{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PDRKXS5BC7KTTNUBLWHI7A2V4X","short_pith_number":"pith:PDRKXS5B","schema_version":"1.0","canonical_sha256":"78e2abcba117d539b6815d8e8f8355e5c0067c616fb9ea6d9ebc0b696e9c7eb3","source":{"kind":"arxiv","id":"1212.2855","version":2},"attestation_state":"computed","paper":{"title":"Graev ultrametrics and free products of Polish groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Konstantin Slutsky","submitted_at":"2012-12-12T16:02:52Z","abstract_excerpt":"We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups G and H can be embedded into a Polish group T in such a way that the subgroup of T generated by G and H is isomorphic to the free product G*H."},"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":"1212.2855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-12T16:02:52Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"7c9e5d96a5fbd715ac95b6489d5276513d3b7ad0e63f0849a97030d29a0434ef","abstract_canon_sha256":"7f824394f62390e7646b26daa3114a10ed562c7d2c184eadd4383a61367da548"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:47.962307Z","signature_b64":"GpD5mdOIYCA0QXcKuxMlGIgyVV87UwD2GQ/WGGDWTGFNpZR1wQHl2fRulnD7ZA3VFTc9x3aBvnICXVQV3n9TCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78e2abcba117d539b6815d8e8f8355e5c0067c616fb9ea6d9ebc0b696e9c7eb3","last_reissued_at":"2026-05-18T03:10:47.961604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:47.961604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graev ultrametrics and free products of Polish groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Konstantin Slutsky","submitted_at":"2012-12-12T16:02:52Z","abstract_excerpt":"We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups G and H can be embedded into a Polish group T in such a way that the subgroup of T generated by G and H is isomorphic to the free product G*H."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2855","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1212.2855","created_at":"2026-05-18T03:10:47.961720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2855v2","created_at":"2026-05-18T03:10:47.961720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2855","created_at":"2026-05-18T03:10:47.961720+00:00"},{"alias_kind":"pith_short_12","alias_value":"PDRKXS5BC7KT","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PDRKXS5BC7KTTNUB","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PDRKXS5B","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X","json":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X.json","graph_json":"https://pith.science/api/pith-number/PDRKXS5BC7KTTNUBLWHI7A2V4X/graph.json","events_json":"https://pith.science/api/pith-number/PDRKXS5BC7KTTNUBLWHI7A2V4X/events.json","paper":"https://pith.science/paper/PDRKXS5B"},"agent_actions":{"view_html":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X","download_json":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X.json","view_paper":"https://pith.science/paper/PDRKXS5B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2855&json=true","fetch_graph":"https://pith.science/api/pith-number/PDRKXS5BC7KTTNUBLWHI7A2V4X/graph.json","fetch_events":"https://pith.science/api/pith-number/PDRKXS5BC7KTTNUBLWHI7A2V4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X/action/storage_attestation","attest_author":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X/action/author_attestation","sign_citation":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X/action/citation_signature","submit_replication":"https://pith.science/pith/PDRKXS5BC7KTTNUBLWHI7A2V4X/action/replication_record"}},"created_at":"2026-05-18T03:10:47.961720+00:00","updated_at":"2026-05-18T03:10:47.961720+00:00"}