{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OR44TAVE3VCNSFXMHBECBADMVO","short_pith_number":"pith:OR44TAVE","canonical_record":{"source":{"id":"1602.05123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-16T18:26:37Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"bb46a4d773949e80cea5de0dcd76abf4c1b957a10a20c628a96873bbf50ef256","abstract_canon_sha256":"521515796da3e8fbbbe15c70f4dd41fb470232b65467e2268c0a87d98af80415"},"schema_version":"1.0"},"canonical_sha256":"7479c982a4dd44d916ec384820806cabb5133ffa6a5b8f0e90b2f5fa92befc53","source":{"kind":"arxiv","id":"1602.05123","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05123","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05123v2","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05123","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"OR44TAVE3VCN","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OR44TAVE3VCNSFXM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OR44TAVE","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OR44TAVE3VCNSFXMHBECBADMVO","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-16T18:26:37Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"bb46a4d773949e80cea5de0dcd76abf4c1b957a10a20c628a96873bbf50ef256","abstract_canon_sha256":"521515796da3e8fbbbe15c70f4dd41fb470232b65467e2268c0a87d98af80415"},"schema_version":"1.0"},"canonical_sha256":"7479c982a4dd44d916ec384820806cabb5133ffa6a5b8f0e90b2f5fa92befc53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:15.481895Z","signature_b64":"nuy7Ax+YaeNYRq8Z5EyIPA9dzGqriNuyOyRYUW5hIbEqUEkgbwtFxwQu36R1tk9K0qitLV6afy4Ht3+/sfPLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7479c982a4dd44d916ec384820806cabb5133ffa6a5b8f0e90b2f5fa92befc53","last_reissued_at":"2026-05-18T00:47:15.481252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:15.481252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05123","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":"2026-05-18T00:47:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5pSVX6HEPy3mUuK1fVyEmkX3DDAQaws0vM1/jomsP9ml2Y54IrlTDx5Rl9S5qOJNDfpgQSpe16+h1h3UUNVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:27:45.769138Z"},"content_sha256":"8f7b5a9e0efe875f735f62ba182e093bce1aeb919130bff8caff38169d8a7731","schema_version":"1.0","event_id":"sha256:8f7b5a9e0efe875f735f62ba182e093bce1aeb919130bff8caff38169d8a7731"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OR44TAVE3VCNSFXMHBECBADMVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surface Lifshits tails for random quantum Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Georgi Raikov, Werner Kirsch","submitted_at":"2016-02-16T18:26:37Z","abstract_excerpt":"We consider Schr\\\"{o}dinger operators on $L^{2}({\\mathbb R}^{d})\\otimes L^{2}({\\mathbb R}^{\\ell})$ of the form $ H_{\\omega}~=~H_{\\perp}\\otimes I_{\\parallel} + I_{\\perp} \\otimes {H_\\parallel} + V_{\\omega}$, where $H_{\\perp}$ and $H_{\\parallel}$ are Schr\\\"{o}dinger operators on $L^{2}({\\mathbb R}^{d})$ and $L^{2}({\\mathbb R}^{\\ell})$ respectively, and $ V_\\omega(x,y)$ : = $\\sum_{\\xi \\in {\\mathbb Z}^{d}} \\lambda_\\xi(\\omega) v(x - \\xi, y)$, $x \\in {\\mathbb R}^d$, $y \\in {\\mathbb R}^\\ell$, is a random 'surface potential'. We investigate the behavior of the integrated density of surface states of $H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05123","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":"2026-05-18T00:47:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/4aZtWnuyQ10xb7/BuT5NLfSAB8wA5haef3thO26UrcsZJH2goYPc/ApJfnuYidmETlFNI+Cm+a+1sMMF39CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:27:45.769505Z"},"content_sha256":"2a1db63b6c78a42b6c45454a3fc6d5e9836721679832f8c2d3d5620eb2266166","schema_version":"1.0","event_id":"sha256:2a1db63b6c78a42b6c45454a3fc6d5e9836721679832f8c2d3d5620eb2266166"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OR44TAVE3VCNSFXMHBECBADMVO/bundle.json","state_url":"https://pith.science/pith/OR44TAVE3VCNSFXMHBECBADMVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OR44TAVE3VCNSFXMHBECBADMVO/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":"2026-06-03T21:27:45Z","links":{"resolver":"https://pith.science/pith/OR44TAVE3VCNSFXMHBECBADMVO","bundle":"https://pith.science/pith/OR44TAVE3VCNSFXMHBECBADMVO/bundle.json","state":"https://pith.science/pith/OR44TAVE3VCNSFXMHBECBADMVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OR44TAVE3VCNSFXMHBECBADMVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OR44TAVE3VCNSFXMHBECBADMVO","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":"521515796da3e8fbbbe15c70f4dd41fb470232b65467e2268c0a87d98af80415","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-16T18:26:37Z","title_canon_sha256":"bb46a4d773949e80cea5de0dcd76abf4c1b957a10a20c628a96873bbf50ef256"},"schema_version":"1.0","source":{"id":"1602.05123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05123","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05123v2","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05123","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"OR44TAVE3VCN","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OR44TAVE3VCNSFXM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OR44TAVE","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:2a1db63b6c78a42b6c45454a3fc6d5e9836721679832f8c2d3d5620eb2266166","target":"graph","created_at":"2026-05-18T00:47:15Z","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":"We consider Schr\\\"{o}dinger operators on $L^{2}({\\mathbb R}^{d})\\otimes L^{2}({\\mathbb R}^{\\ell})$ of the form $ H_{\\omega}~=~H_{\\perp}\\otimes I_{\\parallel} + I_{\\perp} \\otimes {H_\\parallel} + V_{\\omega}$, where $H_{\\perp}$ and $H_{\\parallel}$ are Schr\\\"{o}dinger operators on $L^{2}({\\mathbb R}^{d})$ and $L^{2}({\\mathbb R}^{\\ell})$ respectively, and $ V_\\omega(x,y)$ : = $\\sum_{\\xi \\in {\\mathbb Z}^{d}} \\lambda_\\xi(\\omega) v(x - \\xi, y)$, $x \\in {\\mathbb R}^d$, $y \\in {\\mathbb R}^\\ell$, is a random 'surface potential'. We investigate the behavior of the integrated density of surface states of $H","authors_text":"Georgi Raikov, Werner Kirsch","cross_cats":["math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-16T18:26:37Z","title":"Surface Lifshits tails for random quantum Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05123","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":"sha256:8f7b5a9e0efe875f735f62ba182e093bce1aeb919130bff8caff38169d8a7731","target":"record","created_at":"2026-05-18T00:47:15Z","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":"521515796da3e8fbbbe15c70f4dd41fb470232b65467e2268c0a87d98af80415","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-16T18:26:37Z","title_canon_sha256":"bb46a4d773949e80cea5de0dcd76abf4c1b957a10a20c628a96873bbf50ef256"},"schema_version":"1.0","source":{"id":"1602.05123","kind":"arxiv","version":2}},"canonical_sha256":"7479c982a4dd44d916ec384820806cabb5133ffa6a5b8f0e90b2f5fa92befc53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7479c982a4dd44d916ec384820806cabb5133ffa6a5b8f0e90b2f5fa92befc53","first_computed_at":"2026-05-18T00:47:15.481252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:15.481252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nuy7Ax+YaeNYRq8Z5EyIPA9dzGqriNuyOyRYUW5hIbEqUEkgbwtFxwQu36R1tk9K0qitLV6afy4Ht3+/sfPLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:15.481895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f7b5a9e0efe875f735f62ba182e093bce1aeb919130bff8caff38169d8a7731","sha256:2a1db63b6c78a42b6c45454a3fc6d5e9836721679832f8c2d3d5620eb2266166"],"state_sha256":"55d907a136bdef12e84a74deb552f33e1cc3e9218b276bda1b09c06dc383b3b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoeQAbky7vNVebmDeqFhwAWX5Gt/Kw1wWqM/2L83+TtvtBSl6tyP1DSBGAJMuoCgoQaZH+QxdCSas4LTBFVICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:27:45.771561Z","bundle_sha256":"4e8e0aadad044d58099dfc6407abb0db4b76cd164b2c0b22880179bbe048cdf1"}}