{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XRSAZMNURJSITVZ3VD6H6SIUCK","short_pith_number":"pith:XRSAZMNU","canonical_record":{"source":{"id":"1206.1365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-06T22:38:19Z","cross_cats_sorted":["cs.CG","math.ST","stat.TH"],"title_canon_sha256":"2b8539f9bd228fa5e2f87d1015c7a98b49a2f16d2a5eabf0aa5e18c1d72a89b2","abstract_canon_sha256":"2bb8cb9eea0ad885d39603384f89bd6cd5fb6af97dc070675a1abc1deba50f3b"},"schema_version":"1.0"},"canonical_sha256":"bc640cb1b48a6489d73ba8fc7f49141280e179b6f42fe68afb1a8320eac607f8","source":{"kind":"arxiv","id":"1206.1365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1365","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1365v1","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1365","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"XRSAZMNURJSI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XRSAZMNURJSITVZ3","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XRSAZMNU","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XRSAZMNURJSITVZ3VD6H6SIUCK","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-06T22:38:19Z","cross_cats_sorted":["cs.CG","math.ST","stat.TH"],"title_canon_sha256":"2b8539f9bd228fa5e2f87d1015c7a98b49a2f16d2a5eabf0aa5e18c1d72a89b2","abstract_canon_sha256":"2bb8cb9eea0ad885d39603384f89bd6cd5fb6af97dc070675a1abc1deba50f3b"},"schema_version":"1.0"},"canonical_sha256":"bc640cb1b48a6489d73ba8fc7f49141280e179b6f42fe68afb1a8320eac607f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:05.326770Z","signature_b64":"vY9XVdU1uhlOLdx9vTEl43uYwffC1O+W1YDtibu3twcVdCBLSEVb1oiqHV2MGwlF98e3niOdptx6jxovPDbYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc640cb1b48a6489d73ba8fc7f49141280e179b6f42fe68afb1a8320eac607f8","last_reissued_at":"2026-05-18T03:54:05.326025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:05.326025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1365","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":"2026-05-18T03:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1n1/JqICWiLCa7dJ/C9GNJICo47qUoT2ZT5lu5PNlX+4/xhbKUWLqW5IGIYIckuREJjoqVxKHcQZdr5bUvQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:39:30.793849Z"},"content_sha256":"4bcde5a9cd411fd0a98210092ddfde2115283a67dc68b562d75752a51ad837ab","schema_version":"1.0","event_id":"sha256:4bcde5a9cd411fd0a98210092ddfde2115283a67dc68b562d75752a51ad837ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XRSAZMNURJSITVZ3VD6H6SIUCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidimensional Interleavings and Applications to Topological Inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.ST","stat.TH"],"primary_cat":"math.AT","authors_text":"Michael Lesnick","submitted_at":"2012-06-06T22:38:19Z","abstract_excerpt":"This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at the (topological) level of filtrations rather than only at the (algebraic) level of persistent homology modules.\n  Our main mathematical objects of study are interleavings. These are tools for quantifying the similarity between two multidimensional filtrations or persistence modules. They were introduced for 1-D filtrations and persistence modules by Chazal, Cohen-Steiner, Glisse, Guibas, and Oudot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1365","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":"2026-05-18T03:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3/7Xsk5S/H56i+OcnyVCFDFMmavtFGpHyP/A+D+qYcC1ygxT2mAbNZaCuqrFo9bYl5zoR5GimdlYtyILRWvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:39:30.794501Z"},"content_sha256":"373be15caf11cf59c6e38106ded14b5a512044512ef35fda1f9950bf612dc7ab","schema_version":"1.0","event_id":"sha256:373be15caf11cf59c6e38106ded14b5a512044512ef35fda1f9950bf612dc7ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRSAZMNURJSITVZ3VD6H6SIUCK/bundle.json","state_url":"https://pith.science/pith/XRSAZMNURJSITVZ3VD6H6SIUCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRSAZMNURJSITVZ3VD6H6SIUCK/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":"2026-05-25T12:39:30Z","links":{"resolver":"https://pith.science/pith/XRSAZMNURJSITVZ3VD6H6SIUCK","bundle":"https://pith.science/pith/XRSAZMNURJSITVZ3VD6H6SIUCK/bundle.json","state":"https://pith.science/pith/XRSAZMNURJSITVZ3VD6H6SIUCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRSAZMNURJSITVZ3VD6H6SIUCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XRSAZMNURJSITVZ3VD6H6SIUCK","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":"2bb8cb9eea0ad885d39603384f89bd6cd5fb6af97dc070675a1abc1deba50f3b","cross_cats_sorted":["cs.CG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-06T22:38:19Z","title_canon_sha256":"2b8539f9bd228fa5e2f87d1015c7a98b49a2f16d2a5eabf0aa5e18c1d72a89b2"},"schema_version":"1.0","source":{"id":"1206.1365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1365","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1365v1","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1365","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"XRSAZMNURJSI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XRSAZMNURJSITVZ3","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XRSAZMNU","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:373be15caf11cf59c6e38106ded14b5a512044512ef35fda1f9950bf612dc7ab","target":"graph","created_at":"2026-05-18T03:54:05Z","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":"This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at the (topological) level of filtrations rather than only at the (algebraic) level of persistent homology modules.\n  Our main mathematical objects of study are interleavings. These are tools for quantifying the similarity between two multidimensional filtrations or persistence modules. They were introduced for 1-D filtrations and persistence modules by Chazal, Cohen-Steiner, Glisse, Guibas, and Oudot","authors_text":"Michael Lesnick","cross_cats":["cs.CG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-06T22:38:19Z","title":"Multidimensional Interleavings and Applications to Topological Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1365","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":"sha256:4bcde5a9cd411fd0a98210092ddfde2115283a67dc68b562d75752a51ad837ab","target":"record","created_at":"2026-05-18T03:54:05Z","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":"2bb8cb9eea0ad885d39603384f89bd6cd5fb6af97dc070675a1abc1deba50f3b","cross_cats_sorted":["cs.CG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-06T22:38:19Z","title_canon_sha256":"2b8539f9bd228fa5e2f87d1015c7a98b49a2f16d2a5eabf0aa5e18c1d72a89b2"},"schema_version":"1.0","source":{"id":"1206.1365","kind":"arxiv","version":1}},"canonical_sha256":"bc640cb1b48a6489d73ba8fc7f49141280e179b6f42fe68afb1a8320eac607f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc640cb1b48a6489d73ba8fc7f49141280e179b6f42fe68afb1a8320eac607f8","first_computed_at":"2026-05-18T03:54:05.326025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:05.326025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vY9XVdU1uhlOLdx9vTEl43uYwffC1O+W1YDtibu3twcVdCBLSEVb1oiqHV2MGwlF98e3niOdptx6jxovPDbYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:05.326770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bcde5a9cd411fd0a98210092ddfde2115283a67dc68b562d75752a51ad837ab","sha256:373be15caf11cf59c6e38106ded14b5a512044512ef35fda1f9950bf612dc7ab"],"state_sha256":"b35b9d702112b9eab7c009bd3642effe30fc47d2bb96dfb962b38560545b498e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8JFsT01EXwHAwlMhftLBIum1WHeLVepfJZA2QwBR3BZm3cpEnrKcrUStIQjZb+NQec4gXrpWIyxdz+9BTNCtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:39:30.797814Z","bundle_sha256":"124617aec9cbe53e4e67d825efd4d4770643f6398ee6ecec2d942c965d999a61"}}