{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5CWYEJ4TUTKOI7MPVEZJNQTXGX","short_pith_number":"pith:5CWYEJ4T","canonical_record":{"source":{"id":"1803.05093","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-14T01:23:33Z","cross_cats_sorted":[],"title_canon_sha256":"43dc0a7e5543ee7be5bceb24789747365c1a71b7a37cfcb211354749bd7ba439","abstract_canon_sha256":"26752006f3b6963b76de8338c747858ae6276f48f21b83ad8438510eaccc1fae"},"schema_version":"1.0"},"canonical_sha256":"e8ad822793a4d4e47d8fa93296c27735dd0fcd71e9ef86958f6d2fdfaecc3e7e","source":{"kind":"arxiv","id":"1803.05093","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05093","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05093v2","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05093","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"5CWYEJ4TUTKO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5CWYEJ4TUTKOI7MP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5CWYEJ4T","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5CWYEJ4TUTKOI7MPVEZJNQTXGX","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05093","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-14T01:23:33Z","cross_cats_sorted":[],"title_canon_sha256":"43dc0a7e5543ee7be5bceb24789747365c1a71b7a37cfcb211354749bd7ba439","abstract_canon_sha256":"26752006f3b6963b76de8338c747858ae6276f48f21b83ad8438510eaccc1fae"},"schema_version":"1.0"},"canonical_sha256":"e8ad822793a4d4e47d8fa93296c27735dd0fcd71e9ef86958f6d2fdfaecc3e7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:29.730083Z","signature_b64":"u5zE3XKTV09sk8HwfEPyDhtmul9cYNncQIRDgq65LOzKuH6I9qFq2ofgqrGPt6rVpevDonYHIluudkYF5yIxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ad822793a4d4e47d8fa93296c27735dd0fcd71e9ef86958f6d2fdfaecc3e7e","last_reissued_at":"2026-05-18T00:20:29.729469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:29.729469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05093","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4HtFkEJyWpTXNO4aUyO120hsy4mtdhaeEoYaErB61Y/NeZroBliuJmyYJSpGwjrmHT2j0WaN9uXsbG490EpoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:50:55.676157Z"},"content_sha256":"76cc03ee4a6f316d5cd643a660b43652dbd1e4111d1d027aa664dd9647b85ccb","schema_version":"1.0","event_id":"sha256:76cc03ee4a6f316d5cd643a660b43652dbd1e4111d1d027aa664dd9647b85ccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5CWYEJ4TUTKOI7MPVEZJNQTXGX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Reconstruction by Discrete Morse Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jiayuan Wang, Tamal K. Dey, Yusu Wang","submitted_at":"2018-03-14T01:23:33Z","abstract_excerpt":"Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first step towards closing this gap. Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05093","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":""},"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":"2026-05-18T00:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUrpKkXxWP+P1i/N0I99PFa7nZsc4Fpqt41p8ah0F/RnCh7aS6NfcK9Drn83VwXO79vlvHaPylyN+wCa4INABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:50:55.676734Z"},"content_sha256":"75b62f6c0945df5a8e9c99658433fe21bb27808d29a1c3d71233e21bbae610f3","schema_version":"1.0","event_id":"sha256:75b62f6c0945df5a8e9c99658433fe21bb27808d29a1c3d71233e21bbae610f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX/bundle.json","state_url":"https://pith.science/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX/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":"2026-05-28T15:50:55Z","links":{"resolver":"https://pith.science/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX","bundle":"https://pith.science/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX/bundle.json","state":"https://pith.science/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CWYEJ4TUTKOI7MPVEZJNQTXGX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5CWYEJ4TUTKOI7MPVEZJNQTXGX","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":"26752006f3b6963b76de8338c747858ae6276f48f21b83ad8438510eaccc1fae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-14T01:23:33Z","title_canon_sha256":"43dc0a7e5543ee7be5bceb24789747365c1a71b7a37cfcb211354749bd7ba439"},"schema_version":"1.0","source":{"id":"1803.05093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05093","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05093v2","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05093","created_at":"2026-05-18T00:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"5CWYEJ4TUTKO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5CWYEJ4TUTKOI7MP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5CWYEJ4T","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:75b62f6c0945df5a8e9c99658433fe21bb27808d29a1c3d71233e21bbae610f3","target":"graph","created_at":"2026-05-18T00:20:29Z","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"},"paper":{"abstract_excerpt":"Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first step towards closing this gap. Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete","authors_text":"Jiayuan Wang, Tamal K. Dey, Yusu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-14T01:23:33Z","title":"Graph Reconstruction by Discrete Morse Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05093","kind":"arxiv","version":2},"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":"sha256:76cc03ee4a6f316d5cd643a660b43652dbd1e4111d1d027aa664dd9647b85ccb","target":"record","created_at":"2026-05-18T00:20:29Z","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":"26752006f3b6963b76de8338c747858ae6276f48f21b83ad8438510eaccc1fae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-14T01:23:33Z","title_canon_sha256":"43dc0a7e5543ee7be5bceb24789747365c1a71b7a37cfcb211354749bd7ba439"},"schema_version":"1.0","source":{"id":"1803.05093","kind":"arxiv","version":2}},"canonical_sha256":"e8ad822793a4d4e47d8fa93296c27735dd0fcd71e9ef86958f6d2fdfaecc3e7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ad822793a4d4e47d8fa93296c27735dd0fcd71e9ef86958f6d2fdfaecc3e7e","first_computed_at":"2026-05-18T00:20:29.729469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:29.729469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5zE3XKTV09sk8HwfEPyDhtmul9cYNncQIRDgq65LOzKuH6I9qFq2ofgqrGPt6rVpevDonYHIluudkYF5yIxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:29.730083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76cc03ee4a6f316d5cd643a660b43652dbd1e4111d1d027aa664dd9647b85ccb","sha256:75b62f6c0945df5a8e9c99658433fe21bb27808d29a1c3d71233e21bbae610f3"],"state_sha256":"e45f2360908e5c67c8086f1c28cc0eccc1add1fe7b6885499e640f21be28c013"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uIqhH70ZxuvMEmPsdnNkfLqyJNcFaJZ4f6Dj6iBOOKWM1PqCKZP1sIo7IdpWbvJI39MBkBYgvo1urDcuVPlKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:50:55.680686Z","bundle_sha256":"b034161be12d7b8e9af3e1e47bf1395e0f632df149530a4401a7d5d1722b8f6e"}}