sha256:3ce5be375b976177f1ddb6ca75b477ce967f24955675eff1a95174a5e464b601","target":"graph","created_at":"2026-07-05T10:25:12Z","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/2410.16935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the diameter of a pipe. Topological methods model edge signals with inherent direction by representing them relative to a so-called orientation assigned to each edge. These approaches can neither model undirected edge signals nor distinguish if an edge itself is directed or undirected. We address these shortcomings by (i) revising the notion of orientation equivar","authors_text":"Dominik Fuchsgruber, Simon Geisler, Stephan G\\\"unnemann, Tim Po\\v{s}tuvan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-22T12:12:43Z","title":"Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16935","kind":"arxiv","version":2},"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:ee3b4ae226f721c5bb69b72607499a1dfc967d0e53c1ef3e6459882a9b2e0ccf","target":"record","created_at":"2026-07-05T10:25:12Z","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":"35a93bc67be5ac0037c365b5f9e4efdd8661cc48c638d763fc00460de1657588","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-22T12:12:43Z","title_canon_sha256":"5a5897cc428b4b0dcec5cf5b47c65f40f5e3574386560248132d34b8940783f4"},"schema_version":"1.0","source":{"id":"2410.16935","kind":"arxiv","version":2}},"canonical_sha256":"3d83332039a3bad50de92d5e28e2d769c391062b65ba9fefbbe1155339248f51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d83332039a3bad50de92d5e28e2d769c391062b65ba9fefbbe1155339248f51","first_computed_at":"2026-07-05T10:25:12.430828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:12.430828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FEw/kdnZNb0vGEgVbW+Tcq4p5vSucA9pssH8EObXVDAeNaI0605ZrXcxkkQi/UdcxTPXGjKssyY4xenXg34tCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:12.431342Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.16935","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee3b4ae226f721c5bb69b72607499a1dfc967d0e53c1ef3e6459882a9b2e0ccf","sha256:3ce5be375b976177f1ddb6ca75b477ce967f24955675eff1a95174a5e464b601"],"state_sha256":"7a0d88cf30f1ec69aadc9a71098768f043277da90e71deb77f6783fc35334f36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YXD3SUszV4dQQkang6IM1w0rl+Yb8mX0V4wOwK9UbhpEEefp6bid4thFxbcJI4AusHTbKSfJc51UC9bfSR9RAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:52:04.165423Z","bundle_sha256":"453dc094bb86f8169fb49a6a50493536063553afbc3d6ee5181540c97853388f"}}