{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ALTNLM5ISSFYO7MR4BKZX6API4","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":"12f2ef9e108e5cab46ff0d4e839d0adaa6f89342aec9f3aa71c97ae37f0df2bb","cross_cats_sorted":["cond-mat.mes-hall","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-04T16:00:05Z","title_canon_sha256":"4480ae12d41074b728e38b94b25fae3477d90f6bc6ccda1cf6677ff1ff0f2913"},"schema_version":"1.0","source":{"id":"2009.02268","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.02268","created_at":"2026-07-05T01:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"2009.02268v2","created_at":"2026-07-05T01:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.02268","created_at":"2026-07-05T01:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"ALTNLM5ISSFY","created_at":"2026-07-05T01:47:32Z"},{"alias_kind":"pith_short_16","alias_value":"ALTNLM5ISSFYO7MR","created_at":"2026-07-05T01:47:32Z"},{"alias_kind":"pith_short_8","alias_value":"ALTNLM5I","created_at":"2026-07-05T01:47:32Z"}],"graph_snapshots":[{"event_id":"sha256:70897982298c5e0b075f042b8af4de18f8bedf2658b82c4e8561aa2cdba77eea","target":"graph","created_at":"2026-07-05T01:47:32Z","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/2009.02268/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide an extensive look at Bott periodicity in the context of complex gapped topological phases of free fermions. In doing so, we remark on the existence of a product structure in the set of inequivalent phases induced by the external tensor product of vector bundles -- a structure which has not yet been explored in condensed-matter literature. Bott periodicity appears in the form of a generalized Dirac monopole built out of a given phase, which is equivalent to the product of a Dirac monopole phase with that same given phase. The complex K-theory cohomology ring is presented as a natural","authors_text":"Bruno Mera","cross_cats":["cond-mat.mes-hall","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-04T16:00:05Z","title":"The product of two independent Su-Schrieffer-Heeger chains yields a two-dimensional Chern insulator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02268","kind":"arxiv","version":2},"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:f80d5f3f1d8dd59122c754955fc2e31e9b9320bd9b61a32ebd5edc375c172036","target":"record","created_at":"2026-07-05T01:47:32Z","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":"12f2ef9e108e5cab46ff0d4e839d0adaa6f89342aec9f3aa71c97ae37f0df2bb","cross_cats_sorted":["cond-mat.mes-hall","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-04T16:00:05Z","title_canon_sha256":"4480ae12d41074b728e38b94b25fae3477d90f6bc6ccda1cf6677ff1ff0f2913"},"schema_version":"1.0","source":{"id":"2009.02268","kind":"arxiv","version":2}},"canonical_sha256":"02e6d5b3a8948b877d91e0559bf80f471c2962de6f742b511695b537dbe6b2a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02e6d5b3a8948b877d91e0559bf80f471c2962de6f742b511695b537dbe6b2a0","first_computed_at":"2026-07-05T01:47:32.689712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:47:32.689712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PorcyRkrUzObgfCo3kOIeZaieAiqd+AyZFvP2OOHE/lWIJ/PboEMoxrObJsMjPISKYf+jlISR/F91GjLFd49Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:47:32.690195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.02268","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f80d5f3f1d8dd59122c754955fc2e31e9b9320bd9b61a32ebd5edc375c172036","sha256:70897982298c5e0b075f042b8af4de18f8bedf2658b82c4e8561aa2cdba77eea"],"state_sha256":"8238a6388f0bc6ba77aaaf48be3c68e545ebfb073d6306e353d3cb7d85dcad92"}