{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KCNDE7KBGBYAXWJTRU4INZGD26","short_pith_number":"pith:KCNDE7KB","canonical_record":{"source":{"id":"1107.0386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-02T15:13:09Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"5ac252bf3c9a3da933a76e04f012a4c88473ffb5f8d7f5d75317a58446f0af97","abstract_canon_sha256":"ca6a976ca17201e08048db1a6c570f2f322b76b2c99dd34d3b4d2ff11758dfe4"},"schema_version":"1.0"},"canonical_sha256":"509a327d4130700bd9338d3886e4c3d7a6e48228021eb4e51d5379b404c247b0","source":{"kind":"arxiv","id":"1107.0386","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0386","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0386v2","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0386","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"KCNDE7KBGBYA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KCNDE7KBGBYAXWJT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KCNDE7KB","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KCNDE7KBGBYAXWJTRU4INZGD26","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-02T15:13:09Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"5ac252bf3c9a3da933a76e04f012a4c88473ffb5f8d7f5d75317a58446f0af97","abstract_canon_sha256":"ca6a976ca17201e08048db1a6c570f2f322b76b2c99dd34d3b4d2ff11758dfe4"},"schema_version":"1.0"},"canonical_sha256":"509a327d4130700bd9338d3886e4c3d7a6e48228021eb4e51d5379b404c247b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:03.338200Z","signature_b64":"PcBB9J79ZpNgb25Z7vTWPBPN8YzsSDxdEshXaf5un/zNkDRSxlgoFFfqp4EhXV1kJAOISICNWChdzNYtRykeDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"509a327d4130700bd9338d3886e4c3d7a6e48228021eb4e51d5379b404c247b0","last_reissued_at":"2026-05-18T00:27:03.337579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:03.337579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0386","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":"2026-05-18T00:27:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"apB115i71eetTdMFWc1MA2kiLOobAuSm8apMCHK9w6XZox+fiTEtESCrU9z9j+/L/AX9opakQ7pGMmYDxzkbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:57:10.553888Z"},"content_sha256":"543e262eade9f08aee316a81b9d9233cbb8a57c11926123fab4ebac07146a6b1","schema_version":"1.0","event_id":"sha256:543e262eade9f08aee316a81b9d9233cbb8a57c11926123fab4ebac07146a6b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KCNDE7KBGBYAXWJTRU4INZGD26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding the Random Displacement Model: From Ground-State Properties to Localization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Fr\\'ed\\'eric Klopp, G\\\"unter Stolz, Michael Loss, Shu Nakamura","submitted_at":"2011-07-02T15:13:09Z","abstract_excerpt":"We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\\\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0386","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":"2026-05-18T00:27:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSalm/5rgZ7FoSC6V+GCxfqZqzAT6CcqHvn37AYfvIFZF9RlVJyUySKjTbIq6soMOulGV4nDVO0ogjeRt4i2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:57:10.554229Z"},"content_sha256":"71a0432df596b897425414b5232ad9e1e072e3e819be6f9db11b821493a98fba","schema_version":"1.0","event_id":"sha256:71a0432df596b897425414b5232ad9e1e072e3e819be6f9db11b821493a98fba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCNDE7KBGBYAXWJTRU4INZGD26/bundle.json","state_url":"https://pith.science/pith/KCNDE7KBGBYAXWJTRU4INZGD26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCNDE7KBGBYAXWJTRU4INZGD26/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":"2026-06-28T21:57:10Z","links":{"resolver":"https://pith.science/pith/KCNDE7KBGBYAXWJTRU4INZGD26","bundle":"https://pith.science/pith/KCNDE7KBGBYAXWJTRU4INZGD26/bundle.json","state":"https://pith.science/pith/KCNDE7KBGBYAXWJTRU4INZGD26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCNDE7KBGBYAXWJTRU4INZGD26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KCNDE7KBGBYAXWJTRU4INZGD26","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":"ca6a976ca17201e08048db1a6c570f2f322b76b2c99dd34d3b4d2ff11758dfe4","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-02T15:13:09Z","title_canon_sha256":"5ac252bf3c9a3da933a76e04f012a4c88473ffb5f8d7f5d75317a58446f0af97"},"schema_version":"1.0","source":{"id":"1107.0386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0386","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0386v2","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0386","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"KCNDE7KBGBYA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KCNDE7KBGBYAXWJT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KCNDE7KB","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:71a0432df596b897425414b5232ad9e1e072e3e819be6f9db11b821493a98fba","target":"graph","created_at":"2026-05-18T00:27:03Z","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 give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\\\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dime","authors_text":"Fr\\'ed\\'eric Klopp, G\\\"unter Stolz, Michael Loss, Shu Nakamura","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-02T15:13:09Z","title":"Understanding the Random Displacement Model: From Ground-State Properties to Localization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0386","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":"sha256:543e262eade9f08aee316a81b9d9233cbb8a57c11926123fab4ebac07146a6b1","target":"record","created_at":"2026-05-18T00:27:03Z","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":"ca6a976ca17201e08048db1a6c570f2f322b76b2c99dd34d3b4d2ff11758dfe4","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-02T15:13:09Z","title_canon_sha256":"5ac252bf3c9a3da933a76e04f012a4c88473ffb5f8d7f5d75317a58446f0af97"},"schema_version":"1.0","source":{"id":"1107.0386","kind":"arxiv","version":2}},"canonical_sha256":"509a327d4130700bd9338d3886e4c3d7a6e48228021eb4e51d5379b404c247b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"509a327d4130700bd9338d3886e4c3d7a6e48228021eb4e51d5379b404c247b0","first_computed_at":"2026-05-18T00:27:03.337579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:03.337579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PcBB9J79ZpNgb25Z7vTWPBPN8YzsSDxdEshXaf5un/zNkDRSxlgoFFfqp4EhXV1kJAOISICNWChdzNYtRykeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:03.338200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:543e262eade9f08aee316a81b9d9233cbb8a57c11926123fab4ebac07146a6b1","sha256:71a0432df596b897425414b5232ad9e1e072e3e819be6f9db11b821493a98fba"],"state_sha256":"e55111e8a5e625a3db52f913bd60cad1e6826c95ef0c85e425025654e98c774e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4HmWFRKnCnvdaP7P7N+Cwu8vRrVpHY4znk+5ilavljQQPVObDxoNSzOByG6IMvwe2ecQt4ADs0iLNf4Z3ysDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T21:57:10.556053Z","bundle_sha256":"f18e22dbf4a504c622d2846ca98ec08e7b147b3825ff62d177b050cebffd7de6"}}