{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JLUUGB7O7XRWRTD6JF3VPWALRB","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":"658807e3e090b3d1b8db4ceb014a9f86534ff43016c626eb47c6762c6e64ac78","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-14T22:59:09Z","title_canon_sha256":"5567bc81ae12fc483e157a9509276294441506b1dcd6cf571232d3e553654db5"},"schema_version":"1.0","source":{"id":"1805.05490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05490","created_at":"2026-05-17T23:44:04Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05490v2","created_at":"2026-05-17T23:44:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05490","created_at":"2026-05-17T23:44:04Z"},{"alias_kind":"pith_short_12","alias_value":"JLUUGB7O7XRW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JLUUGB7O7XRWRTD6","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JLUUGB7O","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:ee98a94740550586284ac41f7ea6f7eb085855c61648a8c776f194668ca7497f","target":"graph","created_at":"2026-05-17T23:44:04Z","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":"The Vol-Det Conjecture relates the volume and the determinant of a hyperbolic alternating link in $S^3$. We use exact computations of Mahler measures of two-variable polynomials to prove the Vol-Det Conjecture for many infinite families of alternating links. We conjecture a new lower bound for the Mahler measure of certain two-variable polynomials in terms of volumes of hyperbolic regular ideal bipyramids. Associating each polynomial to a toroidal link using the toroidal dimer model, we show that every polynomial which satisfies this conjecture with a strict inequality gives rise to many infin","authors_text":"Abhijit Champanerkar, Ilya Kofman, Matilde Lal\\'in","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-14T22:59:09Z","title":"Mahler Measure and the Vol-Det Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05490","kind":"arxiv","version":2},"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":"sha256:7d8cee88e38a4b1719625bd6e7e0bc35353fe4bd90d66a6b31b122945362a406","target":"record","created_at":"2026-05-17T23:44:04Z","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":"658807e3e090b3d1b8db4ceb014a9f86534ff43016c626eb47c6762c6e64ac78","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-14T22:59:09Z","title_canon_sha256":"5567bc81ae12fc483e157a9509276294441506b1dcd6cf571232d3e553654db5"},"schema_version":"1.0","source":{"id":"1805.05490","kind":"arxiv","version":2}},"canonical_sha256":"4ae94307eefde368cc7e497757d80b8846f5b5c514127914aed5cfa7567ca483","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ae94307eefde368cc7e497757d80b8846f5b5c514127914aed5cfa7567ca483","first_computed_at":"2026-05-17T23:44:04.691633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:04.691633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0vRj2rVqv9IisurZL/3MqkHKLU/MGXRMW+2Q7zL00WbEbtsc9DjIAyQ8LJo8nN4OpeH1LhJ7PKhDT+Ev+7AqCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:04.692123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d8cee88e38a4b1719625bd6e7e0bc35353fe4bd90d66a6b31b122945362a406","sha256:ee98a94740550586284ac41f7ea6f7eb085855c61648a8c776f194668ca7497f"],"state_sha256":"769dfc8390630f75042aa1116799697a2890655a09fe0b2ce3ea18a919a0acd2"}