{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WK77YHNQG7JMZXJIGUYUCQ7X3K","short_pith_number":"pith:WK77YHNQ","canonical_record":{"source":{"id":"1706.00229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-01T09:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"e65f0c86d6d854aecde34951cb1eba8625323a3bf0fceb0e251688b186ef2d63","abstract_canon_sha256":"7ad90e1a3437d3c669843f766287a282404b5cb0918500f5e966899f922789e8"},"schema_version":"1.0"},"canonical_sha256":"b2bffc1db037d2ccdd2835314143f7dabb21bdbf27a6116ca050648d58222d6d","source":{"kind":"arxiv","id":"1706.00229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00229","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00229v1","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00229","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"WK77YHNQG7JM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WK77YHNQG7JMZXJI","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WK77YHNQ","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WK77YHNQG7JMZXJIGUYUCQ7X3K","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-01T09:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"e65f0c86d6d854aecde34951cb1eba8625323a3bf0fceb0e251688b186ef2d63","abstract_canon_sha256":"7ad90e1a3437d3c669843f766287a282404b5cb0918500f5e966899f922789e8"},"schema_version":"1.0"},"canonical_sha256":"b2bffc1db037d2ccdd2835314143f7dabb21bdbf27a6116ca050648d58222d6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:14.682465Z","signature_b64":"cGIIwQLw436WJmE1obCfoxVQAZN5bYiUDEt5x6lN8mXggJjT/FrxRxZfGeNoVsbH2V9OA1taMSZMfGz6yC1fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2bffc1db037d2ccdd2835314143f7dabb21bdbf27a6116ca050648d58222d6d","last_reissued_at":"2026-05-18T00:43:14.681809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:14.681809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00229","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":"2026-05-18T00:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXMxrwNOmocoI+7LKfM1gXm9ULIJwah7qFG4kgufT0Z5eVb1Q0GlluyYorii+N4HoIqbizte8w3KAzCFesPeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:37:10.993551Z"},"content_sha256":"6723a4ee21d002d81d1caf866b83ba5859293f960fda03bf7fe5472632ece4fa","schema_version":"1.0","event_id":"sha256:6723a4ee21d002d81d1caf866b83ba5859293f960fda03bf7fe5472632ece4fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WK77YHNQG7JMZXJIGUYUCQ7X3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"${\\mathcal L}^1$ limit solutions in impulsive control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Caterina Sartori, Monica Motta","submitted_at":"2017-06-01T09:33:46Z","abstract_excerpt":"We consider a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization problems lacking coercivity, [1] proposed a notion of generalized solution x for this system, called {\\it limit solution,} associated to measurable u and v, and with u of possibly unbounded variation in [0,T]. As shown in [1], when u and x have bounded variation, such a solution (called in this case BV simple limit solution) coincides with the most used graph compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00229","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":"2026-05-18T00:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38bkxkOPw7iAVjSCJy8gc6JDmUbrXrsrblScCQ19dCQxiTBVppEwy+wPAlFaSwRSHbWmiazfJyM0Cu/LcSFUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:37:10.993893Z"},"content_sha256":"fcd2cbbc85837e691a670a8cb62e4e6f1c6716afb4bb1e0ff12733adbcbe339c","schema_version":"1.0","event_id":"sha256:fcd2cbbc85837e691a670a8cb62e4e6f1c6716afb4bb1e0ff12733adbcbe339c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K/bundle.json","state_url":"https://pith.science/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K/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":"2026-06-26T06:37:10Z","links":{"resolver":"https://pith.science/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K","bundle":"https://pith.science/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K/bundle.json","state":"https://pith.science/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WK77YHNQG7JMZXJIGUYUCQ7X3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WK77YHNQG7JMZXJIGUYUCQ7X3K","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":"7ad90e1a3437d3c669843f766287a282404b5cb0918500f5e966899f922789e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-01T09:33:46Z","title_canon_sha256":"e65f0c86d6d854aecde34951cb1eba8625323a3bf0fceb0e251688b186ef2d63"},"schema_version":"1.0","source":{"id":"1706.00229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00229","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00229v1","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00229","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"WK77YHNQG7JM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WK77YHNQG7JMZXJI","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WK77YHNQ","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:fcd2cbbc85837e691a670a8cb62e4e6f1c6716afb4bb1e0ff12733adbcbe339c","target":"graph","created_at":"2026-05-18T00:43:14Z","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 a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization problems lacking coercivity, [1] proposed a notion of generalized solution x for this system, called {\\it limit solution,} associated to measurable u and v, and with u of possibly unbounded variation in [0,T]. As shown in [1], when u and x have bounded variation, such a solution (called in this case BV simple limit solution) coincides with the most used graph compl","authors_text":"Caterina Sartori, Monica Motta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-01T09:33:46Z","title":"${\\mathcal L}^1$ limit solutions in impulsive control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00229","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":"sha256:6723a4ee21d002d81d1caf866b83ba5859293f960fda03bf7fe5472632ece4fa","target":"record","created_at":"2026-05-18T00:43:14Z","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":"7ad90e1a3437d3c669843f766287a282404b5cb0918500f5e966899f922789e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-01T09:33:46Z","title_canon_sha256":"e65f0c86d6d854aecde34951cb1eba8625323a3bf0fceb0e251688b186ef2d63"},"schema_version":"1.0","source":{"id":"1706.00229","kind":"arxiv","version":1}},"canonical_sha256":"b2bffc1db037d2ccdd2835314143f7dabb21bdbf27a6116ca050648d58222d6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2bffc1db037d2ccdd2835314143f7dabb21bdbf27a6116ca050648d58222d6d","first_computed_at":"2026-05-18T00:43:14.681809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:14.681809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGIIwQLw436WJmE1obCfoxVQAZN5bYiUDEt5x6lN8mXggJjT/FrxRxZfGeNoVsbH2V9OA1taMSZMfGz6yC1fBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:14.682465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6723a4ee21d002d81d1caf866b83ba5859293f960fda03bf7fe5472632ece4fa","sha256:fcd2cbbc85837e691a670a8cb62e4e6f1c6716afb4bb1e0ff12733adbcbe339c"],"state_sha256":"2920317936121e4440661d2b2617a63bfd49dd6e8b50d45fcb7a3f961b55b333"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"78tu/10tMi4TzND1dOoMwh8NG/+mgBjPaREkxrBw7HcvdbjH8tEbQu3zbu+rRSqrhuKSuMEyJGC63JyRWfYZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T06:37:10.996151Z","bundle_sha256":"9de32b63822266baed97543782ed0af6cde580a379821215dfdfc72d74992324"}}