{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PB2H5VCFXFVO2SXL7JXJ6DR2SJ","short_pith_number":"pith:PB2H5VCF","canonical_record":{"source":{"id":"1203.0895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-05T12:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"4bca3ed2df1d3ff71b23ed76fb35d1197a9ed0f8bf80c2e3f6a342e4acd0ffe1","abstract_canon_sha256":"da2a555abaf76f05f08f7c017990eacc7152540a7b9c1d1feed30022d6666207"},"schema_version":"1.0"},"canonical_sha256":"78747ed445b96aed4aebfa6e9f0e3a925c252737a187f535ebb4d68893a9b3f8","source":{"kind":"arxiv","id":"1203.0895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0895","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0895v2","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0895","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"PB2H5VCFXFVO","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PB2H5VCFXFVO2SXL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PB2H5VCF","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PB2H5VCFXFVO2SXL7JXJ6DR2SJ","target":"record","payload":{"canonical_record":{"source":{"id":"1203.0895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-05T12:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"4bca3ed2df1d3ff71b23ed76fb35d1197a9ed0f8bf80c2e3f6a342e4acd0ffe1","abstract_canon_sha256":"da2a555abaf76f05f08f7c017990eacc7152540a7b9c1d1feed30022d6666207"},"schema_version":"1.0"},"canonical_sha256":"78747ed445b96aed4aebfa6e9f0e3a925c252737a187f535ebb4d68893a9b3f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:13.427039Z","signature_b64":"b4hDYHUAMbLPLHXlzhPSytN428VhucW17xJmTxiKO3mdgUsv1F4+a+Lfj6WVb7pWdu4/vDL1jLRnx6wS4ZG1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78747ed445b96aed4aebfa6e9f0e3a925c252737a187f535ebb4d68893a9b3f8","last_reissued_at":"2026-05-18T03:19:13.426621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:13.426621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.0895","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":"2026-05-18T03:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sf1SBJCEhqYMCm9HbJt3uJON+sqLB5tA1WSSdneWIkHMBMj2FaFIdk9lEr/UKlcigUl5kFYgKLFtyS47iHQMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:52:10.026884Z"},"content_sha256":"721a871f303dcd40247aeb24381043455c3541c0db353153f78058be74b29ff4","schema_version":"1.0","event_id":"sha256:721a871f303dcd40247aeb24381043455c3541c0db353153f78058be74b29ff4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PB2H5VCFXFVO2SXL7JXJ6DR2SJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of the optimal boundaries in reversible investment problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"CREST), Huyen Pham (LPMA, Salvatore Federico","submitted_at":"2012-03-05T12:56:58Z","abstract_excerpt":"This paper studies a {\\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as well as general cost functional. The resulting optimization problem leads to a degenerate two-dimensional bounded variation singular stochastic control problem, for which explicit solution is not available in general and the standard verification approach can not be applied a priori. We use a direct viscosity solutions approach for deriving some features of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0895","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":""},"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":"2026-05-18T03:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P0EdZgGtPbPsbpFiRGgQhsF9uB5TQpPgJoKGuP0bSzI4WPlP4Y0dUcczSmotdxbD67Jq3ccWuCQ+uKKot/22CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:52:10.027481Z"},"content_sha256":"c0231695bb5204e4edb46ce695076f97889ec51df8a713de724e79559fd8db1c","schema_version":"1.0","event_id":"sha256:c0231695bb5204e4edb46ce695076f97889ec51df8a713de724e79559fd8db1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ/bundle.json","state_url":"https://pith.science/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ/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":"2026-05-21T18:52:10Z","links":{"resolver":"https://pith.science/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ","bundle":"https://pith.science/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ/bundle.json","state":"https://pith.science/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PB2H5VCFXFVO2SXL7JXJ6DR2SJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PB2H5VCFXFVO2SXL7JXJ6DR2SJ","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":"da2a555abaf76f05f08f7c017990eacc7152540a7b9c1d1feed30022d6666207","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-05T12:56:58Z","title_canon_sha256":"4bca3ed2df1d3ff71b23ed76fb35d1197a9ed0f8bf80c2e3f6a342e4acd0ffe1"},"schema_version":"1.0","source":{"id":"1203.0895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0895","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0895v2","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0895","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"PB2H5VCFXFVO","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PB2H5VCFXFVO2SXL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PB2H5VCF","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:c0231695bb5204e4edb46ce695076f97889ec51df8a713de724e79559fd8db1c","target":"graph","created_at":"2026-05-18T03:19:13Z","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":"This paper studies a {\\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as well as general cost functional. The resulting optimization problem leads to a degenerate two-dimensional bounded variation singular stochastic control problem, for which explicit solution is not available in general and the standard verification approach can not be applied a priori. We use a direct viscosity solutions approach for deriving some features of ","authors_text":"CREST), Huyen Pham (LPMA, Salvatore Federico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-05T12:56:58Z","title":"Characterization of the optimal boundaries in reversible investment problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0895","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":"sha256:721a871f303dcd40247aeb24381043455c3541c0db353153f78058be74b29ff4","target":"record","created_at":"2026-05-18T03:19:13Z","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":"da2a555abaf76f05f08f7c017990eacc7152540a7b9c1d1feed30022d6666207","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-05T12:56:58Z","title_canon_sha256":"4bca3ed2df1d3ff71b23ed76fb35d1197a9ed0f8bf80c2e3f6a342e4acd0ffe1"},"schema_version":"1.0","source":{"id":"1203.0895","kind":"arxiv","version":2}},"canonical_sha256":"78747ed445b96aed4aebfa6e9f0e3a925c252737a187f535ebb4d68893a9b3f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78747ed445b96aed4aebfa6e9f0e3a925c252737a187f535ebb4d68893a9b3f8","first_computed_at":"2026-05-18T03:19:13.426621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:13.426621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4hDYHUAMbLPLHXlzhPSytN428VhucW17xJmTxiKO3mdgUsv1F4+a+Lfj6WVb7pWdu4/vDL1jLRnx6wS4ZG1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:13.427039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:721a871f303dcd40247aeb24381043455c3541c0db353153f78058be74b29ff4","sha256:c0231695bb5204e4edb46ce695076f97889ec51df8a713de724e79559fd8db1c"],"state_sha256":"3aa7854468c72e48c904942d83f4e35db8c04e4ca59ccc87b06d76b55463d3cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zV/bqw6+QZpqWaRq9AkEL//FwiGb2nOhWy9pT02m5kJ7BciIK/G/0n8mVwyFtjbPjBJxT1oC8Kn9HI4dHQzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T18:52:10.030578Z","bundle_sha256":"62e59c7e08dc8a6fad6c9addb9b17e5dc766b60b70918da519d695a0cbb230ec"}}