{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AUFSEMSFHXMDXG66TR4NPZUSZY","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":"4549433ceecf4dd122f96144e5bf6f0e3a7b52d66237ab7a5c44daffe91e3f36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-09T22:25:47Z","title_canon_sha256":"f5b0db1880a6e8a2cae646c7d98149a0b1b2e5ea7f8cfd03964f83be5f2a3bd3"},"schema_version":"1.0","source":{"id":"1704.02666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02666","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02666v1","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02666","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"AUFSEMSFHXMD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AUFSEMSFHXMDXG66","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AUFSEMSF","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:080187d3c8d02bed2d0709cec93df6d8f06c7a3bcc60ead7a3f58021824e4ed6","target":"graph","created_at":"2026-05-18T00:20:56Z","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":"It is a classical theorem that the free product of ordered groups is orderable. In this note we show that, using a method of G. Bergman, an ordering of the free product can be constructed in a functorial manner, in the category of ordered groups and order-preserving homomorphisms. With this functor interpreted as a tensor product this category becomes a tensor (or monoidal) category. Moreover, if $O(G)$ denotes the space of orderings of the group $G$ with the natural topology, then for fixed groups $F$ and $G$ our construction can be considered a function $O(F) \\times O(G) \\to O(F * G)$. We sh","authors_text":"Dale Rolfsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-09T22:25:47Z","title":"Ordered groups as a tensor category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02666","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":"sha256:96ddc91463f448ff732642f0877a595648fd71dd1ea9a203847d56d1134564da","target":"record","created_at":"2026-05-18T00:20:56Z","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":"4549433ceecf4dd122f96144e5bf6f0e3a7b52d66237ab7a5c44daffe91e3f36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-09T22:25:47Z","title_canon_sha256":"f5b0db1880a6e8a2cae646c7d98149a0b1b2e5ea7f8cfd03964f83be5f2a3bd3"},"schema_version":"1.0","source":{"id":"1704.02666","kind":"arxiv","version":1}},"canonical_sha256":"050b2232453dd83b9bde9c78d7e692ce36eedfff11f3804b77ae44513b529fec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"050b2232453dd83b9bde9c78d7e692ce36eedfff11f3804b77ae44513b529fec","first_computed_at":"2026-05-18T00:20:56.539125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:56.539125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0MCqKKljH5UeoPFlbSimT7DRl37Sst49SSz/JcKRTrdGTcAZCI0GzcfBQP69GdLC6NEthWA1w7uCzTddXD5FBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:56.539620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96ddc91463f448ff732642f0877a595648fd71dd1ea9a203847d56d1134564da","sha256:080187d3c8d02bed2d0709cec93df6d8f06c7a3bcc60ead7a3f58021824e4ed6"],"state_sha256":"ecce9154b252a5a5c0dc3f1b22086c4392cd496d379ea93c11007a319641dcca"}