{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CWONWWXGYTMS23AIKF4Q2D4G3C","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":"af0a4951102cd31fc308eb5fee2d9cbac339e3886b1f07aa8fe4c39451e9d37c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-02T11:38:11Z","title_canon_sha256":"00775376f5f006715b0deb94ee3718ab430e1f34bd13e24fb0ff334f849b32d2"},"schema_version":"1.0","source":{"id":"2607.02060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02060","created_at":"2026-07-03T01:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02060v1","created_at":"2026-07-03T01:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02060","created_at":"2026-07-03T01:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"CWONWWXGYTMS","created_at":"2026-07-03T01:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"CWONWWXGYTMS23AI","created_at":"2026-07-03T01:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"CWONWWXG","created_at":"2026-07-03T01:17:38Z"}],"graph_snapshots":[{"event_id":"sha256:f78aaa027fd1295df018306b1a001795db2421b286a53493606e73290c273d4d","target":"graph","created_at":"2026-07-03T01:17:38Z","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/2607.02060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a $C_2$-commutative ring spectrum $R$, a twisted $R$-algebra is an $R$-module with a multiplication whose order is switched by the $C_2$-action. In this paper, we construct various quotients of $R$ as twisted $R$-algebras, when $R$ is an even real commutative ring spectrum. These are constructed as Thom spectra of maps out of suitable $C_2$-actions on $S^1$ and $U(n)$. One such example is given by $K\\mathbb{R}$ which is endowed with a twisted $K\\mathbb{R}$-algebra structure. Other examples include quotients such as $M\\mathbb{R}/(2,x_1,\\dots, x_{n-1})$ over the real bordism spectrum $M\\math","authors_text":"Abhinandan Das, Samik Basu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-02T11:38:11Z","title":"Equivariant twisted $R$-algebras via Thom spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02060","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:e8ada45c00a3b5b2b3451deeb19b23ccefd5d7c3bbb044e9d9ff95dca04139c8","target":"record","created_at":"2026-07-03T01:17:38Z","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":"af0a4951102cd31fc308eb5fee2d9cbac339e3886b1f07aa8fe4c39451e9d37c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-02T11:38:11Z","title_canon_sha256":"00775376f5f006715b0deb94ee3718ab430e1f34bd13e24fb0ff334f849b32d2"},"schema_version":"1.0","source":{"id":"2607.02060","kind":"arxiv","version":1}},"canonical_sha256":"159cdb5ae6c4d92d6c0851790d0f86d8a478bb400960b21ed7cedad1b1fd4986","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"159cdb5ae6c4d92d6c0851790d0f86d8a478bb400960b21ed7cedad1b1fd4986","first_computed_at":"2026-07-03T01:17:38.360226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:38.360226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2PKZRUTmRq3D7TTjgkn3ycjvB9nkQ259nNhMnNz/rDSRaIqQfEHdf2dhETI7qtUZrPTaN/DfjfSeq1v/tv/cDQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:38.360646Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8ada45c00a3b5b2b3451deeb19b23ccefd5d7c3bbb044e9d9ff95dca04139c8","sha256:f78aaa027fd1295df018306b1a001795db2421b286a53493606e73290c273d4d"],"state_sha256":"16747fabc891c1fb2964b19bbbd88335bfe67c8f1d0adff0f2f2f5092ec64346"}