{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6S4EBP6KSTFUCJED5SKRF733FC","short_pith_number":"pith:6S4EBP6K","canonical_record":{"source":{"id":"1410.8829","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-31T18:00:33Z","cross_cats_sorted":[],"title_canon_sha256":"88a1443cd2ec93b48b734528c05df4e2d0217b7151a45d71985bd02035545d56","abstract_canon_sha256":"d4e27d221a248ac90540727fa18988a4dd7844331705e2d27c0751d920056acc"},"schema_version":"1.0"},"canonical_sha256":"f4b840bfca94cb412483ec9512ff7b2888db3e773ec2862581533c8f8221d624","source":{"kind":"arxiv","id":"1410.8829","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8829","created_at":"2026-05-18T01:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8829v4","created_at":"2026-05-18T01:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8829","created_at":"2026-05-18T01:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"6S4EBP6KSTFU","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6S4EBP6KSTFUCJED","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6S4EBP6K","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6S4EBP6KSTFUCJED5SKRF733FC","target":"record","payload":{"canonical_record":{"source":{"id":"1410.8829","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-31T18:00:33Z","cross_cats_sorted":[],"title_canon_sha256":"88a1443cd2ec93b48b734528c05df4e2d0217b7151a45d71985bd02035545d56","abstract_canon_sha256":"d4e27d221a248ac90540727fa18988a4dd7844331705e2d27c0751d920056acc"},"schema_version":"1.0"},"canonical_sha256":"f4b840bfca94cb412483ec9512ff7b2888db3e773ec2862581533c8f8221d624","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:25.404303Z","signature_b64":"Fmx6CqUs5qz7Lj/WoquwI9ohgUkmhif5MwEeNlDOfAPY7TdFfZqGiAlyPdR+o+u0b2KN8mJg1x+5iq/novKsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4b840bfca94cb412483ec9512ff7b2888db3e773ec2862581533c8f8221d624","last_reissued_at":"2026-05-18T01:34:25.403874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:25.403874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.8829","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USxTNwtc3qt0pb1p8yaixeWs3NzHa5T4UfBZrRNc3JRiLnYcUNz3ld+zR7Mk4kecoRq5TOymbGDXsHzsmvLyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:53:43.616549Z"},"content_sha256":"e99f9f9e7f1a7c80c2f17bb2765936543221d300664663746bf1123d235f8a80","schema_version":"1.0","event_id":"sha256:e99f9f9e7f1a7c80c2f17bb2765936543221d300664663746bf1123d235f8a80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6S4EBP6KSTFUCJED5SKRF733FC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersive Estimates for Scalar and Matrix Schr\\\"odinger operators on $\\mathbb{H}^{n+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Borthwick, Jeremy L. Marzuola","submitted_at":"2014-10-31T18:00:33Z","abstract_excerpt":"We study resolvent estimates, spectral theory and long time dispersive properties of scalar and matrix Schr\\\"odinger-type operators on $\\mathbb{H}^{n+1}$ for $n \\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8829","kind":"arxiv","version":4},"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":"2026-05-18T01:34:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QHKoSiO25vlJ8IVHc8xWlkbhd/wxtzi53qLHfSr2hwkMN77P4l1z8p1ID+QbOfFDIuoDYjFJIM7/iuwJhwvrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:53:43.616917Z"},"content_sha256":"27c6402eef58fd9b6f3c21faa1b149f057945035bbac8f50e2ab0f2eccfba047","schema_version":"1.0","event_id":"sha256:27c6402eef58fd9b6f3c21faa1b149f057945035bbac8f50e2ab0f2eccfba047"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6S4EBP6KSTFUCJED5SKRF733FC/bundle.json","state_url":"https://pith.science/pith/6S4EBP6KSTFUCJED5SKRF733FC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6S4EBP6KSTFUCJED5SKRF733FC/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":"2026-05-30T03:53:43Z","links":{"resolver":"https://pith.science/pith/6S4EBP6KSTFUCJED5SKRF733FC","bundle":"https://pith.science/pith/6S4EBP6KSTFUCJED5SKRF733FC/bundle.json","state":"https://pith.science/pith/6S4EBP6KSTFUCJED5SKRF733FC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6S4EBP6KSTFUCJED5SKRF733FC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6S4EBP6KSTFUCJED5SKRF733FC","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":"d4e27d221a248ac90540727fa18988a4dd7844331705e2d27c0751d920056acc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-31T18:00:33Z","title_canon_sha256":"88a1443cd2ec93b48b734528c05df4e2d0217b7151a45d71985bd02035545d56"},"schema_version":"1.0","source":{"id":"1410.8829","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8829","created_at":"2026-05-18T01:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8829v4","created_at":"2026-05-18T01:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8829","created_at":"2026-05-18T01:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"6S4EBP6KSTFU","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6S4EBP6KSTFUCJED","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6S4EBP6K","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:27c6402eef58fd9b6f3c21faa1b149f057945035bbac8f50e2ab0f2eccfba047","target":"graph","created_at":"2026-05-18T01:34:25Z","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 resolvent estimates, spectral theory and long time dispersive properties of scalar and matrix Schr\\\"odinger-type operators on $\\mathbb{H}^{n+1}$ for $n \\geq 1$.","authors_text":"David Borthwick, Jeremy L. Marzuola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-31T18:00:33Z","title":"Dispersive Estimates for Scalar and Matrix Schr\\\"odinger operators on $\\mathbb{H}^{n+1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8829","kind":"arxiv","version":4},"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:e99f9f9e7f1a7c80c2f17bb2765936543221d300664663746bf1123d235f8a80","target":"record","created_at":"2026-05-18T01:34:25Z","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":"d4e27d221a248ac90540727fa18988a4dd7844331705e2d27c0751d920056acc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-31T18:00:33Z","title_canon_sha256":"88a1443cd2ec93b48b734528c05df4e2d0217b7151a45d71985bd02035545d56"},"schema_version":"1.0","source":{"id":"1410.8829","kind":"arxiv","version":4}},"canonical_sha256":"f4b840bfca94cb412483ec9512ff7b2888db3e773ec2862581533c8f8221d624","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4b840bfca94cb412483ec9512ff7b2888db3e773ec2862581533c8f8221d624","first_computed_at":"2026-05-18T01:34:25.403874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:25.403874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fmx6CqUs5qz7Lj/WoquwI9ohgUkmhif5MwEeNlDOfAPY7TdFfZqGiAlyPdR+o+u0b2KN8mJg1x+5iq/novKsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:25.404303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8829","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e99f9f9e7f1a7c80c2f17bb2765936543221d300664663746bf1123d235f8a80","sha256:27c6402eef58fd9b6f3c21faa1b149f057945035bbac8f50e2ab0f2eccfba047"],"state_sha256":"0beec3dd16f31d20b421cab198193205839e2b4052980b88888d1d1cfa13afcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2RXgvJi2t49pxVwn3IMQoPsQfL8h6j2rAa1A+lMZGFZxqGt6VmL1mKa6g9n5PbMGixQdrSA2hE5rbQwvQe3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:53:43.619252Z","bundle_sha256":"39fefd63fdfca2f2e6d0836cc68ba1949a265529da1f9f9d42dfaf5206e7b1d5"}}