{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DD7I4FS2Z6KWZAJLBJEFYJZMLX","short_pith_number":"pith:DD7I4FS2","canonical_record":{"source":{"id":"1904.02700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-04T17:57:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d5b7066a7759fa47b60bff294eef2bde35f64aed97a75a392bb5d349c91d88f7","abstract_canon_sha256":"8e341f7fb8a6b1f3ab4dbc4f1329379d66f7da788f14560778c681e575644915"},"schema_version":"1.0"},"canonical_sha256":"18fe8e165acf956c812b0a485c272c5ded1060cc575a484929d26e783b40ea93","source":{"kind":"arxiv","id":"1904.02700","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02700","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02700v3","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02700","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"DD7I4FS2Z6KW","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"pith_short_16","alias_value":"DD7I4FS2Z6KWZAJL","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"pith_short_8","alias_value":"DD7I4FS2","created_at":"2026-07-05T00:17:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DD7I4FS2Z6KWZAJLBJEFYJZMLX","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-04T17:57:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d5b7066a7759fa47b60bff294eef2bde35f64aed97a75a392bb5d349c91d88f7","abstract_canon_sha256":"8e341f7fb8a6b1f3ab4dbc4f1329379d66f7da788f14560778c681e575644915"},"schema_version":"1.0"},"canonical_sha256":"18fe8e165acf956c812b0a485c272c5ded1060cc575a484929d26e783b40ea93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:17:26.159944Z","signature_b64":"17OGZpSrbQUMbgXEExmsEVg2y6tCWmK8W9ED8vHHO46huW7CTUWp/xo3bqv27F6MudDUT0DqrSmJpLgddHPaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18fe8e165acf956c812b0a485c272c5ded1060cc575a484929d26e783b40ea93","last_reissued_at":"2026-07-05T00:17:26.159491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:17:26.159491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02700","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:17:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gbxt1DaHZwXiznihFjhR5TiR+F3wMk0CSNpYNVJ3ezqZ+ODlgmYLVlJBocYQ67Ef2Tn+JtarYgOuDpQGy3prCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:18:03.868567Z"},"content_sha256":"956ec9f3577fbc3ea6de411b249a5ef4b5f3a731c65a60b05897d921be3a3d44","schema_version":"1.0","event_id":"sha256:956ec9f3577fbc3ea6de411b249a5ef4b5f3a731c65a60b05897d921be3a3d44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DD7I4FS2Z6KWZAJLBJEFYJZMLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proof of the Bloch theorem for lattice models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Haruki Watanabe","submitted_at":"2019-04-04T17:57:57Z","abstract_excerpt":"The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium at a finite temperature, irrespective of the details of the Hamiltonian as far as all terms in the Hamiltonian are finite ranged. In this work we present a simple yet rigorous proof for general lattice models. For large but finite systems, we find that both the discussion and the conclusion are sensitive to the boundary condition one assumes: under the peri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02700","kind":"arxiv","version":3},"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/1904.02700/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":"2026-07-05T00:17:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QL9J/TLwKg5ZcfsOcIvwOjql0BuJAFypwNF6lyGRkhtK9W/JVePjbZt4sZrKxBv3ouO7gW3+ScxRUrOdq3tnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:18:03.869480Z"},"content_sha256":"8edb1103909b101ce63d4deea4852459090210dca5d60ee8de031614fce81abf","schema_version":"1.0","event_id":"sha256:8edb1103909b101ce63d4deea4852459090210dca5d60ee8de031614fce81abf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX/bundle.json","state_url":"https://pith.science/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX/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":"2026-08-18T07:18:03Z","links":{"resolver":"https://pith.science/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX","bundle":"https://pith.science/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX/bundle.json","state":"https://pith.science/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DD7I4FS2Z6KWZAJLBJEFYJZMLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DD7I4FS2Z6KWZAJLBJEFYJZMLX","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":"8e341f7fb8a6b1f3ab4dbc4f1329379d66f7da788f14560778c681e575644915","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-04T17:57:57Z","title_canon_sha256":"d5b7066a7759fa47b60bff294eef2bde35f64aed97a75a392bb5d349c91d88f7"},"schema_version":"1.0","source":{"id":"1904.02700","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02700","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02700v3","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02700","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"DD7I4FS2Z6KW","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"pith_short_16","alias_value":"DD7I4FS2Z6KWZAJL","created_at":"2026-07-05T00:17:26Z"},{"alias_kind":"pith_short_8","alias_value":"DD7I4FS2","created_at":"2026-07-05T00:17:26Z"}],"graph_snapshots":[{"event_id":"sha256:8edb1103909b101ce63d4deea4852459090210dca5d60ee8de031614fce81abf","target":"graph","created_at":"2026-07-05T00:17:26Z","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/1904.02700/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium at a finite temperature, irrespective of the details of the Hamiltonian as far as all terms in the Hamiltonian are finite ranged. In this work we present a simple yet rigorous proof for general lattice models. For large but finite systems, we find that both the discussion and the conclusion are sensitive to the boundary condition one assumes: under the peri","authors_text":"Haruki Watanabe","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-04T17:57:57Z","title":"A proof of the Bloch theorem for lattice models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02700","kind":"arxiv","version":3},"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":"sha256:956ec9f3577fbc3ea6de411b249a5ef4b5f3a731c65a60b05897d921be3a3d44","target":"record","created_at":"2026-07-05T00:17:26Z","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":"8e341f7fb8a6b1f3ab4dbc4f1329379d66f7da788f14560778c681e575644915","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-04T17:57:57Z","title_canon_sha256":"d5b7066a7759fa47b60bff294eef2bde35f64aed97a75a392bb5d349c91d88f7"},"schema_version":"1.0","source":{"id":"1904.02700","kind":"arxiv","version":3}},"canonical_sha256":"18fe8e165acf956c812b0a485c272c5ded1060cc575a484929d26e783b40ea93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18fe8e165acf956c812b0a485c272c5ded1060cc575a484929d26e783b40ea93","first_computed_at":"2026-07-05T00:17:26.159491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:17:26.159491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"17OGZpSrbQUMbgXEExmsEVg2y6tCWmK8W9ED8vHHO46huW7CTUWp/xo3bqv27F6MudDUT0DqrSmJpLgddHPaAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:17:26.159944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02700","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:956ec9f3577fbc3ea6de411b249a5ef4b5f3a731c65a60b05897d921be3a3d44","sha256:8edb1103909b101ce63d4deea4852459090210dca5d60ee8de031614fce81abf"],"state_sha256":"2a1a05b9158e88f1bd7359f3c39dd1fd45c62e70d6e884190979de8d096093f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cyBijXZ0bnTJ5/WINPZe1PAH8l+Ltgwt9NcgtkCdqu9dyUx0ZcUSd4XDlCqzF+rSAzl06g5J81DNUib4yHhuCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:18:03.874590Z","bundle_sha256":"f92861a884423a442777f19aea75fd421342188d4054a88011d3cd2ec1865a02"}}