{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:Q244CU7PA37U26Z3ONHMEIU3SA","short_pith_number":"pith:Q244CU7P","canonical_record":{"source":{"id":"2412.20905","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-30T12:33:28Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"4f2979b79207b88594665177440eeca145e7c08c7ac28f6ebab45dc2b4a7e8bd","abstract_canon_sha256":"214133f0cf740c6c2fa8d594f2d702132f210393afc4b70759c2f811207b11a6"},"schema_version":"1.0"},"canonical_sha256":"86b9c153ef06ff4d7b3b734ec2229b903bf9e3c50c50410e0e77f740114c6b22","source":{"kind":"arxiv","id":"2412.20905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20905","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20905v1","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20905","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"Q244CU7PA37U","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q244CU7PA37U26Z3","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q244CU7P","created_at":"2026-07-05T09:55:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:Q244CU7PA37U26Z3ONHMEIU3SA","target":"record","payload":{"canonical_record":{"source":{"id":"2412.20905","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-30T12:33:28Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"4f2979b79207b88594665177440eeca145e7c08c7ac28f6ebab45dc2b4a7e8bd","abstract_canon_sha256":"214133f0cf740c6c2fa8d594f2d702132f210393afc4b70759c2f811207b11a6"},"schema_version":"1.0"},"canonical_sha256":"86b9c153ef06ff4d7b3b734ec2229b903bf9e3c50c50410e0e77f740114c6b22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:24.448039Z","signature_b64":"aTjGY9z9mgsGicL8mN+8onSyyGExmsEebYo4YaEgOxYtmbfGt1fID8IPg1gbaNx80e/2cQlLzqiqGYyJp/4IBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86b9c153ef06ff4d7b3b734ec2229b903bf9e3c50c50410e0e77f740114c6b22","last_reissued_at":"2026-07-05T09:55:24.447409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:24.447409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.20905","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ymR/KoeL4lWiEsvjQrrIaR9sigCTj0jZjiuJKAvHP6NUKMH6fYeFXr6B8pF2QRNEEeQZkXh3hdzJEf6jurcXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:22:18.991946Z"},"content_sha256":"6752dd13e2c9ec666f7d939dc729e2534543b45a69ae1b08ed1a5dd385c7c551","schema_version":"1.0","event_id":"sha256:6752dd13e2c9ec666f7d939dc729e2534543b45a69ae1b08ed1a5dd385c7c551"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:Q244CU7PA37U26Z3ONHMEIU3SA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parametrized topological phases in 1d and T-duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Roman Geiko","submitted_at":"2024-12-30T12:33:28Z","abstract_excerpt":"There are families of physical systems that cannot be adiabatically evolved to the trivial system uniformly across the parameter space, even if each system in the family belongs to the trivial phase. The obstruction is measured by higher Berry class. We analyze families of topological systems in 1+1d using families of invertible TQFTs and families of RG fixed states of spin chains. We use the generalized matrix-product states to describe RG fixed points of all translation invariant pure splits states on spin chains. Families of such fixed points correspond to bundles of Hilbert-Schmidt operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20905","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20905/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fK7qREcS+NkVVf0ebYv/1HgiOuxg0JypaUqayxYZpEn3fVI+iV55PjMwET8PEZRickZxLcCCXFPbtgsSaAo2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:22:18.992472Z"},"content_sha256":"3f7d5aec5bc9e2e8bda7d0a76d3614e5615230c57312201053a63f577488935e","schema_version":"1.0","event_id":"sha256:3f7d5aec5bc9e2e8bda7d0a76d3614e5615230c57312201053a63f577488935e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q244CU7PA37U26Z3ONHMEIU3SA/bundle.json","state_url":"https://pith.science/pith/Q244CU7PA37U26Z3ONHMEIU3SA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q244CU7PA37U26Z3ONHMEIU3SA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T10:22:18Z","links":{"resolver":"https://pith.science/pith/Q244CU7PA37U26Z3ONHMEIU3SA","bundle":"https://pith.science/pith/Q244CU7PA37U26Z3ONHMEIU3SA/bundle.json","state":"https://pith.science/pith/Q244CU7PA37U26Z3ONHMEIU3SA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q244CU7PA37U26Z3ONHMEIU3SA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:Q244CU7PA37U26Z3ONHMEIU3SA","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":"214133f0cf740c6c2fa8d594f2d702132f210393afc4b70759c2f811207b11a6","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-30T12:33:28Z","title_canon_sha256":"4f2979b79207b88594665177440eeca145e7c08c7ac28f6ebab45dc2b4a7e8bd"},"schema_version":"1.0","source":{"id":"2412.20905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20905","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20905v1","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20905","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"Q244CU7PA37U","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q244CU7PA37U26Z3","created_at":"2026-07-05T09:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q244CU7P","created_at":"2026-07-05T09:55:24Z"}],"graph_snapshots":[{"event_id":"sha256:3f7d5aec5bc9e2e8bda7d0a76d3614e5615230c57312201053a63f577488935e","target":"graph","created_at":"2026-07-05T09:55:24Z","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/2412.20905/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There are families of physical systems that cannot be adiabatically evolved to the trivial system uniformly across the parameter space, even if each system in the family belongs to the trivial phase. The obstruction is measured by higher Berry class. We analyze families of topological systems in 1+1d using families of invertible TQFTs and families of RG fixed states of spin chains. We use the generalized matrix-product states to describe RG fixed points of all translation invariant pure splits states on spin chains. Families of such fixed points correspond to bundles of Hilbert-Schmidt operato","authors_text":"Roman Geiko","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-30T12:33:28Z","title":"Parametrized topological phases in 1d and T-duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20905","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":"sha256:6752dd13e2c9ec666f7d939dc729e2534543b45a69ae1b08ed1a5dd385c7c551","target":"record","created_at":"2026-07-05T09:55:24Z","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":"214133f0cf740c6c2fa8d594f2d702132f210393afc4b70759c2f811207b11a6","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-30T12:33:28Z","title_canon_sha256":"4f2979b79207b88594665177440eeca145e7c08c7ac28f6ebab45dc2b4a7e8bd"},"schema_version":"1.0","source":{"id":"2412.20905","kind":"arxiv","version":1}},"canonical_sha256":"86b9c153ef06ff4d7b3b734ec2229b903bf9e3c50c50410e0e77f740114c6b22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86b9c153ef06ff4d7b3b734ec2229b903bf9e3c50c50410e0e77f740114c6b22","first_computed_at":"2026-07-05T09:55:24.447409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:55:24.447409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aTjGY9z9mgsGicL8mN+8onSyyGExmsEebYo4YaEgOxYtmbfGt1fID8IPg1gbaNx80e/2cQlLzqiqGYyJp/4IBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:55:24.448039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.20905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6752dd13e2c9ec666f7d939dc729e2534543b45a69ae1b08ed1a5dd385c7c551","sha256:3f7d5aec5bc9e2e8bda7d0a76d3614e5615230c57312201053a63f577488935e"],"state_sha256":"1594571f4c7c0f881abc4546967f14607c1a57bd6dbe1a485150b85bad70f037"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vK6OLhilL3ZLKeeXx1i7SAHDufBSVUSMf/Jrcx/zmtCGmexiGuoBalM8rwveIjqYJxbYdyKezrcdG0CoWIU2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T10:22:18.997065Z","bundle_sha256":"205b7b2cbdfe1da2b0c7d89c433e5dec59e962422d3d04149b0c4f6e7811f5f8"}}