{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AMLQS4XRMTM5NK3VIIUTKJOHRG","short_pith_number":"pith:AMLQS4XR","canonical_record":{"source":{"id":"2411.16029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T01:08:41Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"44f2477b00a7110a74913b0e28a3044ddd99183a82320ce66c99d66c16f8e8b4","abstract_canon_sha256":"c46b4b766ebfae1f3f45f8193c34b95a1a410d4d03d2dc09b2e131c5ad87a07e"},"schema_version":"1.0"},"canonical_sha256":"03170972f164d9d6ab7542293525c7899409d4490b38af7474c2574715c9efc1","source":{"kind":"arxiv","id":"2411.16029","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16029","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16029v2","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16029","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"AMLQS4XRMTM5","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"pith_short_16","alias_value":"AMLQS4XRMTM5NK3V","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"pith_short_8","alias_value":"AMLQS4XR","created_at":"2026-07-05T10:56:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AMLQS4XRMTM5NK3VIIUTKJOHRG","target":"record","payload":{"canonical_record":{"source":{"id":"2411.16029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T01:08:41Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"44f2477b00a7110a74913b0e28a3044ddd99183a82320ce66c99d66c16f8e8b4","abstract_canon_sha256":"c46b4b766ebfae1f3f45f8193c34b95a1a410d4d03d2dc09b2e131c5ad87a07e"},"schema_version":"1.0"},"canonical_sha256":"03170972f164d9d6ab7542293525c7899409d4490b38af7474c2574715c9efc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:56:12.620171Z","signature_b64":"2mGl6L5zisconDw6bapDeciMZk39SDaiNddTSIiiJjJ90RRLSgxEJ3YEYdn2L0YIBE2qn1ylAa8dtHLMB1GLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03170972f164d9d6ab7542293525c7899409d4490b38af7474c2574715c9efc1","last_reissued_at":"2026-07-05T10:56:12.619690Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:56:12.619690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.16029","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pWhdQisi4WSrW9/i5tVvVCdYfTTHpdMZqopZIEAnkDOh3tk+m4F6K9RhH3Ob/M8mRXNOul2CoN1DCJzule8ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:05:26.433656Z"},"content_sha256":"78466d831f132bb4af2e4618e249593f36cbdf3853ff569f1a31e434a0f3d68d","schema_version":"1.0","event_id":"sha256:78466d831f132bb4af2e4618e249593f36cbdf3853ff569f1a31e434a0f3d68d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AMLQS4XRMTM5NK3VIIUTKJOHRG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Junyong Zhang, Qiuye Jia","submitted_at":"2024-11-25T01:08:41Z","abstract_excerpt":"We study the pointwise decay estimates for the Schr\\\"odinger and wave equations on a product cone $(X,g)$, where the metric $g=dr^2+r^2 h$ and $X=C(Y)=(0,\\infty)\\times Y$ is a product cone over the closed Riemannian manifold $(Y,h)$ with metric $h$. Under the assumption that the conjugate radius $\\epsilon$ of $Y$ satisfies $\\epsilon>\\pi$, we prove the pointwise dispersive estimates for the Schr\\\"odinger and half-wave propagator in this setting. The key ingredient is the modified Hadamard parametrix on $Y$ in which the role of the conjugate points does not come to play if $\\epsilon>\\pi$. In a w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16029","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16029/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"72ktK/OgTBSiwgb+y491H8Rh1D8u7k74ZUQL2PfvijOpsHDbZwpoM88EKkd6sDs+UJlsu9+uTi+oXhznY7hPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:05:26.434300Z"},"content_sha256":"9b8f21ea67d4d56e91a2a938cf83c60bdc986f85dfd94715754ab2ed97f853b4","schema_version":"1.0","event_id":"sha256:9b8f21ea67d4d56e91a2a938cf83c60bdc986f85dfd94715754ab2ed97f853b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG/bundle.json","state_url":"https://pith.science/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG/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":"2026-07-07T05:05:26Z","links":{"resolver":"https://pith.science/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG","bundle":"https://pith.science/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG/bundle.json","state":"https://pith.science/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMLQS4XRMTM5NK3VIIUTKJOHRG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AMLQS4XRMTM5NK3VIIUTKJOHRG","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":"c46b4b766ebfae1f3f45f8193c34b95a1a410d4d03d2dc09b2e131c5ad87a07e","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T01:08:41Z","title_canon_sha256":"44f2477b00a7110a74913b0e28a3044ddd99183a82320ce66c99d66c16f8e8b4"},"schema_version":"1.0","source":{"id":"2411.16029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16029","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16029v2","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16029","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"AMLQS4XRMTM5","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"pith_short_16","alias_value":"AMLQS4XRMTM5NK3V","created_at":"2026-07-05T10:56:12Z"},{"alias_kind":"pith_short_8","alias_value":"AMLQS4XR","created_at":"2026-07-05T10:56:12Z"}],"graph_snapshots":[{"event_id":"sha256:9b8f21ea67d4d56e91a2a938cf83c60bdc986f85dfd94715754ab2ed97f853b4","target":"graph","created_at":"2026-07-05T10:56:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.16029/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the pointwise decay estimates for the Schr\\\"odinger and wave equations on a product cone $(X,g)$, where the metric $g=dr^2+r^2 h$ and $X=C(Y)=(0,\\infty)\\times Y$ is a product cone over the closed Riemannian manifold $(Y,h)$ with metric $h$. Under the assumption that the conjugate radius $\\epsilon$ of $Y$ satisfies $\\epsilon>\\pi$, we prove the pointwise dispersive estimates for the Schr\\\"odinger and half-wave propagator in this setting. The key ingredient is the modified Hadamard parametrix on $Y$ in which the role of the conjugate points does not come to play if $\\epsilon>\\pi$. In a w","authors_text":"Junyong Zhang, Qiuye Jia","cross_cats":["math.DG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T01:08:41Z","title":"Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16029","kind":"arxiv","version":2},"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":"sha256:78466d831f132bb4af2e4618e249593f36cbdf3853ff569f1a31e434a0f3d68d","target":"record","created_at":"2026-07-05T10:56:12Z","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":"c46b4b766ebfae1f3f45f8193c34b95a1a410d4d03d2dc09b2e131c5ad87a07e","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T01:08:41Z","title_canon_sha256":"44f2477b00a7110a74913b0e28a3044ddd99183a82320ce66c99d66c16f8e8b4"},"schema_version":"1.0","source":{"id":"2411.16029","kind":"arxiv","version":2}},"canonical_sha256":"03170972f164d9d6ab7542293525c7899409d4490b38af7474c2574715c9efc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03170972f164d9d6ab7542293525c7899409d4490b38af7474c2574715c9efc1","first_computed_at":"2026-07-05T10:56:12.619690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:56:12.619690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2mGl6L5zisconDw6bapDeciMZk39SDaiNddTSIiiJjJ90RRLSgxEJ3YEYdn2L0YIBE2qn1ylAa8dtHLMB1GLAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:56:12.620171Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78466d831f132bb4af2e4618e249593f36cbdf3853ff569f1a31e434a0f3d68d","sha256:9b8f21ea67d4d56e91a2a938cf83c60bdc986f85dfd94715754ab2ed97f853b4"],"state_sha256":"56b75c4ea8350d273c69ed3674c04b062b22a1daaa48354966362a456c06756f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+WndZw/gtgqb60aDkdSG/PJltJq+NOC6eKb0uBmKKLyuUfDfr/cwRIszFBMrupsP5ymMvduFOy5YkCLoiWlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:05:26.437814Z","bundle_sha256":"8da7e1cdc014860977265397757e60ae2bc0c0a547cedf73de43bc2e9f8eabab"}}