{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WRFTKBWIDO2NYTX3KMMABZOVKG","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":"161ce6aa11a01ed188836283205add0c6792f96f4616bb53a5e18dbb1d3a1b0e","cross_cats_sorted":["cs.CC","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-03T12:46:53Z","title_canon_sha256":"16d57687459308579266bfbd5129ff9c7f37b870ed84f8175a542d7cf5552da7"},"schema_version":"1.0","source":{"id":"2607.03278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03278","created_at":"2026-07-07T02:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03278v1","created_at":"2026-07-07T02:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03278","created_at":"2026-07-07T02:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"WRFTKBWIDO2N","created_at":"2026-07-07T02:17:34Z"},{"alias_kind":"pith_short_16","alias_value":"WRFTKBWIDO2NYTX3","created_at":"2026-07-07T02:17:34Z"},{"alias_kind":"pith_short_8","alias_value":"WRFTKBWI","created_at":"2026-07-07T02:17:34Z"}],"graph_snapshots":[{"event_id":"sha256:d3a94e37e197fe69de113f541489aaa1e6948b57f4cc2c94637fae8222031e50","target":"graph","created_at":"2026-07-07T02:17:34Z","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/2607.03278/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Topological data analysis (TDA) is a machine learning technique that uses topology to extract patterns from data and has shown the potential to exhibit quantum advantage. A key concept in TDA is persistent homology, which measures the robustness of topological information at different lengthscales. In this paper, we introduce and study the problem of normalized persistence, a practically motivated and easily interpretable version of persistent homology that counts the fraction of holes that persist at different lengthscales. We prove that a variant of normalized persistence is $\\mathsf{DQC}_1$","authors_text":"Dominic Lowe, M.S. Kim, Roberto Bondesan, Ryu Hayakawa","cross_cats":["cs.CC","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-03T12:46:53Z","title":"Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03278","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":"sha256:5a1f4422ecaed8f98353fabdbe1fb064a81058bcea718b4ac0bd82a4efd3962c","target":"record","created_at":"2026-07-07T02:17:34Z","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":"161ce6aa11a01ed188836283205add0c6792f96f4616bb53a5e18dbb1d3a1b0e","cross_cats_sorted":["cs.CC","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-03T12:46:53Z","title_canon_sha256":"16d57687459308579266bfbd5129ff9c7f37b870ed84f8175a542d7cf5552da7"},"schema_version":"1.0","source":{"id":"2607.03278","kind":"arxiv","version":1}},"canonical_sha256":"b44b3506c81bb4dc4efb531800e5d5518894058c2bf84a6db74a3f6c15681c56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b44b3506c81bb4dc4efb531800e5d5518894058c2bf84a6db74a3f6c15681c56","first_computed_at":"2026-07-07T02:17:34.705440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:34.705440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvPmV5EFu7fQg0bHnc2/EhLBM3mUbQEMrbieb+jSwU1qa+lkA9Q8IXckHMnLp+N39D0k3rbcquiOy0zEltuPDQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:34.706660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a1f4422ecaed8f98353fabdbe1fb064a81058bcea718b4ac0bd82a4efd3962c","sha256:d3a94e37e197fe69de113f541489aaa1e6948b57f4cc2c94637fae8222031e50"],"state_sha256":"5cfaf55373b0fab2979a9e5d296f766a9c960833c964c222b4af9d0af232aa03"}