{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:F7BDVCPSXXP7JYQOO3TNWDPKUA","short_pith_number":"pith:F7BDVCPS","schema_version":"1.0","canonical_sha256":"2fc23a89f2bddff4e20e76e6db0deaa035b7076555f65748a0a4536270d6a723","source":{"kind":"arxiv","id":"2507.05425","version":1},"attestation_state":"computed","paper":{"title":"A Low-Dimensional Counterexample to the HK-Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.KT"],"primary_cat":"math.OA","authors_text":"Rachel Chaiser","submitted_at":"2025-07-07T19:13:32Z","abstract_excerpt":"We provide a counterexample to the HK-conjecture using the flat manifold odometers constructed by Deeley. Deeley's counterexample uses an odometer built from a flat manifold of dimension 9 and an expansive self-cover. We strengthen this result by showing that for each dimension $d\\geq 4$ there is a counterexample to the HK-conjecture built from a flat manifold of dimension $d$. Moreover, we show that this dimension is minimal, as if $d\\leq 3$ the HK-conjecture holds for the associated odometer. We also discuss implications for the stable and unstable groupoid of a Smale space."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.05425","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2025-07-07T19:13:32Z","cross_cats_sorted":["math.GT","math.KT"],"title_canon_sha256":"5ac7ac802a74573589c824715e962e8ed1f5cf0a565404ced9ad06b1a993ef01","abstract_canon_sha256":"a3bfe23a99ad8c67689699c2709b1d8f5d12f9075346d784f0c4e0247c851b2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:30.156626Z","signature_b64":"JCO7+qaqkhEppM0J/4SjPej4JD4hVJxt08CiQd0CP+hCepM6umeY7fXAnjv1dciG+/oYMlyT8BdLXu3EUSvjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fc23a89f2bddff4e20e76e6db0deaa035b7076555f65748a0a4536270d6a723","last_reissued_at":"2026-07-05T11:33:30.156197Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:30.156197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Low-Dimensional Counterexample to the HK-Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.KT"],"primary_cat":"math.OA","authors_text":"Rachel Chaiser","submitted_at":"2025-07-07T19:13:32Z","abstract_excerpt":"We provide a counterexample to the HK-conjecture using the flat manifold odometers constructed by Deeley. Deeley's counterexample uses an odometer built from a flat manifold of dimension 9 and an expansive self-cover. We strengthen this result by showing that for each dimension $d\\geq 4$ there is a counterexample to the HK-conjecture built from a flat manifold of dimension $d$. Moreover, we show that this dimension is minimal, as if $d\\leq 3$ the HK-conjecture holds for the associated odometer. We also discuss implications for the stable and unstable groupoid of a Smale space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05425","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05425/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.05425","created_at":"2026-07-05T11:33:30.156254+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.05425v1","created_at":"2026-07-05T11:33:30.156254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05425","created_at":"2026-07-05T11:33:30.156254+00:00"},{"alias_kind":"pith_short_12","alias_value":"F7BDVCPSXXP7","created_at":"2026-07-05T11:33:30.156254+00:00"},{"alias_kind":"pith_short_16","alias_value":"F7BDVCPSXXP7JYQO","created_at":"2026-07-05T11:33:30.156254+00:00"},{"alias_kind":"pith_short_8","alias_value":"F7BDVCPS","created_at":"2026-07-05T11:33:30.156254+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.03759","citing_title":"A trace pairing and Elliott invariant for groupoid homology","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA","json":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA.json","graph_json":"https://pith.science/api/pith-number/F7BDVCPSXXP7JYQOO3TNWDPKUA/graph.json","events_json":"https://pith.science/api/pith-number/F7BDVCPSXXP7JYQOO3TNWDPKUA/events.json","paper":"https://pith.science/paper/F7BDVCPS"},"agent_actions":{"view_html":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA","download_json":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA.json","view_paper":"https://pith.science/paper/F7BDVCPS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.05425&json=true","fetch_graph":"https://pith.science/api/pith-number/F7BDVCPSXXP7JYQOO3TNWDPKUA/graph.json","fetch_events":"https://pith.science/api/pith-number/F7BDVCPSXXP7JYQOO3TNWDPKUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA/action/storage_attestation","attest_author":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA/action/author_attestation","sign_citation":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA/action/citation_signature","submit_replication":"https://pith.science/pith/F7BDVCPSXXP7JYQOO3TNWDPKUA/action/replication_record"}},"created_at":"2026-07-05T11:33:30.156254+00:00","updated_at":"2026-07-05T11:33:30.156254+00:00"}