{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3GGKYPBKSTLNC7YXDUTWUI6A5E","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":"e13aa4381d23a464d17374db8cb07d3620f55b696d81e85de28f5885566042f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-21T05:23:41Z","title_canon_sha256":"ef7f0a03d25baad82070082dd5868e398fd772a1f0e7bea4d4f693f88a2f7dcd"},"schema_version":"1.0","source":{"id":"1408.4885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4885","created_at":"2026-05-18T02:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4885v1","created_at":"2026-05-18T02:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4885","created_at":"2026-05-18T02:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"3GGKYPBKSTLN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3GGKYPBKSTLNC7YX","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3GGKYPBK","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:89f8684c0a9ec336a5a390ad2cd29b07917f92c06ecf43d527e102fb9651dc59","target":"graph","created_at":"2026-05-18T02:44:41Z","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":"Let $M(\\alpha)$ denote the Mahler measure of the algebraic number $\\alpha$. In a recent paper, Dubickas and Smyth constructed a metric version of the Mahler measure on the multiplicative group of algebraic numbers. Later, Fili and the author used similar techniques to study a non-Archimedean version. We show how to generalize the above constructions in order to associate, to each point in $(0,\\infty]$, a metric version $M_x$ of the Mahler measure, each having a triangle inequality of a different strength. We are able to compute $M_x(\\alpha)$ for sufficiently small $x$, identifying, in the proc","authors_text":"Charles L. Samuels","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-21T05:23:41Z","title":"A collection of metric Mahler measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4885","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":"sha256:11763110b0b42256bc647dfc19167836f160b88de1d34e05f15e85d72a379583","target":"record","created_at":"2026-05-18T02:44:41Z","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":"e13aa4381d23a464d17374db8cb07d3620f55b696d81e85de28f5885566042f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-21T05:23:41Z","title_canon_sha256":"ef7f0a03d25baad82070082dd5868e398fd772a1f0e7bea4d4f693f88a2f7dcd"},"schema_version":"1.0","source":{"id":"1408.4885","kind":"arxiv","version":1}},"canonical_sha256":"d98cac3c2a94d6d17f171d276a23c0e9027ad73b7cd1be2ec01af1f66d6c76f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d98cac3c2a94d6d17f171d276a23c0e9027ad73b7cd1be2ec01af1f66d6c76f5","first_computed_at":"2026-05-18T02:44:41.428147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:41.428147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"maHq8wseVVp6j6+bVo23f6q5XXTTJ6rscdQ4CRlGrcepou6TvLgGCYTiF+2dAs2ljSE6A5JxB6kTpCkK2zLTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:41.428813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11763110b0b42256bc647dfc19167836f160b88de1d34e05f15e85d72a379583","sha256:89f8684c0a9ec336a5a390ad2cd29b07917f92c06ecf43d527e102fb9651dc59"],"state_sha256":"ade6a2cc8661e224e3b12ea52381c81518e15d11c7d9f0a2fd355af99d806b5a"}