{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BHWFRGYRUTN5YKXCPUQ7TFPDXN","short_pith_number":"pith:BHWFRGYR","schema_version":"1.0","canonical_sha256":"09ec589b11a4dbdc2ae27d21f995e3bb5c46eb0169ca6e2be484303f7a6ec5c8","source":{"kind":"arxiv","id":"2607.15536","version":1},"attestation_state":"computed","paper":{"title":"E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Chankyo Kim, Maani Ghaffari","submitted_at":"2026-07-17T01:12:26Z","abstract_excerpt":"3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry (position, covariance) with view-dependent photometry (Spherical Harmonics). However, building $\\mathrm{SE}(3)$-equivariant architectures on these primitives presents a fundamental representation bottleneck. Color has been treated as a signal rather than a geometric entity, making it nontrivial to unify symmetry across geometry and appearance as the camera frame changes. While translations are handled by relative coordinates, rotations act heterogeneously across attributes: $\\mu\\mapsto R\\mu$, $\\Sigma\\mapsto R\\Sigma R^\\t"},"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":"2607.15536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-07-17T01:12:26Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"249d0df61f62e795c36235c7cfe084c226323b72520b0b2137c6ac2e0abcfcc3","abstract_canon_sha256":"d53e1f10245538ff18cec456c08bdfafa9198b162d1d761d378d803896ddfc70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T00:18:38.824934Z","signature_b64":"m17t3ndTPnnb4xTfctouC1Aq64Li38uFJV6IjvOb3lfwxzkOqcPhiSpvU3f/wQgW7jUTISIiZqxb0iqFXT9nDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09ec589b11a4dbdc2ae27d21f995e3bb5c46eb0169ca6e2be484303f7a6ec5c8","last_reissued_at":"2026-07-20T00:18:38.823929Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T00:18:38.823929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Chankyo Kim, Maani Ghaffari","submitted_at":"2026-07-17T01:12:26Z","abstract_excerpt":"3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry (position, covariance) with view-dependent photometry (Spherical Harmonics). However, building $\\mathrm{SE}(3)$-equivariant architectures on these primitives presents a fundamental representation bottleneck. Color has been treated as a signal rather than a geometric entity, making it nontrivial to unify symmetry across geometry and appearance as the camera frame changes. While translations are handled by relative coordinates, rotations act heterogeneously across attributes: $\\mu\\mapsto R\\mu$, $\\Sigma\\mapsto R\\Sigma R^\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15536","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/2607.15536/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":"2607.15536","created_at":"2026-07-20T00:18:38.824422+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.15536v1","created_at":"2026-07-20T00:18:38.824422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15536","created_at":"2026-07-20T00:18:38.824422+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHWFRGYRUTN5","created_at":"2026-07-20T00:18:38.824422+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHWFRGYRUTN5YKXC","created_at":"2026-07-20T00:18:38.824422+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHWFRGYR","created_at":"2026-07-20T00:18:38.824422+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/BHWFRGYRUTN5YKXCPUQ7TFPDXN","json":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN.json","graph_json":"https://pith.science/api/pith-number/BHWFRGYRUTN5YKXCPUQ7TFPDXN/graph.json","events_json":"https://pith.science/api/pith-number/BHWFRGYRUTN5YKXCPUQ7TFPDXN/events.json","paper":"https://pith.science/paper/BHWFRGYR"},"agent_actions":{"view_html":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN","download_json":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN.json","view_paper":"https://pith.science/paper/BHWFRGYR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.15536&json=true","fetch_graph":"https://pith.science/api/pith-number/BHWFRGYRUTN5YKXCPUQ7TFPDXN/graph.json","fetch_events":"https://pith.science/api/pith-number/BHWFRGYRUTN5YKXCPUQ7TFPDXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN/action/storage_attestation","attest_author":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN/action/author_attestation","sign_citation":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN/action/citation_signature","submit_replication":"https://pith.science/pith/BHWFRGYRUTN5YKXCPUQ7TFPDXN/action/replication_record"}},"created_at":"2026-07-20T00:18:38.824422+00:00","updated_at":"2026-07-20T00:18:38.824422+00:00"}