{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5C2XCYGS4AK4WFQ32QMCTJKIDG","short_pith_number":"pith:5C2XCYGS","canonical_record":{"source":{"id":"1101.4468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-24T08:56:41Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"ea3a6d00c11fa5745d4ce609758b246238be24ad7d55697624e2bf076f97d7a3","abstract_canon_sha256":"d78fa4bf6e1ebb202ef6dab91f7f965906ddfd5137fd6196c6eba7677c4b8738"},"schema_version":"1.0"},"canonical_sha256":"e8b57160d2e015cb161bd41829a548199f8b44f37f833f4f2c52bcb38729e5c3","source":{"kind":"arxiv","id":"1101.4468","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4468","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4468v3","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4468","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"5C2XCYGS4AK4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5C2XCYGS4AK4WFQ3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5C2XCYGS","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5C2XCYGS4AK4WFQ32QMCTJKIDG","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-24T08:56:41Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"ea3a6d00c11fa5745d4ce609758b246238be24ad7d55697624e2bf076f97d7a3","abstract_canon_sha256":"d78fa4bf6e1ebb202ef6dab91f7f965906ddfd5137fd6196c6eba7677c4b8738"},"schema_version":"1.0"},"canonical_sha256":"e8b57160d2e015cb161bd41829a548199f8b44f37f833f4f2c52bcb38729e5c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:50.219350Z","signature_b64":"9LAChIRnTm/lUBFsFKOYKj+JNYUknZvpJ9pBMQ47Fna8iOxuIZ5/g39lW3nrFOl4fYUju23uz/IaJOLYYpReAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8b57160d2e015cb161bd41829a548199f8b44f37f833f4f2c52bcb38729e5c3","last_reissued_at":"2026-05-18T02:22:50.218757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:50.218757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4468","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":"2026-05-18T02:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkLOF/UdVy29UiJrAAtrshhYmPaBcid0euwiv7v53LKxmEFJa/6Jw1ZJqvmlx7TIRLNNsEEGkJx2vg+0ngweBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:27:56.416337Z"},"content_sha256":"55e765c7d36380a9e75cd5a08301b8dbcc8b7dc49a6601634e89ccaa1ab6765d","schema_version":"1.0","event_id":"sha256:55e765c7d36380a9e75cd5a08301b8dbcc8b7dc49a6601634e89ccaa1ab6765d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5C2XCYGS4AK4WFQ32QMCTJKIDG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifshits tails in the hierarchical Anderson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Peter M\\\"uller, Simon Kuttruf","submitted_at":"2011-01-24T08:56:41Z","abstract_excerpt":"We prove that the homogeneous hierarchical Anderson model exhibits a Lifshits tail at the upper edge of its spectrum. The Lifshits exponent is given in terms of the spectral dimension of the homogeneous hierarchical structure. Our approach is based on Dirichlet-Neumann bracketing for the hierarchical Laplacian and a large-deviation argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4468","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":""},"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":"2026-05-18T02:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRsJHdZwFsIELN0EWccawMOYCQ9nOPGVySWRpXCQBQ524FtqccI10TdpH7EcEpqzavHUKVZXUzwAV98DreefCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:27:56.416681Z"},"content_sha256":"b63b333ba5f7f0e27576c61bcbeee0b9e47af0599837b81c64d06f4fc706f6f8","schema_version":"1.0","event_id":"sha256:b63b333ba5f7f0e27576c61bcbeee0b9e47af0599837b81c64d06f4fc706f6f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG/bundle.json","state_url":"https://pith.science/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG/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":"2026-06-06T17:27:56Z","links":{"resolver":"https://pith.science/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG","bundle":"https://pith.science/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG/bundle.json","state":"https://pith.science/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5C2XCYGS4AK4WFQ32QMCTJKIDG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5C2XCYGS4AK4WFQ32QMCTJKIDG","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":"d78fa4bf6e1ebb202ef6dab91f7f965906ddfd5137fd6196c6eba7677c4b8738","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-24T08:56:41Z","title_canon_sha256":"ea3a6d00c11fa5745d4ce609758b246238be24ad7d55697624e2bf076f97d7a3"},"schema_version":"1.0","source":{"id":"1101.4468","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4468","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4468v3","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4468","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"5C2XCYGS4AK4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5C2XCYGS4AK4WFQ3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5C2XCYGS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:b63b333ba5f7f0e27576c61bcbeee0b9e47af0599837b81c64d06f4fc706f6f8","target":"graph","created_at":"2026-05-18T02:22:50Z","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 prove that the homogeneous hierarchical Anderson model exhibits a Lifshits tail at the upper edge of its spectrum. The Lifshits exponent is given in terms of the spectral dimension of the homogeneous hierarchical structure. Our approach is based on Dirichlet-Neumann bracketing for the hierarchical Laplacian and a large-deviation argument.","authors_text":"Peter M\\\"uller, Simon Kuttruf","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-24T08:56:41Z","title":"Lifshits tails in the hierarchical Anderson model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4468","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":"sha256:55e765c7d36380a9e75cd5a08301b8dbcc8b7dc49a6601634e89ccaa1ab6765d","target":"record","created_at":"2026-05-18T02:22:50Z","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":"d78fa4bf6e1ebb202ef6dab91f7f965906ddfd5137fd6196c6eba7677c4b8738","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-24T08:56:41Z","title_canon_sha256":"ea3a6d00c11fa5745d4ce609758b246238be24ad7d55697624e2bf076f97d7a3"},"schema_version":"1.0","source":{"id":"1101.4468","kind":"arxiv","version":3}},"canonical_sha256":"e8b57160d2e015cb161bd41829a548199f8b44f37f833f4f2c52bcb38729e5c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8b57160d2e015cb161bd41829a548199f8b44f37f833f4f2c52bcb38729e5c3","first_computed_at":"2026-05-18T02:22:50.218757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:50.218757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9LAChIRnTm/lUBFsFKOYKj+JNYUknZvpJ9pBMQ47Fna8iOxuIZ5/g39lW3nrFOl4fYUju23uz/IaJOLYYpReAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:50.219350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4468","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55e765c7d36380a9e75cd5a08301b8dbcc8b7dc49a6601634e89ccaa1ab6765d","sha256:b63b333ba5f7f0e27576c61bcbeee0b9e47af0599837b81c64d06f4fc706f6f8"],"state_sha256":"1469b34ec1d9b46d21576c097fe2c7f8db839f4d7e78fbddb6287a3541ef03ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZn1lIWCk/5sDV/32Vh4NeFWQ8YuuLQSjbo+OAjQuMscxzYozfYSeSK5wEYStA+BSwuKIU2ZQG/0ceSYf89bBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:27:56.418906Z","bundle_sha256":"8d8089961a66f0cc0a581591b4cd51eec7ea7e0056bd301444690a36ad9eff6a"}}