{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2O36O7JSWSCQR7GAS6IQUBMQNT","short_pith_number":"pith:2O36O7JS","canonical_record":{"source":{"id":"1004.0108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-01T10:59:41Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP"],"title_canon_sha256":"e72276228e311cc5bf9e891ba6b8f09a3ab5d07d9db07102e5f72328691c2ec5","abstract_canon_sha256":"e546f3145daef46cc5f2c4d6c672193aeb9e30a69737fa3c44f8efffec42dbdd"},"schema_version":"1.0"},"canonical_sha256":"d3b7e77d32b48508fcc097910a05906cc2704874af94d748a08e60421b1e3aa5","source":{"kind":"arxiv","id":"1004.0108","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0108","created_at":"2026-05-18T02:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0108v2","created_at":"2026-05-18T02:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0108","created_at":"2026-05-18T02:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"2O36O7JSWSCQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2O36O7JSWSCQR7GA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2O36O7JS","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2O36O7JSWSCQR7GAS6IQUBMQNT","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-01T10:59:41Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP"],"title_canon_sha256":"e72276228e311cc5bf9e891ba6b8f09a3ab5d07d9db07102e5f72328691c2ec5","abstract_canon_sha256":"e546f3145daef46cc5f2c4d6c672193aeb9e30a69737fa3c44f8efffec42dbdd"},"schema_version":"1.0"},"canonical_sha256":"d3b7e77d32b48508fcc097910a05906cc2704874af94d748a08e60421b1e3aa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:15.087920Z","signature_b64":"EbjX0y41ISpH4kug6Q+ks9EW5rJ6cWia8nhvg8V6c3BUBJ3xirRjvLtCUSskl7GvHif0wUKQPCf2JfYgV6MSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3b7e77d32b48508fcc097910a05906cc2704874af94d748a08e60421b1e3aa5","last_reissued_at":"2026-05-18T02:08:15.087507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:15.087507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0108","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":"2026-05-18T02:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Euij9MXL21iAI68o3t0vWrCjO65UJCxIsZv3mNecy+Pi1VxdjIDlnHZr5bFDOSj+glIHSkc6pbozN7CBRoMJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:26:15.549921Z"},"content_sha256":"e1a858db316e8f6c0bbcdabdce6adfa84d50c18841a05427847d56061349e23e","schema_version":"1.0","event_id":"sha256:e1a858db316e8f6c0bbcdabdce6adfa84d50c18841a05427847d56061349e23e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2O36O7JSWSCQR7GAS6IQUBMQNT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faraday effect revisited: sum rules and convergence issues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP"],"primary_cat":"math-ph","authors_text":"Gheorghe Nenciu, Horia D. Cornean","submitted_at":"2010-04-01T10:59:41Z","abstract_excerpt":"This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid state physics, and they give rise to certain convergence problems widely ignored by physicists. We give a complete answer in the case of smooth potentials and formulate an open problem related to less regular perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0108","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":""},"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":"2026-05-18T02:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKdiMvK0IsykwEstYp1i/8s6xBJIq1aIpCHfcZAtqeCPT8UvFEo8UZWWcQnMgc9cAo8X8mezzA/4v1mFaMAvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:26:15.550693Z"},"content_sha256":"ca7e36c92732826be186134d2c94093306097f0a87412dd2bef2e018afca0132","schema_version":"1.0","event_id":"sha256:ca7e36c92732826be186134d2c94093306097f0a87412dd2bef2e018afca0132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2O36O7JSWSCQR7GAS6IQUBMQNT/bundle.json","state_url":"https://pith.science/pith/2O36O7JSWSCQR7GAS6IQUBMQNT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2O36O7JSWSCQR7GAS6IQUBMQNT/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":"2026-06-10T22:26:15Z","links":{"resolver":"https://pith.science/pith/2O36O7JSWSCQR7GAS6IQUBMQNT","bundle":"https://pith.science/pith/2O36O7JSWSCQR7GAS6IQUBMQNT/bundle.json","state":"https://pith.science/pith/2O36O7JSWSCQR7GAS6IQUBMQNT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2O36O7JSWSCQR7GAS6IQUBMQNT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2O36O7JSWSCQR7GAS6IQUBMQNT","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":"e546f3145daef46cc5f2c4d6c672193aeb9e30a69737fa3c44f8efffec42dbdd","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-01T10:59:41Z","title_canon_sha256":"e72276228e311cc5bf9e891ba6b8f09a3ab5d07d9db07102e5f72328691c2ec5"},"schema_version":"1.0","source":{"id":"1004.0108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0108","created_at":"2026-05-18T02:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0108v2","created_at":"2026-05-18T02:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0108","created_at":"2026-05-18T02:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"2O36O7JSWSCQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2O36O7JSWSCQR7GA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2O36O7JS","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:ca7e36c92732826be186134d2c94093306097f0a87412dd2bef2e018afca0132","target":"graph","created_at":"2026-05-18T02:08:15Z","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"},"paper":{"abstract_excerpt":"This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid state physics, and they give rise to certain convergence problems widely ignored by physicists. We give a complete answer in the case of smooth potentials and formulate an open problem related to less regular perturbations.","authors_text":"Gheorghe Nenciu, Horia D. Cornean","cross_cats":["cond-mat.mtrl-sci","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-01T10:59:41Z","title":"Faraday effect revisited: sum rules and convergence issues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0108","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:e1a858db316e8f6c0bbcdabdce6adfa84d50c18841a05427847d56061349e23e","target":"record","created_at":"2026-05-18T02:08:15Z","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":"e546f3145daef46cc5f2c4d6c672193aeb9e30a69737fa3c44f8efffec42dbdd","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-01T10:59:41Z","title_canon_sha256":"e72276228e311cc5bf9e891ba6b8f09a3ab5d07d9db07102e5f72328691c2ec5"},"schema_version":"1.0","source":{"id":"1004.0108","kind":"arxiv","version":2}},"canonical_sha256":"d3b7e77d32b48508fcc097910a05906cc2704874af94d748a08e60421b1e3aa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3b7e77d32b48508fcc097910a05906cc2704874af94d748a08e60421b1e3aa5","first_computed_at":"2026-05-18T02:08:15.087507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:15.087507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EbjX0y41ISpH4kug6Q+ks9EW5rJ6cWia8nhvg8V6c3BUBJ3xirRjvLtCUSskl7GvHif0wUKQPCf2JfYgV6MSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:15.087920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1a858db316e8f6c0bbcdabdce6adfa84d50c18841a05427847d56061349e23e","sha256:ca7e36c92732826be186134d2c94093306097f0a87412dd2bef2e018afca0132"],"state_sha256":"119cde375ba1d43c934c15215287c44951cac33f741e5b2da8578aa2899bdd61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqHa5UgcqbsYmiIeLfSEH10962itkm9YVItII+6S46qlmkqb/rxvERlUerYFvhAtfNtSOQJ4u8ZUr3/qOnzXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:26:15.554906Z","bundle_sha256":"e84469c8061edac45261cc7f4111537865a39b3541b5ff926a438265088dba9e"}}