{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VWWMS6COXUX7SOE4CBILMMMK7C","short_pith_number":"pith:VWWMS6CO","canonical_record":{"source":{"id":"1010.0315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-02T09:12:35Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"3ab6bab6410ade7f8a1083fabed2884f725c515b0e116a2cd3e4a71a6888e4db","abstract_canon_sha256":"70da6112b7fce43b5139cb11cc0a7ae629630cac2550fc2f670a205d66101d16"},"schema_version":"1.0"},"canonical_sha256":"adacc9784ebd2ff9389c1050b6318af8a7fbc56dbdf4ba60a03c2b28b6ca6988","source":{"kind":"arxiv","id":"1010.0315","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0315","created_at":"2026-05-18T02:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0315v2","created_at":"2026-05-18T02:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0315","created_at":"2026-05-18T02:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"VWWMS6COXUX7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VWWMS6COXUX7SOE4","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VWWMS6CO","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VWWMS6COXUX7SOE4CBILMMMK7C","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-02T09:12:35Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"3ab6bab6410ade7f8a1083fabed2884f725c515b0e116a2cd3e4a71a6888e4db","abstract_canon_sha256":"70da6112b7fce43b5139cb11cc0a7ae629630cac2550fc2f670a205d66101d16"},"schema_version":"1.0"},"canonical_sha256":"adacc9784ebd2ff9389c1050b6318af8a7fbc56dbdf4ba60a03c2b28b6ca6988","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:12.369953Z","signature_b64":"oUBulUH6g/CKAGAjhZEEgPBwAYE3XzeXVVWmhJJmlMt/4IdkRJgVoP5qPuOOApTybPpQ5IyXronw9fOiuTAMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adacc9784ebd2ff9389c1050b6318af8a7fbc56dbdf4ba60a03c2b28b6ca6988","last_reissued_at":"2026-05-18T02:05:12.369285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:12.369285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0315","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":"2026-05-18T02:05:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8briGJNqvA8vfh9Q1HsmMD4YqERO8SqTShBLAShrzeqo6sw1IwF2i82q6lFtysfC29bUuDR/siaiYs9rw4z+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:38:15.987826Z"},"content_sha256":"22d200ef1be0bbdc374c28bb7e10b029cfcc3925aa46c776b4525e03a30c4f3f","schema_version":"1.0","event_id":"sha256:22d200ef1be0bbdc374c28bb7e10b029cfcc3925aa46c776b4525e03a30c4f3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VWWMS6COXUX7SOE4CBILMMMK7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low lying spectrum of weak-disorder quantum waveguides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.SP","authors_text":"Denis Borisov, Ivan Veselic'","submitted_at":"2010-10-02T09:12:35Z","abstract_excerpt":"We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0315","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":"2026-05-18T02:05:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o85yYUS6Gd677ysd7VHGdbSYP1q00H0hW7PlY0bH+R28cHqC8Q/lxjxe+o9RHHiDHhS8qiejOpZbZj0gq0d6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:38:15.988182Z"},"content_sha256":"9578ba7abd155ea0ae9dcbeb96ac314d9ebb3a2957540a1dfb3dd1e5063a64ff","schema_version":"1.0","event_id":"sha256:9578ba7abd155ea0ae9dcbeb96ac314d9ebb3a2957540a1dfb3dd1e5063a64ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWWMS6COXUX7SOE4CBILMMMK7C/bundle.json","state_url":"https://pith.science/pith/VWWMS6COXUX7SOE4CBILMMMK7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWWMS6COXUX7SOE4CBILMMMK7C/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":"2026-06-01T02:38:15Z","links":{"resolver":"https://pith.science/pith/VWWMS6COXUX7SOE4CBILMMMK7C","bundle":"https://pith.science/pith/VWWMS6COXUX7SOE4CBILMMMK7C/bundle.json","state":"https://pith.science/pith/VWWMS6COXUX7SOE4CBILMMMK7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWWMS6COXUX7SOE4CBILMMMK7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VWWMS6COXUX7SOE4CBILMMMK7C","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":"70da6112b7fce43b5139cb11cc0a7ae629630cac2550fc2f670a205d66101d16","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-02T09:12:35Z","title_canon_sha256":"3ab6bab6410ade7f8a1083fabed2884f725c515b0e116a2cd3e4a71a6888e4db"},"schema_version":"1.0","source":{"id":"1010.0315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0315","created_at":"2026-05-18T02:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0315v2","created_at":"2026-05-18T02:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0315","created_at":"2026-05-18T02:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"VWWMS6COXUX7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VWWMS6COXUX7SOE4","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VWWMS6CO","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:9578ba7abd155ea0ae9dcbeb96ac314d9ebb3a2957540a1dfb3dd1e5063a64ff","target":"graph","created_at":"2026-05-18T02:05:12Z","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 low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.","authors_text":"Denis Borisov, Ivan Veselic'","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-02T09:12:35Z","title":"Low lying spectrum of weak-disorder quantum waveguides"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0315","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":"sha256:22d200ef1be0bbdc374c28bb7e10b029cfcc3925aa46c776b4525e03a30c4f3f","target":"record","created_at":"2026-05-18T02:05:12Z","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":"70da6112b7fce43b5139cb11cc0a7ae629630cac2550fc2f670a205d66101d16","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-10-02T09:12:35Z","title_canon_sha256":"3ab6bab6410ade7f8a1083fabed2884f725c515b0e116a2cd3e4a71a6888e4db"},"schema_version":"1.0","source":{"id":"1010.0315","kind":"arxiv","version":2}},"canonical_sha256":"adacc9784ebd2ff9389c1050b6318af8a7fbc56dbdf4ba60a03c2b28b6ca6988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adacc9784ebd2ff9389c1050b6318af8a7fbc56dbdf4ba60a03c2b28b6ca6988","first_computed_at":"2026-05-18T02:05:12.369285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:12.369285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oUBulUH6g/CKAGAjhZEEgPBwAYE3XzeXVVWmhJJmlMt/4IdkRJgVoP5qPuOOApTybPpQ5IyXronw9fOiuTAMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:12.369953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22d200ef1be0bbdc374c28bb7e10b029cfcc3925aa46c776b4525e03a30c4f3f","sha256:9578ba7abd155ea0ae9dcbeb96ac314d9ebb3a2957540a1dfb3dd1e5063a64ff"],"state_sha256":"c5911b188d2fbf8780bb2b3cc742e0e227539b7f00bf553a7877a70d4872acdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOJLcvut7puGPJtSeSqIrzWNdjWJUJPN/Po48OCi+8t+3Y9JFXDVMLnKA5IV17Fe4oqPFDivQwlSupEV9/UBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:38:15.990594Z","bundle_sha256":"96ef512958636c89a5dda5a234cdb3849c8734121a6b72d66081e59d67690e7a"}}