{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VX242V5LRCUAJ5GAL7WLWM57GM","short_pith_number":"pith:VX242V5L","canonical_record":{"source":{"id":"1011.6499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-30T09:40:03Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.MP"],"title_canon_sha256":"991a43ead3eab52dae784a2bf39e3736f21cd13ffbd970ef918d137cc7897626","abstract_canon_sha256":"11945bca794f36eec14a1f93f78ac925c63a6fe2ec970dff267c9721ce5db738"},"schema_version":"1.0"},"canonical_sha256":"adf5cd57ab88a804f4c05fecbb33bf3321e647396198c875c7471b3392eaaeb6","source":{"kind":"arxiv","id":"1011.6499","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6499","created_at":"2026-05-18T04:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6499v2","created_at":"2026-05-18T04:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6499","created_at":"2026-05-18T04:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"VX242V5LRCUA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VX242V5LRCUAJ5GA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VX242V5L","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VX242V5LRCUAJ5GAL7WLWM57GM","target":"record","payload":{"canonical_record":{"source":{"id":"1011.6499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-30T09:40:03Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.MP"],"title_canon_sha256":"991a43ead3eab52dae784a2bf39e3736f21cd13ffbd970ef918d137cc7897626","abstract_canon_sha256":"11945bca794f36eec14a1f93f78ac925c63a6fe2ec970dff267c9721ce5db738"},"schema_version":"1.0"},"canonical_sha256":"adf5cd57ab88a804f4c05fecbb33bf3321e647396198c875c7471b3392eaaeb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:25.576408Z","signature_b64":"IWnSFhZkoLdRVjEXkOVT6zvvDLvClfTUH10xSxa3z26cw/zawtebflx8qnGUFIXTBsSKtUhDBlcV3TM0Pm3/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf5cd57ab88a804f4c05fecbb33bf3321e647396198c875c7471b3392eaaeb6","last_reissued_at":"2026-05-18T04:25:25.575609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:25.575609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.6499","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":"2026-05-18T04:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rpDq79cnFeEueFbN4q6uuroi38F65hNhnfZM2zJdMno9gbzXm7eiItVRCqQnHF6c4e4vKRuMfCcKoAx+QYWHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:24:35.829416Z"},"content_sha256":"abe69fe0cb425933fd0b1dda93d039688f7df2e4c118d45ccade2e43b3d93245","schema_version":"1.0","event_id":"sha256:abe69fe0cb425933fd0b1dda93d039688f7df2e4c118d45ccade2e43b3d93245"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VX242V5LRCUAJ5GAL7WLWM57GM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A rigorous proof of the Landau-Peierls formula and much more","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Aalborg University), Baptiste Savoie (CPT), Horia D. Cornean (MATH. Dept., Philippe Briet (CPT)","submitted_at":"2010-11-30T09:40:03Z","abstract_excerpt":"We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6499","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":"2026-05-18T04:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VdmPMgxSAf+VLU/j8oZEQW7Ag2zpLyXCkhZeHkrZphAtUFMuYx5EER/xcKzJW3G+2OCXj77lhGyEUDsDo7rhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:24:35.829759Z"},"content_sha256":"7807dc91e65798323928cd5451431759529460a39f902bfb343f46c63de34054","schema_version":"1.0","event_id":"sha256:7807dc91e65798323928cd5451431759529460a39f902bfb343f46c63de34054"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VX242V5LRCUAJ5GAL7WLWM57GM/bundle.json","state_url":"https://pith.science/pith/VX242V5LRCUAJ5GAL7WLWM57GM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VX242V5LRCUAJ5GAL7WLWM57GM/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":"2026-06-02T12:24:35Z","links":{"resolver":"https://pith.science/pith/VX242V5LRCUAJ5GAL7WLWM57GM","bundle":"https://pith.science/pith/VX242V5LRCUAJ5GAL7WLWM57GM/bundle.json","state":"https://pith.science/pith/VX242V5LRCUAJ5GAL7WLWM57GM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VX242V5LRCUAJ5GAL7WLWM57GM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VX242V5LRCUAJ5GAL7WLWM57GM","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":"11945bca794f36eec14a1f93f78ac925c63a6fe2ec970dff267c9721ce5db738","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-30T09:40:03Z","title_canon_sha256":"991a43ead3eab52dae784a2bf39e3736f21cd13ffbd970ef918d137cc7897626"},"schema_version":"1.0","source":{"id":"1011.6499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6499","created_at":"2026-05-18T04:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6499v2","created_at":"2026-05-18T04:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6499","created_at":"2026-05-18T04:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"VX242V5LRCUA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VX242V5LRCUAJ5GA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VX242V5L","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:7807dc91e65798323928cd5451431759529460a39f902bfb343f46c63de34054","target":"graph","created_at":"2026-05-18T04:25:25Z","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":"We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.","authors_text":"Aalborg University), Baptiste Savoie (CPT), Horia D. Cornean (MATH. Dept., Philippe Briet (CPT)","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-30T09:40:03Z","title":"A rigorous proof of the Landau-Peierls formula and much more"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6499","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:abe69fe0cb425933fd0b1dda93d039688f7df2e4c118d45ccade2e43b3d93245","target":"record","created_at":"2026-05-18T04:25:25Z","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":"11945bca794f36eec14a1f93f78ac925c63a6fe2ec970dff267c9721ce5db738","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-30T09:40:03Z","title_canon_sha256":"991a43ead3eab52dae784a2bf39e3736f21cd13ffbd970ef918d137cc7897626"},"schema_version":"1.0","source":{"id":"1011.6499","kind":"arxiv","version":2}},"canonical_sha256":"adf5cd57ab88a804f4c05fecbb33bf3321e647396198c875c7471b3392eaaeb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adf5cd57ab88a804f4c05fecbb33bf3321e647396198c875c7471b3392eaaeb6","first_computed_at":"2026-05-18T04:25:25.575609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:25.575609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IWnSFhZkoLdRVjEXkOVT6zvvDLvClfTUH10xSxa3z26cw/zawtebflx8qnGUFIXTBsSKtUhDBlcV3TM0Pm3/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:25.576408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abe69fe0cb425933fd0b1dda93d039688f7df2e4c118d45ccade2e43b3d93245","sha256:7807dc91e65798323928cd5451431759529460a39f902bfb343f46c63de34054"],"state_sha256":"a35c073af15714cac6950a1db6130528e7bc05877829dd0a43dec7df9e1abd74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fH/m2tg8Cx60u1fGXocGULC5U4HEx0f2Hnm66x41h9UVTOmNi/QU40ScE0qyaY0jLyGjDkWANGY404dS5VbFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:24:35.831836Z","bundle_sha256":"595a2332b03b8191562d0921c1b4ebb0d1535964a9f30c0af25acb05b79f5f6c"}}