{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6NW2C42CUCZ7OG34DOLDFNROTW","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":"7b271a69fccc43bda12dc4743481e54110d8f8e9304e794b65889c8bbbda9ba6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-29T18:55:45Z","title_canon_sha256":"a84feabb25e1cf509f36626a097ef3fb4252a3a7caed8500ea8e12fa0f6a8aa2"},"schema_version":"1.0","source":{"id":"1811.12392","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12392","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12392v3","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12392","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"pith_short_12","alias_value":"6NW2C42CUCZ7","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6NW2C42CUCZ7OG34","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6NW2C42C","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:d57fce0d5b8c26b6bc4b24e01611ed4f498baf67af4bd81225638e9ddd52d504","target":"graph","created_at":"2026-05-17T23:52:45Z","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 paper we introduce the problem of counting embedded spheres in R^3 whose projection to the z-axis yields a level set barcode of a particular type. Two embedded spheres are considered height equivalent if they are related by a z-level set preserving isotopy. A formula previously used to count functions on the interval with the same sub-level set persistence barcode provides a lower bound on height equivalence classes with the same level set persistence. A conjectured upper bound is provided as well.","authors_text":"Justin Curry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-29T18:55:45Z","title":"When Left and Right Turns Inside Out: A Geometric and Categorical Introduction to an Inverse Problem in Persistence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12392","kind":"arxiv","version":3},"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":"sha256:77c97750ec78984e1f1f3282ae0671223116edc3b3da5d57f6a2f8646bfbd0eb","target":"record","created_at":"2026-05-17T23:52:45Z","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":"7b271a69fccc43bda12dc4743481e54110d8f8e9304e794b65889c8bbbda9ba6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-11-29T18:55:45Z","title_canon_sha256":"a84feabb25e1cf509f36626a097ef3fb4252a3a7caed8500ea8e12fa0f6a8aa2"},"schema_version":"1.0","source":{"id":"1811.12392","kind":"arxiv","version":3}},"canonical_sha256":"f36da17342a0b3f71b7c1b9632b62e9d9d1432df4b47325d136e3a7554b3d5af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f36da17342a0b3f71b7c1b9632b62e9d9d1432df4b47325d136e3a7554b3d5af","first_computed_at":"2026-05-17T23:52:45.357782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:45.357782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4sGwVsqG4TPdv591awSpbRNtOqgLCLkFi3qKTW2NhrqI0oMebx9gLBZHYSDPbnhzqurEihmwN7JLRlE7ZDytCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:45.358399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12392","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77c97750ec78984e1f1f3282ae0671223116edc3b3da5d57f6a2f8646bfbd0eb","sha256:d57fce0d5b8c26b6bc4b24e01611ed4f498baf67af4bd81225638e9ddd52d504"],"state_sha256":"985c07ff0bf02e2ac4834a705000181b42e1d08adb472f75e49aa79853a90660"}