{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NC6VPC4DVUMVSM7AEW6LW4R42C","short_pith_number":"pith:NC6VPC4D","canonical_record":{"source":{"id":"2403.18948","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-03-27T18:51:14Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"085f17d20048649c6ddb13eb545749ab4c447875a7b74eecb14452d51688e67d","abstract_canon_sha256":"c20e39ce5e001146207964d96e9a9bae2268d528ebe8f9528c72d3a9f2229754"},"schema_version":"1.0"},"canonical_sha256":"68bd578b83ad195933e025bcbb723cd0a2e54f8317ff32d16deceb65db68d9bb","source":{"kind":"arxiv","id":"2403.18948","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18948","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18948v1","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18948","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"NC6VPC4DVUMV","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"pith_short_16","alias_value":"NC6VPC4DVUMVSM7A","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"pith_short_8","alias_value":"NC6VPC4D","created_at":"2026-07-05T08:01:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NC6VPC4DVUMVSM7AEW6LW4R42C","target":"record","payload":{"canonical_record":{"source":{"id":"2403.18948","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-03-27T18:51:14Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"085f17d20048649c6ddb13eb545749ab4c447875a7b74eecb14452d51688e67d","abstract_canon_sha256":"c20e39ce5e001146207964d96e9a9bae2268d528ebe8f9528c72d3a9f2229754"},"schema_version":"1.0"},"canonical_sha256":"68bd578b83ad195933e025bcbb723cd0a2e54f8317ff32d16deceb65db68d9bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:01:41.925906Z","signature_b64":"+PSxiE8C9FKQuazfZVqYtLybKe4pw6HBLbdXaCiLP5T+VNNRutG0pB4r1mxmm7pRX1BKqVtxaSFGFm9OXyEZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68bd578b83ad195933e025bcbb723cd0a2e54f8317ff32d16deceb65db68d9bb","last_reissued_at":"2026-07-05T08:01:41.925408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:01:41.925408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.18948","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":"2026-07-05T08:01:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbipsBqD7VPcR7nU4OF3X/9qZ3XT4bXFtp4L3epIEr0lBwSrXvB4JMPKucZ+qh6LnrlwyzDuOH7yafj/ZJ6SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:13:20.509476Z"},"content_sha256":"1a1921691edbb930735f65d359081b57a6d34cdb8665cf625a5941ebee5c7e95","schema_version":"1.0","event_id":"sha256:1a1921691edbb930735f65d359081b57a6d34cdb8665cf625a5941ebee5c7e95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NC6VPC4DVUMVSM7AEW6LW4R42C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological indices in condensed matter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hermann Schulz-Baldes","submitted_at":"2024-03-27T18:51:14Z","abstract_excerpt":"This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18948","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/2403.18948/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":"2026-07-05T08:01:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AmuqChNONeFyIColGD8poiy544xmYPMKFCinEIP/jiQtiTL+Hn7IYxPYazdlPh8lyrZUne71uNp/Ga+Yr0rjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:13:20.510032Z"},"content_sha256":"d50ded7dbe97e1fb6b493ba7d0c538a6ebc76e712df093fde52020de8575a05a","schema_version":"1.0","event_id":"sha256:d50ded7dbe97e1fb6b493ba7d0c538a6ebc76e712df093fde52020de8575a05a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NC6VPC4DVUMVSM7AEW6LW4R42C/bundle.json","state_url":"https://pith.science/pith/NC6VPC4DVUMVSM7AEW6LW4R42C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NC6VPC4DVUMVSM7AEW6LW4R42C/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":"2026-08-12T05:13:20Z","links":{"resolver":"https://pith.science/pith/NC6VPC4DVUMVSM7AEW6LW4R42C","bundle":"https://pith.science/pith/NC6VPC4DVUMVSM7AEW6LW4R42C/bundle.json","state":"https://pith.science/pith/NC6VPC4DVUMVSM7AEW6LW4R42C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NC6VPC4DVUMVSM7AEW6LW4R42C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NC6VPC4DVUMVSM7AEW6LW4R42C","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":"c20e39ce5e001146207964d96e9a9bae2268d528ebe8f9528c72d3a9f2229754","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-03-27T18:51:14Z","title_canon_sha256":"085f17d20048649c6ddb13eb545749ab4c447875a7b74eecb14452d51688e67d"},"schema_version":"1.0","source":{"id":"2403.18948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18948","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18948v1","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18948","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"NC6VPC4DVUMV","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"pith_short_16","alias_value":"NC6VPC4DVUMVSM7A","created_at":"2026-07-05T08:01:41Z"},{"alias_kind":"pith_short_8","alias_value":"NC6VPC4D","created_at":"2026-07-05T08:01:41Z"}],"graph_snapshots":[{"event_id":"sha256:d50ded7dbe97e1fb6b493ba7d0c538a6ebc76e712df093fde52020de8575a05a","target":"graph","created_at":"2026-07-05T08:01:41Z","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/2403.18948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.","authors_text":"Hermann Schulz-Baldes","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-03-27T18:51:14Z","title":"Topological indices in condensed matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18948","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":"sha256:1a1921691edbb930735f65d359081b57a6d34cdb8665cf625a5941ebee5c7e95","target":"record","created_at":"2026-07-05T08:01:41Z","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":"c20e39ce5e001146207964d96e9a9bae2268d528ebe8f9528c72d3a9f2229754","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-03-27T18:51:14Z","title_canon_sha256":"085f17d20048649c6ddb13eb545749ab4c447875a7b74eecb14452d51688e67d"},"schema_version":"1.0","source":{"id":"2403.18948","kind":"arxiv","version":1}},"canonical_sha256":"68bd578b83ad195933e025bcbb723cd0a2e54f8317ff32d16deceb65db68d9bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68bd578b83ad195933e025bcbb723cd0a2e54f8317ff32d16deceb65db68d9bb","first_computed_at":"2026-07-05T08:01:41.925408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:01:41.925408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+PSxiE8C9FKQuazfZVqYtLybKe4pw6HBLbdXaCiLP5T+VNNRutG0pB4r1mxmm7pRX1BKqVtxaSFGFm9OXyEZCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:01:41.925906Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.18948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a1921691edbb930735f65d359081b57a6d34cdb8665cf625a5941ebee5c7e95","sha256:d50ded7dbe97e1fb6b493ba7d0c538a6ebc76e712df093fde52020de8575a05a"],"state_sha256":"fe93d68bf0de40a8edffa55a3405665fddec1c4b4bd52c96287e9f4cb8b4356e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTFzhUt/7QINKszW8k6BYPWwZBBq1VNp20jFFYiJpd8NtAAImucWq00uFyJwRHfpf5OwaX4LSLqye2xH5jkDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T05:13:20.513687Z","bundle_sha256":"1870b8478d56c1bf2297eca7d3201c85978a8871cf6052d6103bb65ae28f1822"}}