{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WET6S7XAMAG5VWSGSX743PCZ4Q","short_pith_number":"pith:WET6S7XA","canonical_record":{"source":{"id":"1507.05568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-20T17:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"bcaf7f5ea81e5ab64d04336e5c3e5635adf99cabd4aa81ef7eddc87949260b3f","abstract_canon_sha256":"37d5c34bb757a17bd440b4dba56675cc5a538e57bd3f405af6d89ec628b37422"},"schema_version":"1.0"},"canonical_sha256":"b127e97ee0600ddada4695ffcdbc59e425737a7915d28f6a19590929dc37c1d9","source":{"kind":"arxiv","id":"1507.05568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05568","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05568v1","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05568","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"WET6S7XAMAG5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WET6S7XAMAG5VWSG","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WET6S7XA","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WET6S7XAMAG5VWSGSX743PCZ4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-20T17:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"bcaf7f5ea81e5ab64d04336e5c3e5635adf99cabd4aa81ef7eddc87949260b3f","abstract_canon_sha256":"37d5c34bb757a17bd440b4dba56675cc5a538e57bd3f405af6d89ec628b37422"},"schema_version":"1.0"},"canonical_sha256":"b127e97ee0600ddada4695ffcdbc59e425737a7915d28f6a19590929dc37c1d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:36.483011Z","signature_b64":"muGtbqw+1kizZHGjwL43/hRG/b1apEJjt9jl1G346oI/3vMIWiu4qBMbDehYe8aUCW/M3eVCOCW1T/Atf5zYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b127e97ee0600ddada4695ffcdbc59e425737a7915d28f6a19590929dc37c1d9","last_reissued_at":"2026-05-18T01:36:36.482430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:36.482430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05568","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":"2026-05-18T01:36:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwtrQenfCXtmH7r/yY9orENBbXHn1fL1FGbQ4P+KwH8NTjyDorAqkYEM+BxkK2B2FMsx6sIma97VlA+LIKh1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:48.457012Z"},"content_sha256":"f5e05888fbb584b74dbe8168b05afecd6cdf0003078665439720ac4dc32c8168","schema_version":"1.0","event_id":"sha256:f5e05888fbb584b74dbe8168b05afecd6cdf0003078665439720ac4dc32c8168"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WET6S7XAMAG5VWSGSX743PCZ4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on observability of the wave equation with moving boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Bchatnia, K. Ammari, K. El Mufti","submitted_at":"2015-07-20T17:43:44Z","abstract_excerpt":"We deal with the wave equation with assigned moving boundary ($0<x<a(t)$) upon which Dirichlet or mixed boundary conditions are specified, here $a(t)$ is assumed to move slower than the light and periodically. Moreover $a$ is continuous, piecewise linear with two independent parameters. Our major concern will be an observation problem which is based measuring, at each $t>0$ of the transverse velocity at $a(t)$. The key to the results is the use of a reduction theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05568","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":"2026-05-18T01:36:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3TpmWkcQoNuqvgcjDwkds+nNxRznum8NQLihYvratggX/AAk7VWymJ5eJp6ekTFIBP3LvhhB5ipKH4G2D6HhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:48.457662Z"},"content_sha256":"5fa6737fa4dd298511eff7286fd05563eb5037fc6571d889e73407908025a823","schema_version":"1.0","event_id":"sha256:5fa6737fa4dd298511eff7286fd05563eb5037fc6571d889e73407908025a823"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WET6S7XAMAG5VWSGSX743PCZ4Q/bundle.json","state_url":"https://pith.science/pith/WET6S7XAMAG5VWSGSX743PCZ4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WET6S7XAMAG5VWSGSX743PCZ4Q/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":"2026-06-04T06:21:48Z","links":{"resolver":"https://pith.science/pith/WET6S7XAMAG5VWSGSX743PCZ4Q","bundle":"https://pith.science/pith/WET6S7XAMAG5VWSGSX743PCZ4Q/bundle.json","state":"https://pith.science/pith/WET6S7XAMAG5VWSGSX743PCZ4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WET6S7XAMAG5VWSGSX743PCZ4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WET6S7XAMAG5VWSGSX743PCZ4Q","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":"37d5c34bb757a17bd440b4dba56675cc5a538e57bd3f405af6d89ec628b37422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-20T17:43:44Z","title_canon_sha256":"bcaf7f5ea81e5ab64d04336e5c3e5635adf99cabd4aa81ef7eddc87949260b3f"},"schema_version":"1.0","source":{"id":"1507.05568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05568","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05568v1","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05568","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"WET6S7XAMAG5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WET6S7XAMAG5VWSG","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WET6S7XA","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:5fa6737fa4dd298511eff7286fd05563eb5037fc6571d889e73407908025a823","target":"graph","created_at":"2026-05-18T01:36:36Z","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 deal with the wave equation with assigned moving boundary ($0<x<a(t)$) upon which Dirichlet or mixed boundary conditions are specified, here $a(t)$ is assumed to move slower than the light and periodically. Moreover $a$ is continuous, piecewise linear with two independent parameters. Our major concern will be an observation problem which is based measuring, at each $t>0$ of the transverse velocity at $a(t)$. The key to the results is the use of a reduction theorem.","authors_text":"A. Bchatnia, K. Ammari, K. El Mufti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-20T17:43:44Z","title":"A remark on observability of the wave equation with moving boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05568","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:f5e05888fbb584b74dbe8168b05afecd6cdf0003078665439720ac4dc32c8168","target":"record","created_at":"2026-05-18T01:36:36Z","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":"37d5c34bb757a17bd440b4dba56675cc5a538e57bd3f405af6d89ec628b37422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-20T17:43:44Z","title_canon_sha256":"bcaf7f5ea81e5ab64d04336e5c3e5635adf99cabd4aa81ef7eddc87949260b3f"},"schema_version":"1.0","source":{"id":"1507.05568","kind":"arxiv","version":1}},"canonical_sha256":"b127e97ee0600ddada4695ffcdbc59e425737a7915d28f6a19590929dc37c1d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b127e97ee0600ddada4695ffcdbc59e425737a7915d28f6a19590929dc37c1d9","first_computed_at":"2026-05-18T01:36:36.482430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:36.482430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"muGtbqw+1kizZHGjwL43/hRG/b1apEJjt9jl1G346oI/3vMIWiu4qBMbDehYe8aUCW/M3eVCOCW1T/Atf5zYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:36.483011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5e05888fbb584b74dbe8168b05afecd6cdf0003078665439720ac4dc32c8168","sha256:5fa6737fa4dd298511eff7286fd05563eb5037fc6571d889e73407908025a823"],"state_sha256":"a3807a4628140d7ae200e36cb6575f2d93c957a6b47f0cd789e8972809ad4377"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKi22SG2UzKPVm+c0SDalRfouRwITiGc8mqsuFxqYpuQvQHAPAEhmtWjDAUAP2zXVu4yRAeQy/suuOx75nLSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:21:48.461236Z","bundle_sha256":"12a2cb3c39bb7cf11ee14656dba6d3be34794dfdfeca630c9287afab71e08eab"}}