{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QZXMMV52KSEYLRFY67ACCVPBM6","short_pith_number":"pith:QZXMMV52","canonical_record":{"source":{"id":"1707.03477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T22:09:47Z","cross_cats_sorted":[],"title_canon_sha256":"e935b94c9e33e7bf12d0e0b8533e58165628fc33a777faa8d3d0c311bbf409cc","abstract_canon_sha256":"8519078dde415a2fde816afad6c702d021efcfa7ef10a622321697ab92e22420"},"schema_version":"1.0"},"canonical_sha256":"866ec657ba548985c4b8f7c02155e167b5336c7243577fa6dbebec1bd7e97b43","source":{"kind":"arxiv","id":"1707.03477","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03477","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03477v1","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03477","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"QZXMMV52KSEY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZXMMV52KSEYLRFY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZXMMV52","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QZXMMV52KSEYLRFY67ACCVPBM6","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T22:09:47Z","cross_cats_sorted":[],"title_canon_sha256":"e935b94c9e33e7bf12d0e0b8533e58165628fc33a777faa8d3d0c311bbf409cc","abstract_canon_sha256":"8519078dde415a2fde816afad6c702d021efcfa7ef10a622321697ab92e22420"},"schema_version":"1.0"},"canonical_sha256":"866ec657ba548985c4b8f7c02155e167b5336c7243577fa6dbebec1bd7e97b43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:25.895676Z","signature_b64":"mPtLTkGpM6GTOHAjh06OcKnCPiB0r6+MzodnIO53BfDSBbUM9f6OyP2SqtD49LS3WWmeu8UKQ0VuwwBQmr2vDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"866ec657ba548985c4b8f7c02155e167b5336c7243577fa6dbebec1bd7e97b43","last_reissued_at":"2026-05-18T00:40:25.895066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:25.895066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03477","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":"2026-05-18T00:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yy5octQo+URmI0evTLy/qLme9eWQ386H7mn+SCPhf8snmhusawrDnLONW8IFteiNIh5Sq4TJDtWr9O5tA8PrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:24:07.194896Z"},"content_sha256":"35558c881b10b98183cb2a4c6ee9f04e3e7f0754321568efc602476a8bd666f7","schema_version":"1.0","event_id":"sha256:35558c881b10b98183cb2a4c6ee9f04e3e7f0754321568efc602476a8bd666f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QZXMMV52KSEYLRFY67ACCVPBM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Grazing Gaussian Beam","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"James Ralston, Neelesh Tiruviluamala","submitted_at":"2017-07-11T22:09:47Z","abstract_excerpt":"We consider Friedlander's wave equation in two space dimensions in the half-space x > 0 with the boundary condition u(x,y,t)=0 when x=0. For a Gaussian beam w(x,y,t;k) concentrated on a ray path that is tangent to x=0 at (x,y,t)=(0,0,0) we calculate the \"reflected\" wave z(x,y,t;k) in t > 0 such that w(x,y,t;k)+z(x,y,t;k) satisfies Friedlander's wave equation and vanishes on x=0. These computations are done to leading order in k on the ray path. The interaction of beams with boundaries has been studied for non-tangential beams and for beams gliding along the boundary. We find that the amplitude"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03477","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":"2026-05-18T00:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggng1Ab3PnzHirG986ccuzHw9HYXfGaXW1IY/aMiJJIj8KNMVliOtETCtL2A7lgZnBM6qlZKksbKla9v/l+2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:24:07.195260Z"},"content_sha256":"4175bb6638f679cc027535432de6bbf2b5e6094688285a083ea121f8ff854527","schema_version":"1.0","event_id":"sha256:4175bb6638f679cc027535432de6bbf2b5e6094688285a083ea121f8ff854527"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZXMMV52KSEYLRFY67ACCVPBM6/bundle.json","state_url":"https://pith.science/pith/QZXMMV52KSEYLRFY67ACCVPBM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZXMMV52KSEYLRFY67ACCVPBM6/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":"2026-05-28T03:24:07Z","links":{"resolver":"https://pith.science/pith/QZXMMV52KSEYLRFY67ACCVPBM6","bundle":"https://pith.science/pith/QZXMMV52KSEYLRFY67ACCVPBM6/bundle.json","state":"https://pith.science/pith/QZXMMV52KSEYLRFY67ACCVPBM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZXMMV52KSEYLRFY67ACCVPBM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QZXMMV52KSEYLRFY67ACCVPBM6","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":"8519078dde415a2fde816afad6c702d021efcfa7ef10a622321697ab92e22420","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T22:09:47Z","title_canon_sha256":"e935b94c9e33e7bf12d0e0b8533e58165628fc33a777faa8d3d0c311bbf409cc"},"schema_version":"1.0","source":{"id":"1707.03477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03477","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03477v1","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03477","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"QZXMMV52KSEY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZXMMV52KSEYLRFY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZXMMV52","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:4175bb6638f679cc027535432de6bbf2b5e6094688285a083ea121f8ff854527","target":"graph","created_at":"2026-05-18T00:40:25Z","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 consider Friedlander's wave equation in two space dimensions in the half-space x > 0 with the boundary condition u(x,y,t)=0 when x=0. For a Gaussian beam w(x,y,t;k) concentrated on a ray path that is tangent to x=0 at (x,y,t)=(0,0,0) we calculate the \"reflected\" wave z(x,y,t;k) in t > 0 such that w(x,y,t;k)+z(x,y,t;k) satisfies Friedlander's wave equation and vanishes on x=0. These computations are done to leading order in k on the ray path. The interaction of beams with boundaries has been studied for non-tangential beams and for beams gliding along the boundary. We find that the amplitude","authors_text":"James Ralston, Neelesh Tiruviluamala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T22:09:47Z","title":"A Grazing Gaussian Beam"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03477","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":"sha256:35558c881b10b98183cb2a4c6ee9f04e3e7f0754321568efc602476a8bd666f7","target":"record","created_at":"2026-05-18T00:40:25Z","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":"8519078dde415a2fde816afad6c702d021efcfa7ef10a622321697ab92e22420","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T22:09:47Z","title_canon_sha256":"e935b94c9e33e7bf12d0e0b8533e58165628fc33a777faa8d3d0c311bbf409cc"},"schema_version":"1.0","source":{"id":"1707.03477","kind":"arxiv","version":1}},"canonical_sha256":"866ec657ba548985c4b8f7c02155e167b5336c7243577fa6dbebec1bd7e97b43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"866ec657ba548985c4b8f7c02155e167b5336c7243577fa6dbebec1bd7e97b43","first_computed_at":"2026-05-18T00:40:25.895066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:25.895066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPtLTkGpM6GTOHAjh06OcKnCPiB0r6+MzodnIO53BfDSBbUM9f6OyP2SqtD49LS3WWmeu8UKQ0VuwwBQmr2vDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:25.895676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35558c881b10b98183cb2a4c6ee9f04e3e7f0754321568efc602476a8bd666f7","sha256:4175bb6638f679cc027535432de6bbf2b5e6094688285a083ea121f8ff854527"],"state_sha256":"9c8b63b16def80f8517a6bf628657a2144788c464db4f45e48b76ed65c25aeff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VXqcs1pIcR0hEQTJfnwO65uh1OeVISBOLBHAfORQlY31+RTldhjxCeqm2RORk1r/B01lknC8Jx0J/SuMdtDSCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:24:07.197215Z","bundle_sha256":"d8166b0fbdcd7d97049fe1cc09bc27fefca749e5cbbeb8845401f68d6883e7f1"}}