{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VUUUVV5LDRKSBMVEXQMZDKKVAT","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":"261431f34ebfe480ba758187c63de7a73ce58c1718eab5e8b2e1381110511233","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-08-08T21:57:40Z","title_canon_sha256":"a5c05eff1f884c6771e4d06990cc6cdf8658ba42a6b37535990747db74178a74"},"schema_version":"1.0","source":{"id":"2308.04601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04601","created_at":"2026-07-05T07:20:53Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04601v2","created_at":"2026-07-05T07:20:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04601","created_at":"2026-07-05T07:20:53Z"},{"alias_kind":"pith_short_12","alias_value":"VUUUVV5LDRKS","created_at":"2026-07-05T07:20:53Z"},{"alias_kind":"pith_short_16","alias_value":"VUUUVV5LDRKSBMVE","created_at":"2026-07-05T07:20:53Z"},{"alias_kind":"pith_short_8","alias_value":"VUUUVV5L","created_at":"2026-07-05T07:20:53Z"}],"graph_snapshots":[{"event_id":"sha256:61388599d3b60564f52e566ecb96d41ee0c651099c78c994e3aa73a7060190cd","target":"graph","created_at":"2026-07-05T07:20:53Z","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/2308.04601/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following the work of Lal\\'in and Mittal on the Mahler measure over arbitrary tori, we investigate the definition of the generalized Mahler measure for all Laurent polynomials in two variables when they do not vanish on the integration torus. We establish certain relations between the standard Mahler measure and the generalized Mahler measure of such polynomials. Later we focus our investigation on a tempered family of polynomials originally studied by Boyd, namely $Q_{r}(x, y) = x + \\frac{1}{x} + y + \\frac{1}{y} + r$ with $r \\in \\mathbb{C},$ and apply our results to this family. For the $r = ","authors_text":"Subham Roy","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-08-08T21:57:40Z","title":"Generalized Mahler measures of Laurent polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04601","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":"sha256:341ba33199c4b33550fa89ffeeb614c246aee0bb5ac7c7fce9f62c9016f1e0ab","target":"record","created_at":"2026-07-05T07:20:53Z","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":"261431f34ebfe480ba758187c63de7a73ce58c1718eab5e8b2e1381110511233","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-08-08T21:57:40Z","title_canon_sha256":"a5c05eff1f884c6771e4d06990cc6cdf8658ba42a6b37535990747db74178a74"},"schema_version":"1.0","source":{"id":"2308.04601","kind":"arxiv","version":2}},"canonical_sha256":"ad294ad7ab1c5520b2a4bc1991a95504f06dc199fc37ff90f9b7b48550f0618d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad294ad7ab1c5520b2a4bc1991a95504f06dc199fc37ff90f9b7b48550f0618d","first_computed_at":"2026-07-05T07:20:53.127553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:20:53.127553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DoDM4Rr78Iff7J1aEEEML1BKbbYtkBNWr7iqgbP2hrYSxWeIQYh/fIUnJ/NndTfcEGpZW85hWoC7JWzdFhxaCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:20:53.128012Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.04601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:341ba33199c4b33550fa89ffeeb614c246aee0bb5ac7c7fce9f62c9016f1e0ab","sha256:61388599d3b60564f52e566ecb96d41ee0c651099c78c994e3aa73a7060190cd"],"state_sha256":"ebfbcd1decff9eb46fdc818806363078f25f1d1290bddff4edad4407f9660619"}