{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VOKXHRJL2BDWFQTPMKSOELIXRK","short_pith_number":"pith:VOKXHRJL","schema_version":"1.0","canonical_sha256":"ab9573c52bd04762c26f62a4e22d178a92627b52ab516e7aab557fece27b5e52","source":{"kind":"arxiv","id":"2408.13885","version":2},"attestation_state":"computed","paper":{"title":"Neural Spacetimes for DAG Representation Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.NE","math.MG","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anastasis Kratsios, Haitz S\\'aez de Oc\\'ariz Borde, Marc T. Law, Michael Bronstein, Xiaowen Dong","submitted_at":"2024-08-25T16:26:55Z","abstract_excerpt":"We propose a class of trainable deep learning-based geometries called Neural Spacetimes (NSTs), which can universally represent nodes in weighted directed acyclic graphs (DAGs) as events in a spacetime manifold. While most works in the literature focus on undirected graph representation learning or causality embedding separately, our differentiable geometry can encode both graph edge weights in its spatial dimensions and causality in the form of edge directionality in its temporal dimensions. We use a product manifold that combines a quasi-metric (for space) and a partial order (for time). NST"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.13885","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-25T16:26:55Z","cross_cats_sorted":["cs.DM","cs.NE","math.MG","stat.ML"],"title_canon_sha256":"98b4bdc7945c4b696c95f5018715e7febb892875a39e3c4eae181f774653ab43","abstract_canon_sha256":"f391449df3ee415cc19e0a66bf61dfd9707ef150051d6ceeb784e91c85215146"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:13.486801Z","signature_b64":"K6n5dC8Pzd4+Ns0SwiTp8MhTEktGfrWYRsC6nBNBnRHbQUE/zjDXR3jdsDvsTJZW374oXZhiyBbknqg0qTYNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab9573c52bd04762c26f62a4e22d178a92627b52ab516e7aab557fece27b5e52","last_reissued_at":"2026-07-05T10:27:13.485957Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:13.485957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Neural Spacetimes for DAG Representation Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.NE","math.MG","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anastasis Kratsios, Haitz S\\'aez de Oc\\'ariz Borde, Marc T. Law, Michael Bronstein, Xiaowen Dong","submitted_at":"2024-08-25T16:26:55Z","abstract_excerpt":"We propose a class of trainable deep learning-based geometries called Neural Spacetimes (NSTs), which can universally represent nodes in weighted directed acyclic graphs (DAGs) as events in a spacetime manifold. While most works in the literature focus on undirected graph representation learning or causality embedding separately, our differentiable geometry can encode both graph edge weights in its spatial dimensions and causality in the form of edge directionality in its temporal dimensions. We use a product manifold that combines a quasi-metric (for space) and a partial order (for time). NST"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.13885","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/2408.13885/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2408.13885","created_at":"2026-07-05T10:27:13.486058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.13885v2","created_at":"2026-07-05T10:27:13.486058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.13885","created_at":"2026-07-05T10:27:13.486058+00:00"},{"alias_kind":"pith_short_12","alias_value":"VOKXHRJL2BDW","created_at":"2026-07-05T10:27:13.486058+00:00"},{"alias_kind":"pith_short_16","alias_value":"VOKXHRJL2BDWFQTP","created_at":"2026-07-05T10:27:13.486058+00:00"},{"alias_kind":"pith_short_8","alias_value":"VOKXHRJL","created_at":"2026-07-05T10:27:13.486058+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK","json":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK.json","graph_json":"https://pith.science/api/pith-number/VOKXHRJL2BDWFQTPMKSOELIXRK/graph.json","events_json":"https://pith.science/api/pith-number/VOKXHRJL2BDWFQTPMKSOELIXRK/events.json","paper":"https://pith.science/paper/VOKXHRJL"},"agent_actions":{"view_html":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK","download_json":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK.json","view_paper":"https://pith.science/paper/VOKXHRJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.13885&json=true","fetch_graph":"https://pith.science/api/pith-number/VOKXHRJL2BDWFQTPMKSOELIXRK/graph.json","fetch_events":"https://pith.science/api/pith-number/VOKXHRJL2BDWFQTPMKSOELIXRK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK/action/storage_attestation","attest_author":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK/action/author_attestation","sign_citation":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK/action/citation_signature","submit_replication":"https://pith.science/pith/VOKXHRJL2BDWFQTPMKSOELIXRK/action/replication_record"}},"created_at":"2026-07-05T10:27:13.486058+00:00","updated_at":"2026-07-05T10:27:13.486058+00:00"}