{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VJK336U6AFABEG7YFRCGET5EZG","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":"4ea21c0dfd6ef0d29a2bceeaaf3c639192861b6c2d628a0364230b6b6b496f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-12T02:29:05Z","title_canon_sha256":"cf3cfc603a80e0ca95f942e778e234ed967752d002d7ad982d7aef88dec18f59"},"schema_version":"1.0","source":{"id":"1201.2464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2464","created_at":"2026-05-18T01:58:52Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2464v1","created_at":"2026-05-18T01:58:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2464","created_at":"2026-05-18T01:58:52Z"},{"alias_kind":"pith_short_12","alias_value":"VJK336U6AFAB","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VJK336U6AFABEG7Y","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VJK336U6","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:f769cf1c61d7093509a827821f735b43d08e49e4fbeda75ac90fad3fa586c998","target":"graph","created_at":"2026-05-18T01:58:52Z","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 consider an $n$-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schr\\\"odiner equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension $n$ and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary $\\beta>0$ loss. This is in c","authors_text":"Hans Christianson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-12T02:29:05Z","title":"Near Sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2464","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:d06200f6297d68007b768f7b9b2bd613bb7dd595615574284991aef47597d823","target":"record","created_at":"2026-05-18T01:58:52Z","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":"4ea21c0dfd6ef0d29a2bceeaaf3c639192861b6c2d628a0364230b6b6b496f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-12T02:29:05Z","title_canon_sha256":"cf3cfc603a80e0ca95f942e778e234ed967752d002d7ad982d7aef88dec18f59"},"schema_version":"1.0","source":{"id":"1201.2464","kind":"arxiv","version":1}},"canonical_sha256":"aa55bdfa9e0140121bf82c44624fa4c9aec1de33ace4cb61562b6e031a249b98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa55bdfa9e0140121bf82c44624fa4c9aec1de33ace4cb61562b6e031a249b98","first_computed_at":"2026-05-18T01:58:52.392716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:52.392716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6P0SqOQ9Qc4Pis/8h5h2x7wxMEKDcr3WBxZcupYUldI+HbiqPW1uVrX2sjkTpETls+jihnZtQL6JH3ylbvXCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:52.393347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d06200f6297d68007b768f7b9b2bd613bb7dd595615574284991aef47597d823","sha256:f769cf1c61d7093509a827821f735b43d08e49e4fbeda75ac90fad3fa586c998"],"state_sha256":"c7f6440c1eecbf2216b04ffadb757f3eadc0fcdedfcc003458f9dabf83b3f334"}