{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:RRAIVYLRNBK5MITVXLPUN3IW46","short_pith_number":"pith:RRAIVYLR","canonical_record":{"source":{"id":"2508.07637","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-08-11T05:41:24Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"4600741af119a96e817e937b21ca95f269e4074cb3cdf987e68ebcb724c509aa","abstract_canon_sha256":"e6aa1a6aa58630e0b95784f960c0047d2e8eb8dedba1bfaea464c4dfbc3a5208"},"schema_version":"1.0"},"canonical_sha256":"8c408ae1716855d62275badf46ed16e78c1b411a45706cdfadfd5612f9ff6864","source":{"kind":"arxiv","id":"2508.07637","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07637","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07637v1","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07637","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"RRAIVYLRNBK5","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"pith_short_16","alias_value":"RRAIVYLRNBK5MITV","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"pith_short_8","alias_value":"RRAIVYLR","created_at":"2026-07-05T11:51:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:RRAIVYLRNBK5MITVXLPUN3IW46","target":"record","payload":{"canonical_record":{"source":{"id":"2508.07637","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-08-11T05:41:24Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"4600741af119a96e817e937b21ca95f269e4074cb3cdf987e68ebcb724c509aa","abstract_canon_sha256":"e6aa1a6aa58630e0b95784f960c0047d2e8eb8dedba1bfaea464c4dfbc3a5208"},"schema_version":"1.0"},"canonical_sha256":"8c408ae1716855d62275badf46ed16e78c1b411a45706cdfadfd5612f9ff6864","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:51:49.611877Z","signature_b64":"FAb32Ui3tEFf2Qf0adKPMjotLdYviGzdTubaBiAcywhfRKn6eRtKZMCWFT0s3J8dS/vYsKVtBnF0KkbhMqeEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c408ae1716855d62275badf46ed16e78c1b411a45706cdfadfd5612f9ff6864","last_reissued_at":"2026-07-05T11:51:49.611285Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:51:49.611285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.07637","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":"2026-07-05T11:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DNXI/XZ1RI8SwDOLWUS1TCibWPvzn8oV1+kGC06qqo1Vp0JdDE0d0UKLjjbpUm4wPOqe/VatNp5o7p52GxWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:34:30.788694Z"},"content_sha256":"48d7a37a400e5e557730521fac07c5975408a87a3ed6a168126c23b707407a3d","schema_version":"1.0","event_id":"sha256:48d7a37a400e5e557730521fac07c5975408a87a3ed6a168126c23b707407a3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:RRAIVYLRNBK5MITVXLPUN3IW46","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extracting Complex Topology from Multivariate Functional Approximation: Contours, Jacobi Sets, and Ridge-Valley Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.LG","authors_text":"Bei Wang, David Lenz, Guanqun Ma, Hanqi Guo, Tom Peterka","submitted_at":"2025-08-11T05:41:24Z","abstract_excerpt":"Implicit continuous models, such as functional models and implicit neural networks, are an increasingly popular method for replacing discrete data representations with continuous, high-order, and differentiable surrogates. These models offer new perspectives on the storage, transfer, and analysis of scientific data. In this paper, we introduce the first framework to directly extract complex topological features -- contours, Jacobi sets, and ridge-valley graphs -- from a type of continuous implicit model known as multivariate functional approximation (MFA). MFA replaces discrete data with conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07637","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/2508.07637/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":"2026-07-05T11:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Av8TyG+1ceCKOGzrOfeQ0TTCt3CVL9I6eagMw5WE0ou7R43YZsx34NizOJQrgdjT4QnMuNSdhentMPCvgeuoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:34:30.789640Z"},"content_sha256":"e97333047103062ec4b7b37a7f66503e26bcbbab69343ef6df742617fb29e3a4","schema_version":"1.0","event_id":"sha256:e97333047103062ec4b7b37a7f66503e26bcbbab69343ef6df742617fb29e3a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RRAIVYLRNBK5MITVXLPUN3IW46/bundle.json","state_url":"https://pith.science/pith/RRAIVYLRNBK5MITVXLPUN3IW46/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RRAIVYLRNBK5MITVXLPUN3IW46/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":"2026-08-09T20:34:30Z","links":{"resolver":"https://pith.science/pith/RRAIVYLRNBK5MITVXLPUN3IW46","bundle":"https://pith.science/pith/RRAIVYLRNBK5MITVXLPUN3IW46/bundle.json","state":"https://pith.science/pith/RRAIVYLRNBK5MITVXLPUN3IW46/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RRAIVYLRNBK5MITVXLPUN3IW46/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RRAIVYLRNBK5MITVXLPUN3IW46","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":"e6aa1a6aa58630e0b95784f960c0047d2e8eb8dedba1bfaea464c4dfbc3a5208","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-08-11T05:41:24Z","title_canon_sha256":"4600741af119a96e817e937b21ca95f269e4074cb3cdf987e68ebcb724c509aa"},"schema_version":"1.0","source":{"id":"2508.07637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07637","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07637v1","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07637","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"RRAIVYLRNBK5","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"pith_short_16","alias_value":"RRAIVYLRNBK5MITV","created_at":"2026-07-05T11:51:49Z"},{"alias_kind":"pith_short_8","alias_value":"RRAIVYLR","created_at":"2026-07-05T11:51:49Z"}],"graph_snapshots":[{"event_id":"sha256:e97333047103062ec4b7b37a7f66503e26bcbbab69343ef6df742617fb29e3a4","target":"graph","created_at":"2026-07-05T11:51:49Z","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/2508.07637/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Implicit continuous models, such as functional models and implicit neural networks, are an increasingly popular method for replacing discrete data representations with continuous, high-order, and differentiable surrogates. These models offer new perspectives on the storage, transfer, and analysis of scientific data. In this paper, we introduce the first framework to directly extract complex topological features -- contours, Jacobi sets, and ridge-valley graphs -- from a type of continuous implicit model known as multivariate functional approximation (MFA). MFA replaces discrete data with conti","authors_text":"Bei Wang, David Lenz, Guanqun Ma, Hanqi Guo, Tom Peterka","cross_cats":["cs.CG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-08-11T05:41:24Z","title":"Extracting Complex Topology from Multivariate Functional Approximation: Contours, Jacobi Sets, and Ridge-Valley Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07637","kind":"arxiv","version":1},"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":"sha256:48d7a37a400e5e557730521fac07c5975408a87a3ed6a168126c23b707407a3d","target":"record","created_at":"2026-07-05T11:51:49Z","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":"e6aa1a6aa58630e0b95784f960c0047d2e8eb8dedba1bfaea464c4dfbc3a5208","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-08-11T05:41:24Z","title_canon_sha256":"4600741af119a96e817e937b21ca95f269e4074cb3cdf987e68ebcb724c509aa"},"schema_version":"1.0","source":{"id":"2508.07637","kind":"arxiv","version":1}},"canonical_sha256":"8c408ae1716855d62275badf46ed16e78c1b411a45706cdfadfd5612f9ff6864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c408ae1716855d62275badf46ed16e78c1b411a45706cdfadfd5612f9ff6864","first_computed_at":"2026-07-05T11:51:49.611285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:51:49.611285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FAb32Ui3tEFf2Qf0adKPMjotLdYviGzdTubaBiAcywhfRKn6eRtKZMCWFT0s3J8dS/vYsKVtBnF0KkbhMqeEBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:51:49.611877Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.07637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48d7a37a400e5e557730521fac07c5975408a87a3ed6a168126c23b707407a3d","sha256:e97333047103062ec4b7b37a7f66503e26bcbbab69343ef6df742617fb29e3a4"],"state_sha256":"bf45560bb78a4afe004a6892d33c5031b0b6e6dc1201b0cac02935d0c58f3c9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YNJXLwxRNyWEXIRckiisMbGrLx70meguBbJrVyDbka0b5CEu3hodAXvxdM5Bry+FKYEeunGhPl7ntOom2oetBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:34:30.797298Z","bundle_sha256":"0411a0449e4e2f5bace3f16f8349264830115e35a36deb46d2a4bccb9a894fbb"}}