{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XO74CC4N2WB22YEQS2LQ3MA7ZN","short_pith_number":"pith:XO74CC4N","canonical_record":{"source":{"id":"1810.10813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-25T09:59:40Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"fde2f7f8d386867844d00cd276699b9b4a7e68bc98b65842cd3ddd6a9deb079f","abstract_canon_sha256":"20e7c05fae2999d94e0e7f3ada82040d0a6c88a4d1c44a1a87ce4080b889a7f5"},"schema_version":"1.0"},"canonical_sha256":"bbbfc10b8dd583ad609096970db01fcb5a40bf7e0d02387c9a2b8f4def090d45","source":{"kind":"arxiv","id":"1810.10813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10813","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10813v1","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10813","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"XO74CC4N2WB2","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XO74CC4N2WB22YEQ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XO74CC4N","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XO74CC4N2WB22YEQS2LQ3MA7ZN","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-25T09:59:40Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"fde2f7f8d386867844d00cd276699b9b4a7e68bc98b65842cd3ddd6a9deb079f","abstract_canon_sha256":"20e7c05fae2999d94e0e7f3ada82040d0a6c88a4d1c44a1a87ce4080b889a7f5"},"schema_version":"1.0"},"canonical_sha256":"bbbfc10b8dd583ad609096970db01fcb5a40bf7e0d02387c9a2b8f4def090d45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:19.618840Z","signature_b64":"BeejKFFIb8S6YMXXQ/f/NzRewiTChrym+2LvgjYgg9rdJVFos5oF4ITLNAQrfG1tP+Mj8Vy35AepeGuwLDEjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbbfc10b8dd583ad609096970db01fcb5a40bf7e0d02387c9a2b8f4def090d45","last_reissued_at":"2026-05-18T00:02:19.618440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:19.618440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10813","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":"2026-05-18T00:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PLfUF9zq/NpJk6d/EjW/mHIYADdQeY1q12ays1MtCxZaEEd8AvMGX79G3D/yQ3E3lu9nbSZaXkbAWnSW6ozHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:04:54.251080Z"},"content_sha256":"9d2507a46e5d3a7852850170c4441239f7927c699adcbc49e1438a54c2b3a103","schema_version":"1.0","event_id":"sha256:9d2507a46e5d3a7852850170c4441239f7927c699adcbc49e1438a54c2b3a103"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XO74CC4N2WB22YEQS2LQ3MA7ZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse Problems in Topological Persistence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Elchanan Solomon, Steve Oudot","submitted_at":"2018-10-25T09:59:40Z","abstract_excerpt":"In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. the existence of right inverses, and the second half focuses on injectivity, i.e. left inverses. Throughout, we highlight the tools and theorems that underlie these advances, and direct the reader's attention to open problems, both theoretical and applied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10813","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":""},"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":"2026-05-18T00:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pFc3XddpL46iUVCa2gzD+vb0ViaGwaVykfYUTv3nJiNlCu1mkps4v6A8ccYFae3nFGlUiRHu0hWlxiHkl6CyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:04:54.251421Z"},"content_sha256":"3af92626f3a31be879f6865e4b553b14cf930decc041f805e94a4c1f7783f768","schema_version":"1.0","event_id":"sha256:3af92626f3a31be879f6865e4b553b14cf930decc041f805e94a4c1f7783f768"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN/bundle.json","state_url":"https://pith.science/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN/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":"2026-06-02T02:04:54Z","links":{"resolver":"https://pith.science/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN","bundle":"https://pith.science/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN/bundle.json","state":"https://pith.science/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XO74CC4N2WB22YEQS2LQ3MA7ZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XO74CC4N2WB22YEQS2LQ3MA7ZN","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":"20e7c05fae2999d94e0e7f3ada82040d0a6c88a4d1c44a1a87ce4080b889a7f5","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-25T09:59:40Z","title_canon_sha256":"fde2f7f8d386867844d00cd276699b9b4a7e68bc98b65842cd3ddd6a9deb079f"},"schema_version":"1.0","source":{"id":"1810.10813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10813","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10813v1","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10813","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"XO74CC4N2WB2","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XO74CC4N2WB22YEQ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XO74CC4N","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:3af92626f3a31be879f6865e4b553b14cf930decc041f805e94a4c1f7783f768","target":"graph","created_at":"2026-05-18T00:02:19Z","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":"In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. the existence of right inverses, and the second half focuses on injectivity, i.e. left inverses. Throughout, we highlight the tools and theorems that underlie these advances, and direct the reader's attention to open problems, both theoretical and applied.","authors_text":"Elchanan Solomon, Steve Oudot","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-25T09:59:40Z","title":"Inverse Problems in Topological Persistence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10813","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":"sha256:9d2507a46e5d3a7852850170c4441239f7927c699adcbc49e1438a54c2b3a103","target":"record","created_at":"2026-05-18T00:02:19Z","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":"20e7c05fae2999d94e0e7f3ada82040d0a6c88a4d1c44a1a87ce4080b889a7f5","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-25T09:59:40Z","title_canon_sha256":"fde2f7f8d386867844d00cd276699b9b4a7e68bc98b65842cd3ddd6a9deb079f"},"schema_version":"1.0","source":{"id":"1810.10813","kind":"arxiv","version":1}},"canonical_sha256":"bbbfc10b8dd583ad609096970db01fcb5a40bf7e0d02387c9a2b8f4def090d45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbbfc10b8dd583ad609096970db01fcb5a40bf7e0d02387c9a2b8f4def090d45","first_computed_at":"2026-05-18T00:02:19.618440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:19.618440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BeejKFFIb8S6YMXXQ/f/NzRewiTChrym+2LvgjYgg9rdJVFos5oF4ITLNAQrfG1tP+Mj8Vy35AepeGuwLDEjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:19.618840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d2507a46e5d3a7852850170c4441239f7927c699adcbc49e1438a54c2b3a103","sha256:3af92626f3a31be879f6865e4b553b14cf930decc041f805e94a4c1f7783f768"],"state_sha256":"1419fdd19426fbb5150791423b459f0d78ebb7670e9e66c6ff98aa8928b7d1c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElMVoQPCGP2JrCNAQnre1C44a73znKrq2f5Xktfe/ZPfHRt5HtCkzmQXs97qYx0L6dDQqfwPuYWJ34E0MKdHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:04:54.253197Z","bundle_sha256":"de48cfb99da881b3dbd629e37d0e628e1b1cf6a06507b4af26aa4a987796196c"}}