{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2IVWHZUIBENNOTZK6QRZIRJIGJ","short_pith_number":"pith:2IVWHZUI","canonical_record":{"source":{"id":"1008.2949","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-17T19:20:58Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6c3f7d208ca9318ea174afbf4aff4d2445b33f145885bbb4327c432d07b41599","abstract_canon_sha256":"40a56e8bc41a833364473181c5e5f37e115044183a4391b2c19c8247fc1f8a6c"},"schema_version":"1.0"},"canonical_sha256":"d22b63e688091ad74f2af4239445283262e5c47e9a008c2a5a98db8fd7782b2e","source":{"kind":"arxiv","id":"1008.2949","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2949","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2949v3","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2949","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"2IVWHZUIBENN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2IVWHZUIBENNOTZK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2IVWHZUI","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2IVWHZUIBENNOTZK6QRZIRJIGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2949","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-17T19:20:58Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6c3f7d208ca9318ea174afbf4aff4d2445b33f145885bbb4327c432d07b41599","abstract_canon_sha256":"40a56e8bc41a833364473181c5e5f37e115044183a4391b2c19c8247fc1f8a6c"},"schema_version":"1.0"},"canonical_sha256":"d22b63e688091ad74f2af4239445283262e5c47e9a008c2a5a98db8fd7782b2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:09.091462Z","signature_b64":"WNpcih4ObcYYm3fKWoKrWEK0Hp7idnc5zXypTFRMDaJhVPTQXBPipko5A373kJCtiJI0KTNXP+Yr7/CLcheeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d22b63e688091ad74f2af4239445283262e5c47e9a008c2a5a98db8fd7782b2e","last_reissued_at":"2026-05-18T04:10:09.090665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:09.090665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2949","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":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tbTXoQ2Y4sPHMqouJ+LstpovHHup96Md2UzExLVr/B1q2G66NNYmvrnjzYKfsMVEVuUZljC181TDueuhPEWJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:19:46.224183Z"},"content_sha256":"4d11570ce2e6bc829ece28e389d66dad2eb6370ca0fca98cdc601fd7a195c763","schema_version":"1.0","event_id":"sha256:4d11570ce2e6bc829ece28e389d66dad2eb6370ca0fca98cdc601fd7a195c763"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2IVWHZUIBENNOTZK6QRZIRJIGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolutely continuous spectrum for the Anderson model on a product of a tree with a finite graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"David Hasler, Florina Halasan, Richard Froese","submitted_at":"2010-08-17T19:20:58Z","abstract_excerpt":"We prove the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2949","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":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4ZV/8PrVVQY3nNDsxDFopRlQ2GOJVWwYIfGlzQu/XZejsd0oGN5+QFGzdCW7NB49j0dZjFZdfOLXxElQHFxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:19:46.224551Z"},"content_sha256":"64dea8b9cafe160311031a0c7995dcd25fda05263af87e6ea254f19f19554513","schema_version":"1.0","event_id":"sha256:64dea8b9cafe160311031a0c7995dcd25fda05263af87e6ea254f19f19554513"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ/bundle.json","state_url":"https://pith.science/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ/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":"2026-06-24T09:19:46Z","links":{"resolver":"https://pith.science/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ","bundle":"https://pith.science/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ/bundle.json","state":"https://pith.science/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IVWHZUIBENNOTZK6QRZIRJIGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2IVWHZUIBENNOTZK6QRZIRJIGJ","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":"40a56e8bc41a833364473181c5e5f37e115044183a4391b2c19c8247fc1f8a6c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-17T19:20:58Z","title_canon_sha256":"6c3f7d208ca9318ea174afbf4aff4d2445b33f145885bbb4327c432d07b41599"},"schema_version":"1.0","source":{"id":"1008.2949","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2949","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2949v3","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2949","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"2IVWHZUIBENN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2IVWHZUIBENNOTZK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2IVWHZUI","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:64dea8b9cafe160311031a0c7995dcd25fda05263af87e6ea254f19f19554513","target":"graph","created_at":"2026-05-18T04:10:09Z","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 the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size.","authors_text":"David Hasler, Florina Halasan, Richard Froese","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-17T19:20:58Z","title":"Absolutely continuous spectrum for the Anderson model on a product of a tree with a finite graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2949","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":"sha256:4d11570ce2e6bc829ece28e389d66dad2eb6370ca0fca98cdc601fd7a195c763","target":"record","created_at":"2026-05-18T04:10:09Z","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":"40a56e8bc41a833364473181c5e5f37e115044183a4391b2c19c8247fc1f8a6c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-17T19:20:58Z","title_canon_sha256":"6c3f7d208ca9318ea174afbf4aff4d2445b33f145885bbb4327c432d07b41599"},"schema_version":"1.0","source":{"id":"1008.2949","kind":"arxiv","version":3}},"canonical_sha256":"d22b63e688091ad74f2af4239445283262e5c47e9a008c2a5a98db8fd7782b2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d22b63e688091ad74f2af4239445283262e5c47e9a008c2a5a98db8fd7782b2e","first_computed_at":"2026-05-18T04:10:09.090665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.090665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WNpcih4ObcYYm3fKWoKrWEK0Hp7idnc5zXypTFRMDaJhVPTQXBPipko5A373kJCtiJI0KTNXP+Yr7/CLcheeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.091462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2949","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d11570ce2e6bc829ece28e389d66dad2eb6370ca0fca98cdc601fd7a195c763","sha256:64dea8b9cafe160311031a0c7995dcd25fda05263af87e6ea254f19f19554513"],"state_sha256":"25942992633322d3202daec57d94054d5b8e3e8c142333d82b8a1e770dfd6d6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/zT66FmGnnB5usjq4C9BvxutV9V9x33sLiH2wX5k7FSRHblxb7HbuLQHkmoVTuKDckmF8/TakbFGVyp5qC9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:19:46.226494Z","bundle_sha256":"fae142f2505ddc87d28cc750d4a9be077235f3ba9d76a0f9a5f21b6a6e7cf74d"}}