{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M3HCWQNNFTDJRXD2NAJ4Y5IBC6","short_pith_number":"pith:M3HCWQNN","canonical_record":{"source":{"id":"1512.08271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-27T20:14:51Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"title_canon_sha256":"cdc28fa6094a8b8358319565d6c5730a5e8755a240ce4d999206748cd9720649","abstract_canon_sha256":"2e63ce1c0a41959ccdb7d398e3c683cd2e4af6ade8dec039e2e1f80e833c8936"},"schema_version":"1.0"},"canonical_sha256":"66ce2b41ad2cc698dc7a6813cc7501178b7b92c94af18e18a141dd07c32b4d7b","source":{"kind":"arxiv","id":"1512.08271","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08271","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08271v1","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08271","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"M3HCWQNNFTDJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"M3HCWQNNFTDJRXD2","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"M3HCWQNN","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M3HCWQNNFTDJRXD2NAJ4Y5IBC6","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-27T20:14:51Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"title_canon_sha256":"cdc28fa6094a8b8358319565d6c5730a5e8755a240ce4d999206748cd9720649","abstract_canon_sha256":"2e63ce1c0a41959ccdb7d398e3c683cd2e4af6ade8dec039e2e1f80e833c8936"},"schema_version":"1.0"},"canonical_sha256":"66ce2b41ad2cc698dc7a6813cc7501178b7b92c94af18e18a141dd07c32b4d7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:36.719527Z","signature_b64":"3jfp0VVAf1wcmXqDQj3+XOZ1RStHq+4kovavmA1+C5jPnYiojTjaaUhNgkUMqduTo5shEIfnWQDvCXfPHxYtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66ce2b41ad2cc698dc7a6813cc7501178b7b92c94af18e18a141dd07c32b4d7b","last_reissued_at":"2026-05-18T01:03:36.718781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:36.718781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08271","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":"2026-05-18T01:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQWmaiYrZLpqrKHp3hyO+V4Coz/KwqR1nMVMSwrkNpar4DFo4U4utavqXJH9ZYr7gYaneXdEcRtuBiDfnKpHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:30:54.442259Z"},"content_sha256":"6d4a6de0745fe1ee500b9e677e9104864894d500ca7a0ec01f7710416680ec05","schema_version":"1.0","event_id":"sha256:6d4a6de0745fe1ee500b9e677e9104864894d500ca7a0ec01f7710416680ec05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M3HCWQNNFTDJRXD2NAJ4Y5IBC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic lower bound for the gap of Hermitian matrices having ergodic ground states and infinitesimal off-diagonal elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"C. Presilla, M. Ostilli","submitted_at":"2015-12-27T20:14:51Z","abstract_excerpt":"Given a $M\\times M$ Hermitian matrix $\\mathcal{H}$ with possibly degenerate eigenvalues $\\mathcal{E}_1 < \\mathcal{E}_2 < \\mathcal{E}_3< \\dots$, we provide, in the limit $M\\to\\infty$, a lower bound for the gap $\\mu_2 = \\mathcal{E}_2 - \\mathcal{E}_1$ assuming that (i) the eigenvector (eigenvectors) associated to $\\mathcal{E}_1$ is ergodic (are all ergodic) and (ii) the off-diagonal terms of $\\mathcal{H}$ vanish for $M\\to\\infty$ more slowly than $M^{-2}$. Under these hypotheses, we find $\\varliminf_{M\\to\\infty} \\mu_2 \\geq \\varlimsup_{M\\to\\infty} \\min_{n} \\mathcal{H}_{n,n}$. This general result tu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08271","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":""},"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":"2026-05-18T01:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MAfMRQodcnteuNbJ+5wLra/lcaGm75NUM0aiLwkvTElobSRMsnOUig1RQrUsYuEqlRjniWJbIohAu2h7Kl49Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:30:54.442631Z"},"content_sha256":"3ef7463a506252cda7aff6d2e0116d4d7cc13e3728e832258e32ea74e3e8f3f6","schema_version":"1.0","event_id":"sha256:3ef7463a506252cda7aff6d2e0116d4d7cc13e3728e832258e32ea74e3e8f3f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6/bundle.json","state_url":"https://pith.science/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6/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":"2026-05-31T00:30:54Z","links":{"resolver":"https://pith.science/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6","bundle":"https://pith.science/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6/bundle.json","state":"https://pith.science/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3HCWQNNFTDJRXD2NAJ4Y5IBC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M3HCWQNNFTDJRXD2NAJ4Y5IBC6","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":"2e63ce1c0a41959ccdb7d398e3c683cd2e4af6ade8dec039e2e1f80e833c8936","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-27T20:14:51Z","title_canon_sha256":"cdc28fa6094a8b8358319565d6c5730a5e8755a240ce4d999206748cd9720649"},"schema_version":"1.0","source":{"id":"1512.08271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08271","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08271v1","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08271","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"M3HCWQNNFTDJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"M3HCWQNNFTDJRXD2","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"M3HCWQNN","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:3ef7463a506252cda7aff6d2e0116d4d7cc13e3728e832258e32ea74e3e8f3f6","target":"graph","created_at":"2026-05-18T01:03:36Z","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":"Given a $M\\times M$ Hermitian matrix $\\mathcal{H}$ with possibly degenerate eigenvalues $\\mathcal{E}_1 < \\mathcal{E}_2 < \\mathcal{E}_3< \\dots$, we provide, in the limit $M\\to\\infty$, a lower bound for the gap $\\mu_2 = \\mathcal{E}_2 - \\mathcal{E}_1$ assuming that (i) the eigenvector (eigenvectors) associated to $\\mathcal{E}_1$ is ergodic (are all ergodic) and (ii) the off-diagonal terms of $\\mathcal{H}$ vanish for $M\\to\\infty$ more slowly than $M^{-2}$. Under these hypotheses, we find $\\varliminf_{M\\to\\infty} \\mu_2 \\geq \\varlimsup_{M\\to\\infty} \\min_{n} \\mathcal{H}_{n,n}$. This general result tu","authors_text":"C. Presilla, M. Ostilli","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-27T20:14:51Z","title":"Asymptotic lower bound for the gap of Hermitian matrices having ergodic ground states and infinitesimal off-diagonal elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08271","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":"sha256:6d4a6de0745fe1ee500b9e677e9104864894d500ca7a0ec01f7710416680ec05","target":"record","created_at":"2026-05-18T01:03:36Z","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":"2e63ce1c0a41959ccdb7d398e3c683cd2e4af6ade8dec039e2e1f80e833c8936","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-27T20:14:51Z","title_canon_sha256":"cdc28fa6094a8b8358319565d6c5730a5e8755a240ce4d999206748cd9720649"},"schema_version":"1.0","source":{"id":"1512.08271","kind":"arxiv","version":1}},"canonical_sha256":"66ce2b41ad2cc698dc7a6813cc7501178b7b92c94af18e18a141dd07c32b4d7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66ce2b41ad2cc698dc7a6813cc7501178b7b92c94af18e18a141dd07c32b4d7b","first_computed_at":"2026-05-18T01:03:36.718781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:36.718781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3jfp0VVAf1wcmXqDQj3+XOZ1RStHq+4kovavmA1+C5jPnYiojTjaaUhNgkUMqduTo5shEIfnWQDvCXfPHxYtCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:36.719527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d4a6de0745fe1ee500b9e677e9104864894d500ca7a0ec01f7710416680ec05","sha256:3ef7463a506252cda7aff6d2e0116d4d7cc13e3728e832258e32ea74e3e8f3f6"],"state_sha256":"8c5d286e853cbe4d802a4f3a88ec5837e7a229e4ea549e842d4bca8a1c2e9434"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kGNc8dBAdjGBxvKo5Gf8k8tRxymM07A8GjrCtX+T0eoruG9umNZQBfsmCksTzX8emPF6i+5tQAoF7gZ2LMUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:30:54.444853Z","bundle_sha256":"2e42dede3fcf8b94641b76cb606ada27ad63ae991e6157d80bfb2e0422352797"}}