{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:WDHNVDWIYSXUPXK2FZHU6U4I6B","short_pith_number":"pith:WDHNVDWI","canonical_record":{"source":{"id":"cond-mat/0007105","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"2000-07-06T15:28:37Z","cross_cats_sorted":["cond-mat.dis-nn","nlin.CD"],"title_canon_sha256":"c6440712964912d037a7a8b36104ac6e5e2e38e0af750d289a736975dc9805bf","abstract_canon_sha256":"4eed6400c1564d7feedf7220884e4d4a6f4e78a875373a1ee4363117746eb625"},"schema_version":"1.0"},"canonical_sha256":"b0ceda8ec8c4af47dd5a2e4f4f5388f04498f6df1bc62ae037f319a210a14e62","source":{"kind":"arxiv","id":"cond-mat/0007105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0007105","created_at":"2026-05-18T01:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0007105v1","created_at":"2026-05-18T01:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0007105","created_at":"2026-05-18T01:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"WDHNVDWIYSXU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"WDHNVDWIYSXUPXK2","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"WDHNVDWI","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:WDHNVDWIYSXUPXK2FZHU6U4I6B","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0007105","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"2000-07-06T15:28:37Z","cross_cats_sorted":["cond-mat.dis-nn","nlin.CD"],"title_canon_sha256":"c6440712964912d037a7a8b36104ac6e5e2e38e0af750d289a736975dc9805bf","abstract_canon_sha256":"4eed6400c1564d7feedf7220884e4d4a6f4e78a875373a1ee4363117746eb625"},"schema_version":"1.0"},"canonical_sha256":"b0ceda8ec8c4af47dd5a2e4f4f5388f04498f6df1bc62ae037f319a210a14e62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:08.386905Z","signature_b64":"d3qtWk3Zuxf0Vh9I1ytRqdCnuf5GYUXm92LIRDI7mgfepPbbi4ed9A559EmQCJ8YG6Dti0Y7WDyTHmtL4jY6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0ceda8ec8c4af47dd5a2e4f4f5388f04498f6df1bc62ae037f319a210a14e62","last_reissued_at":"2026-05-18T01:40:08.386310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:08.386310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0007105","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":"2026-05-18T01:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WBaauOfdBHKGQnICUMkQB6+1ZWESiV2uP28Mh0bHATVyYZrVmZXyLhyCiqQ+biu0YvMU5idDEEMz1rlZQqVJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:37:58.953030Z"},"content_sha256":"aa061deb3f9fa9fa7055b4b61df368ab06bac51141f1c8211e87c2afda9848ce","schema_version":"1.0","event_id":"sha256:aa061deb3f9fa9fa7055b4b61df368ab06bac51141f1c8211e87c2afda9848ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:WDHNVDWIYSXUPXK2FZHU6U4I6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistics of resonances and of delay times in quasiperiodic Schr\"odinger equations","license":"","headline":"","cross_cats":["cond-mat.dis-nn","nlin.CD"],"primary_cat":"cond-mat.mes-hall","authors_text":"A. Ossipov, F. Steinbach, T. Geisel, Tsampikos Kottos","submitted_at":"2000-07-06T15:28:37Z","abstract_excerpt":"We study the statistical distributions of the resonance widths ${\\cal P} (\\Gamma)$, and of delay times ${\\cal P} (\\tau)$ in one dimensional quasi-periodic tight-binding systems with one open channel. Both quantities are found to decay algebraically as $\\Gamma^{-\\alpha}$, and $\\tau^{-\\gamma}$ on small and large scales respectively. The exponents $\\alpha$, and $\\gamma$ are related to the fractal dimension $D_0^E$ of the spectrum of the closed system as $\\alpha=1+D_0^E$ and $\\gamma=2-D_0^E$. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0007105","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":"2026-05-18T01:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JC5DTMaaj/CneHzYypHK4ni1xwfwaHPVsKAxCCK/83dn/gF6VNSpKISrwP5c0DJ1tX6MgDoxqAYhQb8OqIiTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:37:58.953449Z"},"content_sha256":"29e7a6eae75f9f46d20a23ba71d3acba26e3330e57154fe65b09be65de9195f7","schema_version":"1.0","event_id":"sha256:29e7a6eae75f9f46d20a23ba71d3acba26e3330e57154fe65b09be65de9195f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B/bundle.json","state_url":"https://pith.science/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B/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":"2026-05-26T12:37:58Z","links":{"resolver":"https://pith.science/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B","bundle":"https://pith.science/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B/bundle.json","state":"https://pith.science/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WDHNVDWIYSXUPXK2FZHU6U4I6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:WDHNVDWIYSXUPXK2FZHU6U4I6B","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":"4eed6400c1564d7feedf7220884e4d4a6f4e78a875373a1ee4363117746eb625","cross_cats_sorted":["cond-mat.dis-nn","nlin.CD"],"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"2000-07-06T15:28:37Z","title_canon_sha256":"c6440712964912d037a7a8b36104ac6e5e2e38e0af750d289a736975dc9805bf"},"schema_version":"1.0","source":{"id":"cond-mat/0007105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0007105","created_at":"2026-05-18T01:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0007105v1","created_at":"2026-05-18T01:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0007105","created_at":"2026-05-18T01:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"WDHNVDWIYSXU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"WDHNVDWIYSXUPXK2","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"WDHNVDWI","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:29e7a6eae75f9f46d20a23ba71d3acba26e3330e57154fe65b09be65de9195f7","target":"graph","created_at":"2026-05-18T01:40:08Z","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 study the statistical distributions of the resonance widths ${\\cal P} (\\Gamma)$, and of delay times ${\\cal P} (\\tau)$ in one dimensional quasi-periodic tight-binding systems with one open channel. Both quantities are found to decay algebraically as $\\Gamma^{-\\alpha}$, and $\\tau^{-\\gamma}$ on small and large scales respectively. The exponents $\\alpha$, and $\\gamma$ are related to the fractal dimension $D_0^E$ of the spectrum of the closed system as $\\alpha=1+D_0^E$ and $\\gamma=2-D_0^E$. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices","authors_text":"A. Ossipov, F. Steinbach, T. Geisel, Tsampikos Kottos","cross_cats":["cond-mat.dis-nn","nlin.CD"],"headline":"","license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"2000-07-06T15:28:37Z","title":"Statistics of resonances and of delay times in quasiperiodic Schr\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0007105","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:aa061deb3f9fa9fa7055b4b61df368ab06bac51141f1c8211e87c2afda9848ce","target":"record","created_at":"2026-05-18T01:40:08Z","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":"4eed6400c1564d7feedf7220884e4d4a6f4e78a875373a1ee4363117746eb625","cross_cats_sorted":["cond-mat.dis-nn","nlin.CD"],"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"2000-07-06T15:28:37Z","title_canon_sha256":"c6440712964912d037a7a8b36104ac6e5e2e38e0af750d289a736975dc9805bf"},"schema_version":"1.0","source":{"id":"cond-mat/0007105","kind":"arxiv","version":1}},"canonical_sha256":"b0ceda8ec8c4af47dd5a2e4f4f5388f04498f6df1bc62ae037f319a210a14e62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0ceda8ec8c4af47dd5a2e4f4f5388f04498f6df1bc62ae037f319a210a14e62","first_computed_at":"2026-05-18T01:40:08.386310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:08.386310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d3qtWk3Zuxf0Vh9I1ytRqdCnuf5GYUXm92LIRDI7mgfepPbbi4ed9A559EmQCJ8YG6Dti0Y7WDyTHmtL4jY6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:08.386905Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0007105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa061deb3f9fa9fa7055b4b61df368ab06bac51141f1c8211e87c2afda9848ce","sha256:29e7a6eae75f9f46d20a23ba71d3acba26e3330e57154fe65b09be65de9195f7"],"state_sha256":"fa9a33ccd76c59993c92d7636d44a747fc8f37bb3a162fc58207f48e508fbe44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NfWyAbqX/xvH0IAIIZ+mZC3oBzsBz44R1gW3YE/41GSgGdbFL0ZphnkwiH6597puotnnEI4VByliNrGRJRwJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:37:58.956259Z","bundle_sha256":"6c22192bcb6436990968eb575d0d188738c5a40ec0db8a755d32b73ce661142c"}}