{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YA77ZUE3ZVKUG2VUZPQEQZGUNZ","short_pith_number":"pith:YA77ZUE3","canonical_record":{"source":{"id":"2605.17011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-16T14:21:08Z","cross_cats_sorted":["cs.CV","cs.LG"],"title_canon_sha256":"f739cafe70b50fdcc58d5b014cd7702e96a8f2a7beba544210e95dbbc72f201d","abstract_canon_sha256":"e5f292caf338144ffb2d54b44fce8acab9809be2d999ac8d92dde17ed1bed514"},"schema_version":"1.0"},"canonical_sha256":"c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad","source":{"kind":"arxiv","id":"2605.17011","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17011","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17011v1","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17011","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"YA77ZUE3ZVKU","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"pith_short_16","alias_value":"YA77ZUE3ZVKUG2VU","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"pith_short_8","alias_value":"YA77ZUE3","created_at":"2026-05-20T00:03:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YA77ZUE3ZVKUG2VUZPQEQZGUNZ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-16T14:21:08Z","cross_cats_sorted":["cs.CV","cs.LG"],"title_canon_sha256":"f739cafe70b50fdcc58d5b014cd7702e96a8f2a7beba544210e95dbbc72f201d","abstract_canon_sha256":"e5f292caf338144ffb2d54b44fce8acab9809be2d999ac8d92dde17ed1bed514"},"schema_version":"1.0"},"canonical_sha256":"c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:35.838806Z","signature_b64":"VppX4oinnZDX+u5oaVWLy+L69DraYUxGHqcUmf/zpESrYDo4RhuiIfvV9UxS9ugSiuzQKWRO6yRufcQNUeDwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad","last_reissued_at":"2026-05-20T00:03:35.837953Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:35.837953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17011","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":"2026-05-20T00:03:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXhSxN6VI2fIY72Sd/IGrRvg9auJ70fkyyPR6aQhvRx1LuV0oF/D1Y3FI60mZCJ3W7JPtv1b/w5sNLQuVKvSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:43:23.399992Z"},"content_sha256":"0660d5a12756ee0685abaa145bc0936d0036b11593d5308d4f7875f1c9746429","schema_version":"1.0","event_id":"sha256:0660d5a12756ee0685abaa145bc0936d0036b11593d5308d4f7875f1c9746429"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YA77ZUE3ZVKUG2VUZPQEQZGUNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints.","cross_cats":["cs.CV","cs.LG"],"primary_cat":"cs.GR","authors_text":"Jo\\~ao Paulo Gois, Luis Gustavo Nonato","submitted_at":"2026-05-16T14:21:08Z","abstract_excerpt":"Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial discontinuities, often failing to represent the continuous density of the underlying manifold. To address these limitations, we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process. Instead of standard photometric losses, Topo-GS is driven by local geometric co"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process... driven by local geometric constraints... solving orthogonal Procrustes targets... aligning the spatial covariance of each Gaussian to the local tangent space... topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That enforcing As-Rigid-As-Possible priors via orthogonal Procrustes alignment of Gaussian covariances to local tangent spaces, combined with topology-specific loss tailoring, will produce faithful continuous volumetric representations without introducing new artifacts or losing fidelity compared to discrete baselines.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Topo-GS repurposes 3D Gaussian Splatting with local geometric constraints and topology-aware losses to produce continuous volumetric embeddings of high-dimensional data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6121102b1c972d6d5df59cadccca9f164e33b634748cbb418813dfe2c09b3848"},"source":{"id":"2605.17011","kind":"arxiv","version":1},"verdict":{"id":"665ff848-f130-4455-a077-6707c0d8de88","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:29:27.568295Z","strongest_claim":"we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process... driven by local geometric constraints... solving orthogonal Procrustes targets... aligning the spatial covariance of each Gaussian to the local tangent space... topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces.","one_line_summary":"Topo-GS repurposes 3D Gaussian Splatting with local geometric constraints and topology-aware losses to produce continuous volumetric embeddings of high-dimensional data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That enforcing As-Rigid-As-Possible priors via orthogonal Procrustes alignment of Gaussian covariances to local tangent spaces, combined with topology-specific loss tailoring, will produce faithful continuous volumetric representations without introducing new artifacts or losing fidelity compared to discrete baselines.","pith_extraction_headline":"Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17011/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"citation_quote_validity","ran_at":"2026-05-19T19:49:49.554858Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.813806Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T18:52:03.155299Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.190697Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:40:52.879363Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:25.018013Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"5db9d01ddea978d0ca849b698f272bd57e527158d1fe730427e3b253ff8a69ee"},"references":{"count":20,"sample":[{"doi":"10.1038/s41587-019-0336-3","year":2019,"title":"Visualizing structure and transitions in high-dimensional biological data,","work_id":"f2403585-c0fa-403a-94ff-51a03ac635ad","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3706598.3713551","year":2025,"title":"Unveiling high-dimensional backstage: A survey for reliable visual analytics with dimensionality reduction","work_id":"3b22c616-77f2-41cd-8b7e-3b426199b18b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3592433","year":2023,"title":"3d gaussian splatting for real-time radiance field rendering,","work_id":"d1e854f7-f01a-46d6-bc88-fe9fe914b4f3","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"A representation the- orem for locally compact quantum groups","work_id":"a1b77a81-dfdc-490e-805b-591b44077c3d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.2312/sgp/","year":2007,"title":"O. Sorkine and M. Alexa, “As-rigid-as-possible surface modeling,” in Proceedings of the Fifth Eurographics Symposium on Geometry Processing, ser. SGP ’07. Goslar, DEU: Eurographics Association, 2007, ","work_id":"aa50ae43-8368-4304-ac7d-9657d176a48c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":20,"snapshot_sha256":"016b603b6c9047a1acfdb217301422e99f50ef5c0f05350d6f462d886f11a79d","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1397ad325fcf5113842ada700a201ee998427c48b4b866431d2df3905a1c7918"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"665ff848-f130-4455-a077-6707c0d8de88"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:03:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xHfcZDJKU3C3x/Qm+aB2xSi/NM1y4N0otUBy6eQzxkfqiG7sSbZAE8B+AIe/4sSk/l4pyOyCCf4p2V81JaNOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:43:23.401376Z"},"content_sha256":"d20b62d24429fd7287c686baf4ba3acf598f50a6445345286b3e5628a7f79326","schema_version":"1.0","event_id":"sha256:d20b62d24429fd7287c686baf4ba3acf598f50a6445345286b3e5628a7f79326"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ/bundle.json","state_url":"https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ/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":"2026-06-10T15:43:23Z","links":{"resolver":"https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ","bundle":"https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ/bundle.json","state":"https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YA77ZUE3ZVKUG2VUZPQEQZGUNZ","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":"e5f292caf338144ffb2d54b44fce8acab9809be2d999ac8d92dde17ed1bed514","cross_cats_sorted":["cs.CV","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-16T14:21:08Z","title_canon_sha256":"f739cafe70b50fdcc58d5b014cd7702e96a8f2a7beba544210e95dbbc72f201d"},"schema_version":"1.0","source":{"id":"2605.17011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17011","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17011v1","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17011","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"YA77ZUE3ZVKU","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"pith_short_16","alias_value":"YA77ZUE3ZVKUG2VU","created_at":"2026-05-20T00:03:35Z"},{"alias_kind":"pith_short_8","alias_value":"YA77ZUE3","created_at":"2026-05-20T00:03:35Z"}],"graph_snapshots":[{"event_id":"sha256:d20b62d24429fd7287c686baf4ba3acf598f50a6445345286b3e5628a7f79326","target":"graph","created_at":"2026-05-20T00:03:35Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process... driven by local geometric constraints... solving orthogonal Procrustes targets... aligning the spatial covariance of each Gaussian to the local tangent space... topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That enforcing As-Rigid-As-Possible priors via orthogonal Procrustes alignment of Gaussian covariances to local tangent spaces, combined with topology-specific loss tailoring, will produce faithful continuous volumetric representations without introducing new artifacts or losing fidelity compared to discrete baselines."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Topo-GS repurposes 3D Gaussian Splatting with local geometric constraints and topology-aware losses to produce continuous volumetric embeddings of high-dimensional data."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints."}],"snapshot_sha256":"6121102b1c972d6d5df59cadccca9f164e33b634748cbb418813dfe2c09b3848"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1397ad325fcf5113842ada700a201ee998427c48b4b866431d2df3905a1c7918"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T19:49:49.554858Z","status":"completed","version":"0.1.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.813806Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T18:52:03.155299Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.190697Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T18:40:52.879363Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:25.018013Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17011/integrity.json","findings":[],"snapshot_sha256":"5db9d01ddea978d0ca849b698f272bd57e527158d1fe730427e3b253ff8a69ee","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial discontinuities, often failing to represent the continuous density of the underlying manifold. To address these limitations, we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process. Instead of standard photometric losses, Topo-GS is driven by local geometric co","authors_text":"Jo\\~ao Paulo Gois, Luis Gustavo Nonato","cross_cats":["cs.CV","cs.LG"],"headline":"Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-16T14:21:08Z","title":"Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting"},"references":{"count":20,"internal_anchors":1,"resolved_work":20,"sample":[{"cited_arxiv_id":"","doi":"10.1038/s41587-019-0336-3","is_internal_anchor":false,"ref_index":1,"title":"Visualizing structure and transitions in high-dimensional biological data,","work_id":"f2403585-c0fa-403a-94ff-51a03ac635ad","year":2019},{"cited_arxiv_id":"","doi":"10.1145/3706598.3713551","is_internal_anchor":false,"ref_index":2,"title":"Unveiling high-dimensional backstage: A survey for reliable visual analytics with dimensionality reduction","work_id":"3b22c616-77f2-41cd-8b7e-3b426199b18b","year":2025},{"cited_arxiv_id":"","doi":"10.1145/3592433","is_internal_anchor":false,"ref_index":3,"title":"3d gaussian splatting for real-time radiance field rendering,","work_id":"d1e854f7-f01a-46d6-bc88-fe9fe914b4f3","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"A representation the- orem for locally compact quantum groups","work_id":"a1b77a81-dfdc-490e-805b-591b44077c3d","year":2004},{"cited_arxiv_id":"","doi":"10.2312/sgp/","is_internal_anchor":false,"ref_index":5,"title":"O. Sorkine and M. Alexa, “As-rigid-as-possible surface modeling,” in Proceedings of the Fifth Eurographics Symposium on Geometry Processing, ser. SGP ’07. Goslar, DEU: Eurographics Association, 2007, ","work_id":"aa50ae43-8368-4304-ac7d-9657d176a48c","year":2007}],"snapshot_sha256":"016b603b6c9047a1acfdb217301422e99f50ef5c0f05350d6f462d886f11a79d"},"source":{"id":"2605.17011","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:29:27.568295Z","id":"665ff848-f130-4455-a077-6707c0d8de88","model_set":{"reader":"grok-4.3"},"one_line_summary":"Topo-GS repurposes 3D Gaussian Splatting with local geometric constraints and topology-aware losses to produce continuous volumetric embeddings of high-dimensional data.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints.","strongest_claim":"we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process... driven by local geometric constraints... solving orthogonal Procrustes targets... aligning the spatial covariance of each Gaussian to the local tangent space... topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces.","weakest_assumption":"That enforcing As-Rigid-As-Possible priors via orthogonal Procrustes alignment of Gaussian covariances to local tangent spaces, combined with topology-specific loss tailoring, will produce faithful continuous volumetric representations without introducing new artifacts or losing fidelity compared to discrete baselines."}},"verdict_id":"665ff848-f130-4455-a077-6707c0d8de88"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0660d5a12756ee0685abaa145bc0936d0036b11593d5308d4f7875f1c9746429","target":"record","created_at":"2026-05-20T00:03:35Z","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":"e5f292caf338144ffb2d54b44fce8acab9809be2d999ac8d92dde17ed1bed514","cross_cats_sorted":["cs.CV","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-16T14:21:08Z","title_canon_sha256":"f739cafe70b50fdcc58d5b014cd7702e96a8f2a7beba544210e95dbbc72f201d"},"schema_version":"1.0","source":{"id":"2605.17011","kind":"arxiv","version":1}},"canonical_sha256":"c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad","first_computed_at":"2026-05-20T00:03:35.837953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:35.837953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VppX4oinnZDX+u5oaVWLy+L69DraYUxGHqcUmf/zpESrYDo4RhuiIfvV9UxS9ugSiuzQKWRO6yRufcQNUeDwCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:35.838806Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0660d5a12756ee0685abaa145bc0936d0036b11593d5308d4f7875f1c9746429","sha256:d20b62d24429fd7287c686baf4ba3acf598f50a6445345286b3e5628a7f79326"],"state_sha256":"50d909fa85f1ad20db7ca9e9f890454094f70f1329919bb481929b1c6562b59e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8m3FDlgS7qF1nIUgQxGeONWmBEb9HL6tqasf9Wng7HWoJN6VeCGaWOSG4CNvv/ph8f8vNOi+sv/0S17pNIhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T15:43:23.407605Z","bundle_sha256":"e837980a6422349f7913b1b97af14e28e24791478cc1b57c43ffb1e905f04d54"}}