{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZMHDCANRECVYHRGRD77D5WF67Q","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":"a9a0443a42a41bce87064c39e41beda97444fa79f021856fa6368d4bed1fe76c","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-07-27T18:07:45Z","title_canon_sha256":"66d8bb911b81361dac75a889f7709a66bb0cb98946381cdc005b0f853f3c5d20"},"schema_version":"1.0","source":{"id":"2307.15130","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.15130","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"2307.15130v7","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.15130","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZMHDCANRECVY","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"pith_short_16","alias_value":"ZMHDCANRECVYHRGR","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"pith_short_8","alias_value":"ZMHDCANR","created_at":"2026-06-19T16:12:12Z"}],"graph_snapshots":[{"event_id":"sha256:0a00d4df3db65b64b25f6c6b268304294cefdb24818ef11da01ce205f3e60041","target":"graph","created_at":"2026-06-19T16:12:12Z","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/2307.15130/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Data consisting of a graph with a function mapping into $\\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such objects is required in a data analysis pipeline, leading to a need for distances between them. In this work, we study the interleaving distance on discretization of these objects, called mapper graphs when $d=1$, where functor representations of the data can be compared by finding pairs of natural transformations between them. However, in many cases, computatio","authors_text":"Bei Wang, Elizabeth Munch, Erin W. Chambers, Sarah Percival","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-07-27T18:07:45Z","title":"Bounding the Interleaving Distance for Mapper Graphs with a Loss Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15130","kind":"arxiv","version":7},"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":"sha256:1c9b6435755ddc3196d7f2394a67a7462eb1ccf5e00b34a2b497afdb64a75c57","target":"record","created_at":"2026-06-19T16:12:12Z","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":"a9a0443a42a41bce87064c39e41beda97444fa79f021856fa6368d4bed1fe76c","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-07-27T18:07:45Z","title_canon_sha256":"66d8bb911b81361dac75a889f7709a66bb0cb98946381cdc005b0f853f3c5d20"},"schema_version":"1.0","source":{"id":"2307.15130","kind":"arxiv","version":7}},"canonical_sha256":"cb0e3101b120ab83c4d11ffe3ed8befc0067553a11c00f5107b7ad0810154515","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb0e3101b120ab83c4d11ffe3ed8befc0067553a11c00f5107b7ad0810154515","first_computed_at":"2026-06-19T16:12:12.355357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:12.355357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZRSil60mxmp+zNsP9/5fnMVC4OLZlYOPXu5+y4rceGO4BA1rAdPbeHByhPfosjoT3pMXK+ZfrHrG+Fkm7uLLCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:12.355787Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.15130","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c9b6435755ddc3196d7f2394a67a7462eb1ccf5e00b34a2b497afdb64a75c57","sha256:0a00d4df3db65b64b25f6c6b268304294cefdb24818ef11da01ce205f3e60041"],"state_sha256":"fba034dc09420c5e9eae595f38ed20bb6b99ae4eff1e8e68151ec260cc113f6f"}