{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MIZGCTW4HOWKUI4MCT5SMTMKWC","short_pith_number":"pith:MIZGCTW4","canonical_record":{"source":{"id":"1908.07450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-18T09:13:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"eb2528808862a514199142f273632c95f54af51a5f80a053af7d348a2c94a416","abstract_canon_sha256":"da86e2e3f63ced9d9fae82adf8456e5df43e9dd7d147b512a184b3a87ada381b"},"schema_version":"1.0"},"canonical_sha256":"6232614edc3bacaa238c14fb264d8ab085b0f9019269413cdc1115be6202b456","source":{"kind":"arxiv","id":"1908.07450","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07450","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07450v2","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07450","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"MIZGCTW4HOWK","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"MIZGCTW4HOWKUI4M","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"MIZGCTW4","created_at":"2026-07-05T02:02:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MIZGCTW4HOWKUI4MCT5SMTMKWC","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-18T09:13:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"eb2528808862a514199142f273632c95f54af51a5f80a053af7d348a2c94a416","abstract_canon_sha256":"da86e2e3f63ced9d9fae82adf8456e5df43e9dd7d147b512a184b3a87ada381b"},"schema_version":"1.0"},"canonical_sha256":"6232614edc3bacaa238c14fb264d8ab085b0f9019269413cdc1115be6202b456","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:02:30.481507Z","signature_b64":"AYrMgD1yXn0fEM+xS5J3RNSSW7HhL8QVIO5yGhADYnzLt5wMrxv8w632Rd7+LvYC5IlH312Jg9HLxLo6ZNnqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6232614edc3bacaa238c14fb264d8ab085b0f9019269413cdc1115be6202b456","last_reissued_at":"2026-07-05T02:02:30.480984Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:02:30.480984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07450","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":"2026-07-05T02:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b5rhr1cWjLzgtlR/Mvknlt6RcsCLLTb9MOx70mMAjtM0FjCsotvvUOqv6Kh2oq8p7RQVRQYhYRaAdb6XRzA9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:59:40.702275Z"},"content_sha256":"01124edf17c923fb00eb6c74ce2c813867de13abcacef827a5a5f7077cd56883","schema_version":"1.0","event_id":"sha256:01124edf17c923fb00eb6c74ce2c813867de13abcacef827a5a5f7077cd56883"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MIZGCTW4HOWKUI4MCT5SMTMKWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Pizzo, J. Fr\\\"ohlich, S. Del Vecchio, S. Rossi","submitted_at":"2019-08-18T09:13:33Z","abstract_excerpt":"We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. For interactions that are form-bounded w.r.t. the on-site Hamiltonian terms, we prove that the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain, for small values of a coupling constant. In our proof we use a novel method introduced "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07450","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/1908.07450/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":"2026-07-05T02:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sC+MTOGMhuSSQCwNzeLVd8IHdIN6NMtc/vDyzJnZ+OvWDGK/ZpjDJFYcEPcXiLKHAqVT3dZhxcp7kfGnuITbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:59:40.703172Z"},"content_sha256":"91082b52dc2ffd2bb418c7883d6b85e83e1679c4b6db8ba38b887af1c47d4fb2","schema_version":"1.0","event_id":"sha256:91082b52dc2ffd2bb418c7883d6b85e83e1679c4b6db8ba38b887af1c47d4fb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC/bundle.json","state_url":"https://pith.science/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC/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":"2026-08-16T06:59:40Z","links":{"resolver":"https://pith.science/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC","bundle":"https://pith.science/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC/bundle.json","state":"https://pith.science/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIZGCTW4HOWKUI4MCT5SMTMKWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MIZGCTW4HOWKUI4MCT5SMTMKWC","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":"da86e2e3f63ced9d9fae82adf8456e5df43e9dd7d147b512a184b3a87ada381b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-18T09:13:33Z","title_canon_sha256":"eb2528808862a514199142f273632c95f54af51a5f80a053af7d348a2c94a416"},"schema_version":"1.0","source":{"id":"1908.07450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07450","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07450v2","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07450","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"MIZGCTW4HOWK","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"MIZGCTW4HOWKUI4M","created_at":"2026-07-05T02:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"MIZGCTW4","created_at":"2026-07-05T02:02:30Z"}],"graph_snapshots":[{"event_id":"sha256:91082b52dc2ffd2bb418c7883d6b85e83e1679c4b6db8ba38b887af1c47d4fb2","target":"graph","created_at":"2026-07-05T02:02:30Z","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/1908.07450/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. For interactions that are form-bounded w.r.t. the on-site Hamiltonian terms, we prove that the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain, for small values of a coupling constant. In our proof we use a novel method introduced ","authors_text":"A. Pizzo, J. Fr\\\"ohlich, S. Del Vecchio, S. Rossi","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-18T09:13:33Z","title":"Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07450","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":"sha256:01124edf17c923fb00eb6c74ce2c813867de13abcacef827a5a5f7077cd56883","target":"record","created_at":"2026-07-05T02:02:30Z","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":"da86e2e3f63ced9d9fae82adf8456e5df43e9dd7d147b512a184b3a87ada381b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-18T09:13:33Z","title_canon_sha256":"eb2528808862a514199142f273632c95f54af51a5f80a053af7d348a2c94a416"},"schema_version":"1.0","source":{"id":"1908.07450","kind":"arxiv","version":2}},"canonical_sha256":"6232614edc3bacaa238c14fb264d8ab085b0f9019269413cdc1115be6202b456","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6232614edc3bacaa238c14fb264d8ab085b0f9019269413cdc1115be6202b456","first_computed_at":"2026-07-05T02:02:30.480984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:02:30.480984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AYrMgD1yXn0fEM+xS5J3RNSSW7HhL8QVIO5yGhADYnzLt5wMrxv8w632Rd7+LvYC5IlH312Jg9HLxLo6ZNnqDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:02:30.481507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01124edf17c923fb00eb6c74ce2c813867de13abcacef827a5a5f7077cd56883","sha256:91082b52dc2ffd2bb418c7883d6b85e83e1679c4b6db8ba38b887af1c47d4fb2"],"state_sha256":"0ef34da6146089d45969b6b23570c02f74c8f70c2ed0fefa33ce042214d053bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zr8FPYoUXoBRGdk/db4q10h46eL63zhdGjGBPEjsOwyJlRm4e8ZwztPH2QdU7GE4FkJCYwLQfooUweJf3AK8DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T06:59:40.709320Z","bundle_sha256":"6ad39c18fb07e94c023e0163c57e13d16fed3a2b95ea7c7b31cd3c4067def9a8"}}