{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LZQI6O6WFOHV2ABICB7VM5URI6","short_pith_number":"pith:LZQI6O6W","canonical_record":{"source":{"id":"1608.07784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-28T08:13:55Z","cross_cats_sorted":[],"title_canon_sha256":"ef1b2363a6d40cff5632d7c0cf68e08dc7a9ec56e597fb3e57983f3e4f3133e4","abstract_canon_sha256":"95845ba3e587482f90834e6fc908d43679845d959f97dfc3d397c117544f59e9"},"schema_version":"1.0"},"canonical_sha256":"5e608f3bd62b8f5d0028107f56769147aaaa966f88a00e1d30b45f844ec68665","source":{"kind":"arxiv","id":"1608.07784","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07784","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07784v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07784","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"LZQI6O6WFOHV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LZQI6O6WFOHV2ABI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LZQI6O6W","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LZQI6O6WFOHV2ABICB7VM5URI6","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-28T08:13:55Z","cross_cats_sorted":[],"title_canon_sha256":"ef1b2363a6d40cff5632d7c0cf68e08dc7a9ec56e597fb3e57983f3e4f3133e4","abstract_canon_sha256":"95845ba3e587482f90834e6fc908d43679845d959f97dfc3d397c117544f59e9"},"schema_version":"1.0"},"canonical_sha256":"5e608f3bd62b8f5d0028107f56769147aaaa966f88a00e1d30b45f844ec68665","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:49.924251Z","signature_b64":"EkX5g8pKZ8PHBSQ/VFHG1jxxFK+CTFhvmMDPBB41bz43HJlgBuBN3DXGPjBnrCqWOIX0H8F103+KW9AqIwk4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e608f3bd62b8f5d0028107f56769147aaaa966f88a00e1d30b45f844ec68665","last_reissued_at":"2026-05-18T01:07:49.923669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:49.923669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07784","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zet9YicMLjdgVl48G1epoNfrSD7EcklhT+0xNF8AlwaXdlfCZc6Vnzf3S0CmFJRKEz9IfdMJQIgpejwzdb1yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:00:21.556207Z"},"content_sha256":"94962c54c475b7ed302cc6a0e5403090c3c1f21903aa3eeeda0746d7fc523df8","schema_version":"1.0","event_id":"sha256:94962c54c475b7ed302cc6a0e5403090c3c1f21903aa3eeeda0746d7fc523df8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LZQI6O6WFOHV2ABICB7VM5URI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decay estimates for fractional wave equations on H-type groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Manli Song","submitted_at":"2016-08-28T08:13:55Z","abstract_excerpt":"The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by $e^{it\\Delta^\\alpha}$, $0<\\alpha<1$. Combing the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07784","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HrOGFMqeWeGbx6Kdbq333W5aoN4X/nSkSaqzjjBh68tf6DObEMQlTmpy6myLZD863MxObgU+dmqU9pjy9BFcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:00:21.556742Z"},"content_sha256":"5df9f8f4a0503c5ce860a5acf1ddc788105a9f2e159cddc2bcd5ad3a3eaf9889","schema_version":"1.0","event_id":"sha256:5df9f8f4a0503c5ce860a5acf1ddc788105a9f2e159cddc2bcd5ad3a3eaf9889"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZQI6O6WFOHV2ABICB7VM5URI6/bundle.json","state_url":"https://pith.science/pith/LZQI6O6WFOHV2ABICB7VM5URI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZQI6O6WFOHV2ABICB7VM5URI6/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":"2026-06-07T12:00:21Z","links":{"resolver":"https://pith.science/pith/LZQI6O6WFOHV2ABICB7VM5URI6","bundle":"https://pith.science/pith/LZQI6O6WFOHV2ABICB7VM5URI6/bundle.json","state":"https://pith.science/pith/LZQI6O6WFOHV2ABICB7VM5URI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZQI6O6WFOHV2ABICB7VM5URI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LZQI6O6WFOHV2ABICB7VM5URI6","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":"95845ba3e587482f90834e6fc908d43679845d959f97dfc3d397c117544f59e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-28T08:13:55Z","title_canon_sha256":"ef1b2363a6d40cff5632d7c0cf68e08dc7a9ec56e597fb3e57983f3e4f3133e4"},"schema_version":"1.0","source":{"id":"1608.07784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07784","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07784v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07784","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"LZQI6O6WFOHV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LZQI6O6WFOHV2ABI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LZQI6O6W","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:5df9f8f4a0503c5ce860a5acf1ddc788105a9f2e159cddc2bcd5ad3a3eaf9889","target":"graph","created_at":"2026-05-18T01:07:49Z","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":"The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by $e^{it\\Delta^\\alpha}$, $0<\\alpha<1$. Combing the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalties.","authors_text":"Manli Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-28T08:13:55Z","title":"Decay estimates for fractional wave equations on H-type groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07784","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":"sha256:94962c54c475b7ed302cc6a0e5403090c3c1f21903aa3eeeda0746d7fc523df8","target":"record","created_at":"2026-05-18T01:07:49Z","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":"95845ba3e587482f90834e6fc908d43679845d959f97dfc3d397c117544f59e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-28T08:13:55Z","title_canon_sha256":"ef1b2363a6d40cff5632d7c0cf68e08dc7a9ec56e597fb3e57983f3e4f3133e4"},"schema_version":"1.0","source":{"id":"1608.07784","kind":"arxiv","version":1}},"canonical_sha256":"5e608f3bd62b8f5d0028107f56769147aaaa966f88a00e1d30b45f844ec68665","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e608f3bd62b8f5d0028107f56769147aaaa966f88a00e1d30b45f844ec68665","first_computed_at":"2026-05-18T01:07:49.923669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:49.923669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EkX5g8pKZ8PHBSQ/VFHG1jxxFK+CTFhvmMDPBB41bz43HJlgBuBN3DXGPjBnrCqWOIX0H8F103+KW9AqIwk4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:49.924251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94962c54c475b7ed302cc6a0e5403090c3c1f21903aa3eeeda0746d7fc523df8","sha256:5df9f8f4a0503c5ce860a5acf1ddc788105a9f2e159cddc2bcd5ad3a3eaf9889"],"state_sha256":"0b80cfa0e7498ef9ec8947d91c26924f9b313898b32f4da01713ac1daa561982"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vPeME71LtFVmUzd8t63mOYWycMrvKxA+wrjYJsIRjy5yKVOyVLzSKoiC7IuDAYX5GQvQsiUQIsFF0P0EpZyDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T12:00:21.559497Z","bundle_sha256":"2d72dfd810333fb56155067bdd207950b49b708cd7314cd748b31827fc8ee9d8"}}