{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:2FSLLZISAGHN5ARY5BGTJCKIUZ","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":"1190e2c74374e93be51f66173cb7ac5cd32154bca6c04d309ded993051b20216","cross_cats_sorted":["math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-07-09T17:00:27Z","title_canon_sha256":"8851fedb181f036b4e5c86283c4fd4fa14fd0be88e1fa2afc2d879fa4491d5e9"},"schema_version":"1.0","source":{"id":"math-ph/0407017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0407017","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0407017v1","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0407017","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"2FSLLZISAGHN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2FSLLZISAGHN5ARY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2FSLLZIS","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:e72c38861fdf5b10351d7258bf9c81d4d2865f81230a184122ccd8a2677ccb30","target":"graph","created_at":"2026-05-18T02:30:23Z","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 discrete one-dimensional Schr\\\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds following a scaling law. As a consequence, we obtain improved dynamical results for the Fibonacci Hamiltonian and related models.","authors_text":"David Damanik (Caltech), Serguei Tcheremchantsev (Universite d'Orleans)","cross_cats":["math.MP","math.SP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-07-09T17:00:27Z","title":"Scaling Estimates for Solutions and Dynamical Lower Bounds on Wavepacket Spreading"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0407017","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":"sha256:191cdb787d13486dd3d2a57fff146012cc873356f963e8b5483964fd546c8a3a","target":"record","created_at":"2026-05-18T02:30:23Z","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":"1190e2c74374e93be51f66173cb7ac5cd32154bca6c04d309ded993051b20216","cross_cats_sorted":["math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-07-09T17:00:27Z","title_canon_sha256":"8851fedb181f036b4e5c86283c4fd4fa14fd0be88e1fa2afc2d879fa4491d5e9"},"schema_version":"1.0","source":{"id":"math-ph/0407017","kind":"arxiv","version":1}},"canonical_sha256":"d164b5e512018ede8238e84d348948a67f092e757d1a24a2f0000743155bd7b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d164b5e512018ede8238e84d348948a67f092e757d1a24a2f0000743155bd7b9","first_computed_at":"2026-05-18T02:30:23.195832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:23.195832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0f6Uuw4dyzIrXX40rLN900nQ8GIRgsk8XVMK+e3TAP0eP2hrlk/Tf9Lz6b8bM+VadzPTknQ6eJyalcvlt7CBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:23.196394Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0407017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:191cdb787d13486dd3d2a57fff146012cc873356f963e8b5483964fd546c8a3a","sha256:e72c38861fdf5b10351d7258bf9c81d4d2865f81230a184122ccd8a2677ccb30"],"state_sha256":"92406559cc8a55b56f7453ef0da0a6b2d209eb5b77845a161760042aba94c092"}