{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:D75WX27JO5CBGOFYWCDVSJEGUE","short_pith_number":"pith:D75WX27J","schema_version":"1.0","canonical_sha256":"1ffb6bebe977441338b8b087592486a100c1c9ab394b0c570b2187fa66770128","source":{"kind":"arxiv","id":"2507.12380","version":1},"attestation_state":"computed","paper":{"title":"Heat Kernel Goes Topological","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Maximilian Krahn, Vikas Garg","submitted_at":"2025-07-16T16:28:10Z","abstract_excerpt":"Topological neural networks have emerged as powerful successors of graph neural networks. However, they typically involve higher-order message passing, which incurs significant computational expense. We circumvent this issue with a novel topological framework that introduces a Laplacian operator on combinatorial complexes (CCs), enabling efficient computation of heat kernels that serve as node descriptors. Our approach captures multiscale information and enables permutation-equivariant representations, allowing easy integration into modern transformer-based architectures.\n  Theoretically, the "},"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":"2507.12380","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-16T16:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"09c88381090d234453801d094f43ed757ab152fdbcb774e77a2e3b6885634e4f","abstract_canon_sha256":"2c6f5a85c6768756ede75c1fda165182794111e3c547a57a1b373557baed45ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:19.303483Z","signature_b64":"E2e9GihP3JVIstQ6fOzcWow1Jpy+WfqOEKkl23oCz+UjoWNglARbTz/0DJRHxIxWe/WcQtapOkO3242eO+SWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ffb6bebe977441338b8b087592486a100c1c9ab394b0c570b2187fa66770128","last_reissued_at":"2026-07-05T11:38:19.302700Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:19.302700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat Kernel Goes Topological","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Maximilian Krahn, Vikas Garg","submitted_at":"2025-07-16T16:28:10Z","abstract_excerpt":"Topological neural networks have emerged as powerful successors of graph neural networks. However, they typically involve higher-order message passing, which incurs significant computational expense. We circumvent this issue with a novel topological framework that introduces a Laplacian operator on combinatorial complexes (CCs), enabling efficient computation of heat kernels that serve as node descriptors. Our approach captures multiscale information and enables permutation-equivariant representations, allowing easy integration into modern transformer-based architectures.\n  Theoretically, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12380","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/2507.12380/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":"2507.12380","created_at":"2026-07-05T11:38:19.302797+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12380v1","created_at":"2026-07-05T11:38:19.302797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12380","created_at":"2026-07-05T11:38:19.302797+00:00"},{"alias_kind":"pith_short_12","alias_value":"D75WX27JO5CB","created_at":"2026-07-05T11:38:19.302797+00:00"},{"alias_kind":"pith_short_16","alias_value":"D75WX27JO5CBGOFY","created_at":"2026-07-05T11:38:19.302797+00:00"},{"alias_kind":"pith_short_8","alias_value":"D75WX27J","created_at":"2026-07-05T11:38:19.302797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.06466","citing_title":"Diversity Curves for Graph Representation Learning","ref_index":40,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE","json":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE.json","graph_json":"https://pith.science/api/pith-number/D75WX27JO5CBGOFYWCDVSJEGUE/graph.json","events_json":"https://pith.science/api/pith-number/D75WX27JO5CBGOFYWCDVSJEGUE/events.json","paper":"https://pith.science/paper/D75WX27J"},"agent_actions":{"view_html":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE","download_json":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE.json","view_paper":"https://pith.science/paper/D75WX27J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12380&json=true","fetch_graph":"https://pith.science/api/pith-number/D75WX27JO5CBGOFYWCDVSJEGUE/graph.json","fetch_events":"https://pith.science/api/pith-number/D75WX27JO5CBGOFYWCDVSJEGUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE/action/storage_attestation","attest_author":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE/action/author_attestation","sign_citation":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE/action/citation_signature","submit_replication":"https://pith.science/pith/D75WX27JO5CBGOFYWCDVSJEGUE/action/replication_record"}},"created_at":"2026-07-05T11:38:19.302797+00:00","updated_at":"2026-07-05T11:38:19.302797+00:00"}