{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZMZJRK3RAY4LIS354JWUAYHOK3","short_pith_number":"pith:ZMZJRK3R","canonical_record":{"source":{"id":"1206.0952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T14:53:55Z","cross_cats_sorted":[],"title_canon_sha256":"bae0abd66471bc6f2996e5bb64cb66426902d779afec43fcfb69064b6bee48e9","abstract_canon_sha256":"2da4990fedeb6d85ed5a3c36f527435c79b2ad7bc909b611f58087b0de023e8c"},"schema_version":"1.0"},"canonical_sha256":"cb3298ab710638b44b7de26d4060ee56e468881d3f39249c1e88b569a2f9f0b7","source":{"kind":"arxiv","id":"1206.0952","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0952","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0952v1","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0952","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZMZJRK3RAY4L","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZMZJRK3RAY4LIS35","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZMZJRK3R","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZMZJRK3RAY4LIS354JWUAYHOK3","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T14:53:55Z","cross_cats_sorted":[],"title_canon_sha256":"bae0abd66471bc6f2996e5bb64cb66426902d779afec43fcfb69064b6bee48e9","abstract_canon_sha256":"2da4990fedeb6d85ed5a3c36f527435c79b2ad7bc909b611f58087b0de023e8c"},"schema_version":"1.0"},"canonical_sha256":"cb3298ab710638b44b7de26d4060ee56e468881d3f39249c1e88b569a2f9f0b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:54.296991Z","signature_b64":"fmax9om0SbX+iIOd2dsc/wjWAtMmLRyuLDlqPJWOsJT9xDVgsPKh0GTaCAXqYmCVwe0IXEgLDZSNAmhz3A10Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb3298ab710638b44b7de26d4060ee56e468881d3f39249c1e88b569a2f9f0b7","last_reissued_at":"2026-05-18T02:42:54.296645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:54.296645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0952","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uj+MDmPpcuBSc0BOdqdqKkEse9IhIEhZRIycmGd60ONqtKMoMBLttNgjTZN4UOEet92sNJ0ghGQuDC/2i+gBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T17:08:11.155098Z"},"content_sha256":"0fb44728af65e43c237722daabb9f83b882288613d8fa184041b2cc4b9f6d556","schema_version":"1.0","event_id":"sha256:0fb44728af65e43c237722daabb9f83b882288613d8fa184041b2cc4b9f6d556"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZMZJRK3RAY4LIS354JWUAYHOK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schr\\\"odinger Equation in a random potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Erez Michaely, Shmuel Fishman","submitted_at":"2012-06-05T14:53:55Z","abstract_excerpt":"The statistical properties of overlap sums of groups of four eigenfunctions of the Anderson model for localization as well as combinations of four eigenenergies are computed. Some of the distributions are found to be scaling functions, as expected from the scaling theory for localization. These enable to compute the distributions in regimes that are otherwise beyond the computational resources. These distributions are of great importance for the exploration of the Nonlinear Schr\\\"odinger Equation (NLSE) in a random potential since in some explorations the terms we study are considered as noise"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0952","kind":"arxiv","version":1},"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":"2026-05-18T02:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2TIeuWiaD3hCa2j4El8gwbixaYDJuI3LA3SsRkk+gV66ow6QZigC4JRSw0Rn6TN9pAA7i99KdfojUaKVUN4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T17:08:11.155767Z"},"content_sha256":"fff3d34ccbe40f82dfea50f2a2036bbc474d1d224edabe41278a322c8c1f6fac","schema_version":"1.0","event_id":"sha256:fff3d34ccbe40f82dfea50f2a2036bbc474d1d224edabe41278a322c8c1f6fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMZJRK3RAY4LIS354JWUAYHOK3/bundle.json","state_url":"https://pith.science/pith/ZMZJRK3RAY4LIS354JWUAYHOK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMZJRK3RAY4LIS354JWUAYHOK3/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":"2026-05-23T17:08:11Z","links":{"resolver":"https://pith.science/pith/ZMZJRK3RAY4LIS354JWUAYHOK3","bundle":"https://pith.science/pith/ZMZJRK3RAY4LIS354JWUAYHOK3/bundle.json","state":"https://pith.science/pith/ZMZJRK3RAY4LIS354JWUAYHOK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMZJRK3RAY4LIS354JWUAYHOK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZMZJRK3RAY4LIS354JWUAYHOK3","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":"2da4990fedeb6d85ed5a3c36f527435c79b2ad7bc909b611f58087b0de023e8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T14:53:55Z","title_canon_sha256":"bae0abd66471bc6f2996e5bb64cb66426902d779afec43fcfb69064b6bee48e9"},"schema_version":"1.0","source":{"id":"1206.0952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0952","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0952v1","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0952","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZMZJRK3RAY4L","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZMZJRK3RAY4LIS35","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZMZJRK3R","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:fff3d34ccbe40f82dfea50f2a2036bbc474d1d224edabe41278a322c8c1f6fac","target":"graph","created_at":"2026-05-18T02:42:54Z","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":"The statistical properties of overlap sums of groups of four eigenfunctions of the Anderson model for localization as well as combinations of four eigenenergies are computed. Some of the distributions are found to be scaling functions, as expected from the scaling theory for localization. These enable to compute the distributions in regimes that are otherwise beyond the computational resources. These distributions are of great importance for the exploration of the Nonlinear Schr\\\"odinger Equation (NLSE) in a random potential since in some explorations the terms we study are considered as noise","authors_text":"Erez Michaely, Shmuel Fishman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T14:53:55Z","title":"Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schr\\\"odinger Equation in a random potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0952","kind":"arxiv","version":1},"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":"sha256:0fb44728af65e43c237722daabb9f83b882288613d8fa184041b2cc4b9f6d556","target":"record","created_at":"2026-05-18T02:42:54Z","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":"2da4990fedeb6d85ed5a3c36f527435c79b2ad7bc909b611f58087b0de023e8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-06-05T14:53:55Z","title_canon_sha256":"bae0abd66471bc6f2996e5bb64cb66426902d779afec43fcfb69064b6bee48e9"},"schema_version":"1.0","source":{"id":"1206.0952","kind":"arxiv","version":1}},"canonical_sha256":"cb3298ab710638b44b7de26d4060ee56e468881d3f39249c1e88b569a2f9f0b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb3298ab710638b44b7de26d4060ee56e468881d3f39249c1e88b569a2f9f0b7","first_computed_at":"2026-05-18T02:42:54.296645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:54.296645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fmax9om0SbX+iIOd2dsc/wjWAtMmLRyuLDlqPJWOsJT9xDVgsPKh0GTaCAXqYmCVwe0IXEgLDZSNAmhz3A10Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:54.296991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fb44728af65e43c237722daabb9f83b882288613d8fa184041b2cc4b9f6d556","sha256:fff3d34ccbe40f82dfea50f2a2036bbc474d1d224edabe41278a322c8c1f6fac"],"state_sha256":"81f2611efed7937770287f7f1a51ff3a0a408f13dd50c471d4f192a6d0c3daab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CGCOab3BR9SEjB/p2mAUuXBnVWhA9PAN9WxUVwwqat61Ce2VmaSrxZjHkBiM+mLUldsndPstZxDHnoo+ihmJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T17:08:11.159064Z","bundle_sha256":"b5f4169729f0b1e6fbf95587e62a11041c0cc713e9c37836ee61721ec4fa4adf"}}