{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M73VPWXUEJCV3LYLDDQ62AABJS","short_pith_number":"pith:M73VPWXU","canonical_record":{"source":{"id":"1501.02006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-08T23:26:46Z","cross_cats_sorted":[],"title_canon_sha256":"43de4798070c4c7d2c3acd0a7d12dda2fdf55f62e7dd77875c936824ff15e116","abstract_canon_sha256":"31c6df7b437cec4a1b3c1bdb687f912a140b777c8f9e1aa65fc7779e71ee3e99"},"schema_version":"1.0"},"canonical_sha256":"67f757daf422455daf0b18e1ed00014cbb8e7cee2a9234d2884dadd070422f25","source":{"kind":"arxiv","id":"1501.02006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02006","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02006v1","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02006","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"M73VPWXUEJCV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M73VPWXUEJCV3LYL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M73VPWXU","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M73VPWXUEJCV3LYLDDQ62AABJS","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-08T23:26:46Z","cross_cats_sorted":[],"title_canon_sha256":"43de4798070c4c7d2c3acd0a7d12dda2fdf55f62e7dd77875c936824ff15e116","abstract_canon_sha256":"31c6df7b437cec4a1b3c1bdb687f912a140b777c8f9e1aa65fc7779e71ee3e99"},"schema_version":"1.0"},"canonical_sha256":"67f757daf422455daf0b18e1ed00014cbb8e7cee2a9234d2884dadd070422f25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:55.672865Z","signature_b64":"mYMPWWionY8w0Gv4tPQmJBpYjx/MCdReY3zHJ5WxXZEaz4LXl2y0Fg51vQVJE+nb67pg2j1MDDZghHuS7463BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67f757daf422455daf0b18e1ed00014cbb8e7cee2a9234d2884dadd070422f25","last_reissued_at":"2026-05-18T00:30:55.672167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:55.672167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02006","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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NcQ+WNow5/0OaHCLDUfWJayN85dSrCbRV1cGYnESr7bKhglNM0fNcDuUat3MSe9XeBN8v7pusmJ8KqRGtwr+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:08:31.915426Z"},"content_sha256":"cc6691a38e882292f9cbbfb89c1cd0afed1a8985e8258199fe1710b48b111931","schema_version":"1.0","event_id":"sha256:cc6691a38e882292f9cbbfb89c1cd0afed1a8985e8258199fe1710b48b111931"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M73VPWXUEJCV3LYLDDQ62AABJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving two-point boundary value problems for a wave equation via the principle of stationary action and optimal control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Peter M. Dower, William M. McEneaney","submitted_at":"2015-01-08T23:26:46Z","abstract_excerpt":"A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In particular, an infinite dimensional optimal control problem is posed so that the wave equation dynamics and temporal boundary data of interest are captured via the characteristics of the associated Hamiltonian and choice of terminal payoff respectively. In order to solve this optimal control problem for any such terminal payoff, and hence solve any two-point boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02006","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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKaqJFLtUGXf6LoEzR5GTd2t3peHXhPWWei4gKWBvXLCdYUepKfW7Cb1ZoiA9Pvhs7NFdbDVdRiNU3+X59S9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:08:31.916219Z"},"content_sha256":"cfc1d0019cf1c7de03165b230880f20262eafe68eedc475f9e62cbed25fb20b8","schema_version":"1.0","event_id":"sha256:cfc1d0019cf1c7de03165b230880f20262eafe68eedc475f9e62cbed25fb20b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M73VPWXUEJCV3LYLDDQ62AABJS/bundle.json","state_url":"https://pith.science/pith/M73VPWXUEJCV3LYLDDQ62AABJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M73VPWXUEJCV3LYLDDQ62AABJS/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":"2026-06-09T19:08:31Z","links":{"resolver":"https://pith.science/pith/M73VPWXUEJCV3LYLDDQ62AABJS","bundle":"https://pith.science/pith/M73VPWXUEJCV3LYLDDQ62AABJS/bundle.json","state":"https://pith.science/pith/M73VPWXUEJCV3LYLDDQ62AABJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M73VPWXUEJCV3LYLDDQ62AABJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M73VPWXUEJCV3LYLDDQ62AABJS","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":"31c6df7b437cec4a1b3c1bdb687f912a140b777c8f9e1aa65fc7779e71ee3e99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-08T23:26:46Z","title_canon_sha256":"43de4798070c4c7d2c3acd0a7d12dda2fdf55f62e7dd77875c936824ff15e116"},"schema_version":"1.0","source":{"id":"1501.02006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02006","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02006v1","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02006","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"M73VPWXUEJCV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M73VPWXUEJCV3LYL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M73VPWXU","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:cfc1d0019cf1c7de03165b230880f20262eafe68eedc475f9e62cbed25fb20b8","target":"graph","created_at":"2026-05-18T00:30:55Z","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":"A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In particular, an infinite dimensional optimal control problem is posed so that the wave equation dynamics and temporal boundary data of interest are captured via the characteristics of the associated Hamiltonian and choice of terminal payoff respectively. In order to solve this optimal control problem for any such terminal payoff, and hence solve any two-point boun","authors_text":"Peter M. Dower, William M. McEneaney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-08T23:26:46Z","title":"Solving two-point boundary value problems for a wave equation via the principle of stationary action and optimal control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02006","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:cc6691a38e882292f9cbbfb89c1cd0afed1a8985e8258199fe1710b48b111931","target":"record","created_at":"2026-05-18T00:30:55Z","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":"31c6df7b437cec4a1b3c1bdb687f912a140b777c8f9e1aa65fc7779e71ee3e99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-08T23:26:46Z","title_canon_sha256":"43de4798070c4c7d2c3acd0a7d12dda2fdf55f62e7dd77875c936824ff15e116"},"schema_version":"1.0","source":{"id":"1501.02006","kind":"arxiv","version":1}},"canonical_sha256":"67f757daf422455daf0b18e1ed00014cbb8e7cee2a9234d2884dadd070422f25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67f757daf422455daf0b18e1ed00014cbb8e7cee2a9234d2884dadd070422f25","first_computed_at":"2026-05-18T00:30:55.672167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:55.672167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mYMPWWionY8w0Gv4tPQmJBpYjx/MCdReY3zHJ5WxXZEaz4LXl2y0Fg51vQVJE+nb67pg2j1MDDZghHuS7463BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:55.672865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc6691a38e882292f9cbbfb89c1cd0afed1a8985e8258199fe1710b48b111931","sha256:cfc1d0019cf1c7de03165b230880f20262eafe68eedc475f9e62cbed25fb20b8"],"state_sha256":"36968e92021098367673a86b3a44d6ae9ffb1c7a34313b0618701e663239b5e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kJ72/RIRY8bIZMiKbZni669IQajKnJx4ASGlhk6SztjcYa1ZDpdiMaTGd8+V4VgH9sjh9Ib7StSGzoBwNDJyDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:08:31.920505Z","bundle_sha256":"22fb08cbc2fe96f09c05627caa0a887edd09ba13c1146421fdc6cd73d3e10d76"}}