{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XUVFJNDUDQUGVWADGBBR7VJNKX","short_pith_number":"pith:XUVFJNDU","canonical_record":{"source":{"id":"1106.4852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T22:48:57Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"cd4ba24c231831aaac60f96c5c8d70ce93417be0d2ac0b327c9027a8c2a44483","abstract_canon_sha256":"fa1f105adf57937d098cf8e46ff158c078e62b0c599fb4c628ac7aafb468246a"},"schema_version":"1.0"},"canonical_sha256":"bd2a54b4741c286ad80330431fd52d55c94e7648e1922b77076959f8d7c6e4a7","source":{"kind":"arxiv","id":"1106.4852","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4852","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4852v2","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4852","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"XUVFJNDUDQUG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XUVFJNDUDQUGVWAD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XUVFJNDU","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XUVFJNDUDQUGVWADGBBR7VJNKX","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T22:48:57Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"cd4ba24c231831aaac60f96c5c8d70ce93417be0d2ac0b327c9027a8c2a44483","abstract_canon_sha256":"fa1f105adf57937d098cf8e46ff158c078e62b0c599fb4c628ac7aafb468246a"},"schema_version":"1.0"},"canonical_sha256":"bd2a54b4741c286ad80330431fd52d55c94e7648e1922b77076959f8d7c6e4a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:01.850812Z","signature_b64":"A/Ue2HYTkXqzJEswYU6rNp1CUYt9JVzVZtAqO/FJCuUOIeOXRe8+ImezyeiPTPs7in00GkmjjS5CDTtmzZpGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd2a54b4741c286ad80330431fd52d55c94e7648e1922b77076959f8d7c6e4a7","last_reissued_at":"2026-05-18T04:02:01.850105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:01.850105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4852","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":"2026-05-18T04:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/jS4uxW1ZpLYcPVZlP+2vBZkRmtdjVfP/3w1C4UUTJi7H6aTxi5ExCgZnYZsuurMgEWE/X7KhJD1QJbGXq4UBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:38:21.126377Z"},"content_sha256":"43f7ecb9ce1022bd7da8b5752be36d9be7e83122bde9299bec14589ef4765de6","schema_version":"1.0","event_id":"sha256:43f7ecb9ce1022bd7da8b5752be36d9be7e83122bde9299bec14589ef4765de6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XUVFJNDUDQUGVWADGBBR7VJNKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Domingos H. U. Marchetti, Walter F. Wreszinski","submitted_at":"2011-06-23T22:48:57Z","abstract_excerpt":"We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4852","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":"2026-05-18T04:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xieHrjhD4E5MQwd90GPEdZsj6lj3pnkLUN1mBKCMbLST2KeaFo+29BT2YZiKxL8qCSRpGf2ukV0pid+CFO8cBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:38:21.126718Z"},"content_sha256":"998d4ef874807a9b428c4bd0b17ef221c6ae41fc59dc16763e451550e8cec9c2","schema_version":"1.0","event_id":"sha256:998d4ef874807a9b428c4bd0b17ef221c6ae41fc59dc16763e451550e8cec9c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUVFJNDUDQUGVWADGBBR7VJNKX/bundle.json","state_url":"https://pith.science/pith/XUVFJNDUDQUGVWADGBBR7VJNKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUVFJNDUDQUGVWADGBBR7VJNKX/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":"2026-06-27T10:38:21Z","links":{"resolver":"https://pith.science/pith/XUVFJNDUDQUGVWADGBBR7VJNKX","bundle":"https://pith.science/pith/XUVFJNDUDQUGVWADGBBR7VJNKX/bundle.json","state":"https://pith.science/pith/XUVFJNDUDQUGVWADGBBR7VJNKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUVFJNDUDQUGVWADGBBR7VJNKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XUVFJNDUDQUGVWADGBBR7VJNKX","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":"fa1f105adf57937d098cf8e46ff158c078e62b0c599fb4c628ac7aafb468246a","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T22:48:57Z","title_canon_sha256":"cd4ba24c231831aaac60f96c5c8d70ce93417be0d2ac0b327c9027a8c2a44483"},"schema_version":"1.0","source":{"id":"1106.4852","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4852","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4852v2","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4852","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"XUVFJNDUDQUG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XUVFJNDUDQUGVWAD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XUVFJNDU","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:998d4ef874807a9b428c4bd0b17ef221c6ae41fc59dc16763e451550e8cec9c2","target":"graph","created_at":"2026-05-18T04:02:01Z","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 show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.","authors_text":"Domingos H. U. Marchetti, Walter F. Wreszinski","cross_cats":["math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T22:48:57Z","title":"Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4852","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":"sha256:43f7ecb9ce1022bd7da8b5752be36d9be7e83122bde9299bec14589ef4765de6","target":"record","created_at":"2026-05-18T04:02:01Z","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":"fa1f105adf57937d098cf8e46ff158c078e62b0c599fb4c628ac7aafb468246a","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T22:48:57Z","title_canon_sha256":"cd4ba24c231831aaac60f96c5c8d70ce93417be0d2ac0b327c9027a8c2a44483"},"schema_version":"1.0","source":{"id":"1106.4852","kind":"arxiv","version":2}},"canonical_sha256":"bd2a54b4741c286ad80330431fd52d55c94e7648e1922b77076959f8d7c6e4a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd2a54b4741c286ad80330431fd52d55c94e7648e1922b77076959f8d7c6e4a7","first_computed_at":"2026-05-18T04:02:01.850105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:01.850105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/Ue2HYTkXqzJEswYU6rNp1CUYt9JVzVZtAqO/FJCuUOIeOXRe8+ImezyeiPTPs7in00GkmjjS5CDTtmzZpGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:01.850812Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4852","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43f7ecb9ce1022bd7da8b5752be36d9be7e83122bde9299bec14589ef4765de6","sha256:998d4ef874807a9b428c4bd0b17ef221c6ae41fc59dc16763e451550e8cec9c2"],"state_sha256":"a93965ffc4a3d14ae57da7450fd86bdb352c94b8ee2ccf9185535eefc1132861"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R2pu0LVL66nNCuYkIOZXrCIFBeU7hOzb5Q2Gja0/2N2wl+X/MhiGZ24POJ4P7MBTK5nh87GWm7ikEu5SWfpxCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:38:21.128690Z","bundle_sha256":"e092ccfc4db6fd68df5522be9f83e0d63335d9009c7b8c7a2f6039ebacbae17f"}}