{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:EOG6E4ZZQ7I2WZW4QNULMAL3Z3","short_pith_number":"pith:EOG6E4ZZ","canonical_record":{"source":{"id":"math-ph/0302029","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2003-02-11T22:10:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0109e922fa4f6a1c78ef06b6f99029d32700c93bfff028ccfb8270afc7a544f1","abstract_canon_sha256":"8fdd46962ad1cc9c0e1c407403af9de069ffc4670e101746b14f5e2c4e5dd3e1"},"schema_version":"1.0"},"canonical_sha256":"238de2733987d1ab66dc8368b6017bceec741ef2247a2e2f21a20d4db6b0be92","source":{"kind":"arxiv","id":"math-ph/0302029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0302029","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0302029v1","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0302029","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"EOG6E4ZZQ7I2","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"EOG6E4ZZQ7I2WZW4","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"EOG6E4ZZ","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:EOG6E4ZZQ7I2WZW4QNULMAL3Z3","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0302029","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2003-02-11T22:10:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0109e922fa4f6a1c78ef06b6f99029d32700c93bfff028ccfb8270afc7a544f1","abstract_canon_sha256":"8fdd46962ad1cc9c0e1c407403af9de069ffc4670e101746b14f5e2c4e5dd3e1"},"schema_version":"1.0"},"canonical_sha256":"238de2733987d1ab66dc8368b6017bceec741ef2247a2e2f21a20d4db6b0be92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:16.538571Z","signature_b64":"usvO60ugXVhlawNZ4Xw2zfsX6/3X29Vdpu8tYMtoCROhS1/aS+rlj4sJUYgtETYDQhVU27ZCJ7quYMQ7SjufAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"238de2733987d1ab66dc8368b6017bceec741ef2247a2e2f21a20d4db6b0be92","last_reissued_at":"2026-05-18T02:30:16.538121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:16.538121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0302029","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":"2026-05-18T02:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f5KHInlI3+ATGPvS1L4KPbRbDsSl5sbGZ+NP/S7KMav19DZdNydOy/EqVKMREGd5VBi+aeTrwEAj9NOtvsEmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:57:46.866506Z"},"content_sha256":"fbf4473db2490f1f2741f93067a55fbb248cfe61ab547447353a33a59e4f2e73","schema_version":"1.0","event_id":"sha256:fbf4473db2490f1f2741f93067a55fbb248cfe61ab547447353a33a59e4f2e73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:EOG6E4ZZQ7I2WZW4QNULMAL3Z3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power-law bounds on transfer matrices and quantum dynamics in one dimension II","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andras Suto, David Damanik, Serguei Tcheremchantsev","submitted_at":"2003-02-11T22:10:23Z","abstract_excerpt":"We establish quantum dynamical lower bounds for a number of discrete one-dimensional Schr\\\"odinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach from part I and study many examples. Particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power-law bounds on transfer matrices. The models discussed in this paper include substitution models, Sturmian models, a hierarchical model, the prime model, and a class of moderately sparse potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0302029","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":"2026-05-18T02:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZgR4hZ56HcBC8rIjXUwEgP4Kkpz6eth9knxgBGZMMEYrzxaiW5n+t6hIP+FFUZei+KoYI410zrczoaamE/LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:57:46.867128Z"},"content_sha256":"febaf24fee10b4cb35fe5b0c6dc8996e0321791024ffd00ff4aed0354690f7ad","schema_version":"1.0","event_id":"sha256:febaf24fee10b4cb35fe5b0c6dc8996e0321791024ffd00ff4aed0354690f7ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3/bundle.json","state_url":"https://pith.science/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3/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":"2026-06-06T00:57:46Z","links":{"resolver":"https://pith.science/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3","bundle":"https://pith.science/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3/bundle.json","state":"https://pith.science/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOG6E4ZZQ7I2WZW4QNULMAL3Z3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:EOG6E4ZZQ7I2WZW4QNULMAL3Z3","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":"8fdd46962ad1cc9c0e1c407403af9de069ffc4670e101746b14f5e2c4e5dd3e1","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-02-11T22:10:23Z","title_canon_sha256":"0109e922fa4f6a1c78ef06b6f99029d32700c93bfff028ccfb8270afc7a544f1"},"schema_version":"1.0","source":{"id":"math-ph/0302029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0302029","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0302029v1","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0302029","created_at":"2026-05-18T02:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"EOG6E4ZZQ7I2","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"EOG6E4ZZQ7I2WZW4","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"EOG6E4ZZ","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:febaf24fee10b4cb35fe5b0c6dc8996e0321791024ffd00ff4aed0354690f7ad","target":"graph","created_at":"2026-05-18T02:30:16Z","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 establish quantum dynamical lower bounds for a number of discrete one-dimensional Schr\\\"odinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach from part I and study many examples. Particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power-law bounds on transfer matrices. The models discussed in this paper include substitution models, Sturmian models, a hierarchical model, the prime model, and a class of moderately sparse potentials.","authors_text":"Andras Suto, David Damanik, Serguei Tcheremchantsev","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2003-02-11T22:10:23Z","title":"Power-law bounds on transfer matrices and quantum dynamics in one dimension II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0302029","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:fbf4473db2490f1f2741f93067a55fbb248cfe61ab547447353a33a59e4f2e73","target":"record","created_at":"2026-05-18T02:30:16Z","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":"8fdd46962ad1cc9c0e1c407403af9de069ffc4670e101746b14f5e2c4e5dd3e1","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-02-11T22:10:23Z","title_canon_sha256":"0109e922fa4f6a1c78ef06b6f99029d32700c93bfff028ccfb8270afc7a544f1"},"schema_version":"1.0","source":{"id":"math-ph/0302029","kind":"arxiv","version":1}},"canonical_sha256":"238de2733987d1ab66dc8368b6017bceec741ef2247a2e2f21a20d4db6b0be92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"238de2733987d1ab66dc8368b6017bceec741ef2247a2e2f21a20d4db6b0be92","first_computed_at":"2026-05-18T02:30:16.538121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:16.538121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"usvO60ugXVhlawNZ4Xw2zfsX6/3X29Vdpu8tYMtoCROhS1/aS+rlj4sJUYgtETYDQhVU27ZCJ7quYMQ7SjufAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:16.538571Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0302029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbf4473db2490f1f2741f93067a55fbb248cfe61ab547447353a33a59e4f2e73","sha256:febaf24fee10b4cb35fe5b0c6dc8996e0321791024ffd00ff4aed0354690f7ad"],"state_sha256":"2f49f3e2035e9f13d94b680a53baedfccd5468d21cdc4bdd0adc6e8b2106f21a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shlkniU4bbSCLqETsjpDSFs25M5j2j3GNJgfn1gZvwubQQQ4xTG0NkSCN2YGdsiOyaOatrX7bXGWsxFGRTBhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T00:57:46.871676Z","bundle_sha256":"5f893f0781baa4c67aa98023848fc2c7aa85b6d08409527053c2e4d28fb91682"}}