{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4V4LZNJPQQTIQK4OJ7625JTXI6","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":"c324bc2904cab43bb116af4d7faf11112e2de95a3d2987c66f6080831e85d999","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-12-28T08:02:00Z","title_canon_sha256":"9459a3bf9ac34cbc1fdd166d64280649d7898fa910bde5ae7fb9a3ce6b50bd5e"},"schema_version":"1.0","source":{"id":"1012.5713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5713","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5713v1","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5713","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"4V4LZNJPQQTI","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4V4LZNJPQQTIQK4O","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4V4LZNJP","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ba18ce8fc6506cad0305f84aeee4b5fc69348ca2efcd944e0e6f3c984b175d51","target":"graph","created_at":"2026-05-18T04:32:22Z","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":"A topological group $(G,\\mu)$ from a class $\\mathcal G$ of MAP topological abelian groups will be called a {\\it Mackey group} in $\\mathcal G$ if it has the following property: if $\\nu$ is a group topology in $G$ such that $(G,\\nu)\\in \\mathcal G$ and $(G,\\nu)$ has the same continuous characters, say $(G,\\nu)^{\\wedge}=(G,\\mu)^{\\wedge}$, then $\\nu\\le \\mu$.\n  If $\\rm{LCS}$ is the class of Hausdorff topological abelian groups which admit a structure of a locally convex topological vector space over $\\mathbb R$, it is well-known that every metrizable $(G,\\mu) \\in \\rm{LCS}$ is a Mackey group in $\\rm{","authors_text":"Dikran Dikranjan, Elena Mart\\'in Peinador, Vaja Tarieladze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-12-28T08:02:00Z","title":"A class of metrizable locally quasi-convex groups which are not Mackey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5713","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":"sha256:2d2eac99b468d219cb3ba28b0d15e8d1075c50fecc87c137f8be43ecf499fad9","target":"record","created_at":"2026-05-18T04:32:22Z","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":"c324bc2904cab43bb116af4d7faf11112e2de95a3d2987c66f6080831e85d999","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-12-28T08:02:00Z","title_canon_sha256":"9459a3bf9ac34cbc1fdd166d64280649d7898fa910bde5ae7fb9a3ce6b50bd5e"},"schema_version":"1.0","source":{"id":"1012.5713","kind":"arxiv","version":1}},"canonical_sha256":"e578bcb52f8426882b8e4ffdaea67747a58b5bcc2da212f97fa26ac6c979ed9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e578bcb52f8426882b8e4ffdaea67747a58b5bcc2da212f97fa26ac6c979ed9d","first_computed_at":"2026-05-18T04:32:22.435650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.435650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0dgk4+4Nd/YHm5ZkTj90Wynh+M7AhNoXh+CvVemm4tTJiTd7d5SHf77uAyECRfVFstylslQsEPAD6O+7xCNHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.436343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d2eac99b468d219cb3ba28b0d15e8d1075c50fecc87c137f8be43ecf499fad9","sha256:ba18ce8fc6506cad0305f84aeee4b5fc69348ca2efcd944e0e6f3c984b175d51"],"state_sha256":"3090033ab0b8c5ce6b9aea6f85404dfd2c970adbb43c6259ff9be71c7c51b60b"}