{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4FPLPZEWG2MWKT4MIYYAB7LRME","short_pith_number":"pith:4FPLPZEW","canonical_record":{"source":{"id":"2002.01312","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-02-04T14:29:57Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"2c8c9b8d4023a9e148a86c31c21a813aea2e9c9e56f6f2b9b201df6cdebfaa2b","abstract_canon_sha256":"95950af6d89364b53e1648ece389cf7245f8579df948423936000761d9f28fb0"},"schema_version":"1.0"},"canonical_sha256":"e15eb7e4963699654f8c463000fd7161148bfd19a44d196a7a2c35417f48d2f4","source":{"kind":"arxiv","id":"2002.01312","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.01312","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"2002.01312v2","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.01312","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"4FPLPZEWG2MW","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"pith_short_16","alias_value":"4FPLPZEWG2MWKT4M","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"pith_short_8","alias_value":"4FPLPZEW","created_at":"2026-07-05T00:48:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4FPLPZEWG2MWKT4MIYYAB7LRME","target":"record","payload":{"canonical_record":{"source":{"id":"2002.01312","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-02-04T14:29:57Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"2c8c9b8d4023a9e148a86c31c21a813aea2e9c9e56f6f2b9b201df6cdebfaa2b","abstract_canon_sha256":"95950af6d89364b53e1648ece389cf7245f8579df948423936000761d9f28fb0"},"schema_version":"1.0"},"canonical_sha256":"e15eb7e4963699654f8c463000fd7161148bfd19a44d196a7a2c35417f48d2f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:23.768365Z","signature_b64":"/sXgiH6aNa3wJhH3QUicnLe/8xwFmgO9qOXl0ZhUJSAOVtFIR04wtVbzRZxsZh/3gO2FVfcGL5IUiWMG1zKDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e15eb7e4963699654f8c463000fd7161148bfd19a44d196a7a2c35417f48d2f4","last_reissued_at":"2026-07-05T00:48:23.767945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:23.767945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.01312","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NAlEkvfh7IqUSlWqiadNdbQk9CaQFNiWN35B031BuajSCLCm/LypkVBcVaumE4v7HWfubpfCxCMGlhzg1sPGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T22:28:09.450788Z"},"content_sha256":"4f0c1497470269ad00cbf93c1aa5b0d3e4ae9ec21439cb197515a0b07e36de4e","schema_version":"1.0","event_id":"sha256:4f0c1497470269ad00cbf93c1aa5b0d3e4ae9ec21439cb197515a0b07e36de4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4FPLPZEWG2MWKT4MIYYAB7LRME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization anisotropy and complex geometry in two-dimensional insulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Bruno Mera","submitted_at":"2020-02-04T14:29:57Z","abstract_excerpt":"The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic limit, it defines a flat Riemannian metric over the twist-angle space, topologically a torus, which endows this space with a complex structure, described by a complex parameter $\\tau$. It is shown that the latter is a physical observable related to the anisotropy of the system. The quantity $\\tau$ and the Riemannian volume of the twist-angle space provide an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.01312","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.01312/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":"2026-07-05T00:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KaNNilF761GBip12hp4nbtMSPo0A5GVyf+oQ+oocfc5Kk1o9+gVn/e6V+q6OxTtGAvnNH5cGQStGUHVksGWfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T22:28:09.451171Z"},"content_sha256":"6c228a8fa20369c9363969cffea227bf699b3d05c2d9a551db6a0decb4f7c672","schema_version":"1.0","event_id":"sha256:6c228a8fa20369c9363969cffea227bf699b3d05c2d9a551db6a0decb4f7c672"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FPLPZEWG2MWKT4MIYYAB7LRME/bundle.json","state_url":"https://pith.science/pith/4FPLPZEWG2MWKT4MIYYAB7LRME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FPLPZEWG2MWKT4MIYYAB7LRME/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":"2026-07-08T22:28:09Z","links":{"resolver":"https://pith.science/pith/4FPLPZEWG2MWKT4MIYYAB7LRME","bundle":"https://pith.science/pith/4FPLPZEWG2MWKT4MIYYAB7LRME/bundle.json","state":"https://pith.science/pith/4FPLPZEWG2MWKT4MIYYAB7LRME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FPLPZEWG2MWKT4MIYYAB7LRME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4FPLPZEWG2MWKT4MIYYAB7LRME","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":"95950af6d89364b53e1648ece389cf7245f8579df948423936000761d9f28fb0","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-02-04T14:29:57Z","title_canon_sha256":"2c8c9b8d4023a9e148a86c31c21a813aea2e9c9e56f6f2b9b201df6cdebfaa2b"},"schema_version":"1.0","source":{"id":"2002.01312","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.01312","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"2002.01312v2","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.01312","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"4FPLPZEWG2MW","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"pith_short_16","alias_value":"4FPLPZEWG2MWKT4M","created_at":"2026-07-05T00:48:23Z"},{"alias_kind":"pith_short_8","alias_value":"4FPLPZEW","created_at":"2026-07-05T00:48:23Z"}],"graph_snapshots":[{"event_id":"sha256:6c228a8fa20369c9363969cffea227bf699b3d05c2d9a551db6a0decb4f7c672","target":"graph","created_at":"2026-07-05T00:48:23Z","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/2002.01312/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic limit, it defines a flat Riemannian metric over the twist-angle space, topologically a torus, which endows this space with a complex structure, described by a complex parameter $\\tau$. It is shown that the latter is a physical observable related to the anisotropy of the system. The quantity $\\tau$ and the Riemannian volume of the twist-angle space provide an ","authors_text":"Bruno Mera","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-02-04T14:29:57Z","title":"Localization anisotropy and complex geometry in two-dimensional insulators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.01312","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":"sha256:4f0c1497470269ad00cbf93c1aa5b0d3e4ae9ec21439cb197515a0b07e36de4e","target":"record","created_at":"2026-07-05T00:48:23Z","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":"95950af6d89364b53e1648ece389cf7245f8579df948423936000761d9f28fb0","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-02-04T14:29:57Z","title_canon_sha256":"2c8c9b8d4023a9e148a86c31c21a813aea2e9c9e56f6f2b9b201df6cdebfaa2b"},"schema_version":"1.0","source":{"id":"2002.01312","kind":"arxiv","version":2}},"canonical_sha256":"e15eb7e4963699654f8c463000fd7161148bfd19a44d196a7a2c35417f48d2f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e15eb7e4963699654f8c463000fd7161148bfd19a44d196a7a2c35417f48d2f4","first_computed_at":"2026-07-05T00:48:23.767945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:48:23.767945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/sXgiH6aNa3wJhH3QUicnLe/8xwFmgO9qOXl0ZhUJSAOVtFIR04wtVbzRZxsZh/3gO2FVfcGL5IUiWMG1zKDAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:48:23.768365Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.01312","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f0c1497470269ad00cbf93c1aa5b0d3e4ae9ec21439cb197515a0b07e36de4e","sha256:6c228a8fa20369c9363969cffea227bf699b3d05c2d9a551db6a0decb4f7c672"],"state_sha256":"c994f64e3558c485d44f70680affeac000f621796ac5461befe30ee282a5916e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZN6/YrrYgirmZkE8n+zrqOi+hH8nnpHZAF4DSVHP4bpK5a5ht+eBjFgHgA0zoHzoB93+RgdfT0S9n1YXqpdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T22:28:09.453231Z","bundle_sha256":"8a162d76979eb54c5007e3104d5c6669188b7c1890204c386f672a80c61f6ee0"}}