{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NBGK75N3GQ6D4EDYVU6MNWBB5Y","short_pith_number":"pith:NBGK75N3","canonical_record":{"source":{"id":"1905.01222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-03T15:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"17017620fa28bc5b784a97dcef982215e5af31d2feb5040f72526041d6055d41","abstract_canon_sha256":"81828b6ce9892d8a8ff0f101d53b19ae2331fc167ccbd49b9b59c43233e54fc0"},"schema_version":"1.0"},"canonical_sha256":"684caff5bb343c3e1078ad3cc6d821ee3666e9bee54c6cc3067708de68fbe8ed","source":{"kind":"arxiv","id":"1905.01222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01222","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01222v1","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01222","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"pith_short_12","alias_value":"NBGK75N3GQ6D","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NBGK75N3GQ6D4EDY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NBGK75N3","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NBGK75N3GQ6D4EDYVU6MNWBB5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-03T15:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"17017620fa28bc5b784a97dcef982215e5af31d2feb5040f72526041d6055d41","abstract_canon_sha256":"81828b6ce9892d8a8ff0f101d53b19ae2331fc167ccbd49b9b59c43233e54fc0"},"schema_version":"1.0"},"canonical_sha256":"684caff5bb343c3e1078ad3cc6d821ee3666e9bee54c6cc3067708de68fbe8ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:06.464779Z","signature_b64":"A8YRya73YnGS/2uy1OR1lkjrUrv4uV+Gc55x0cNVbbvXiNjPeNWiY9lwYEgCRJNDsijDrNzgcmml/d9fm+c/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"684caff5bb343c3e1078ad3cc6d821ee3666e9bee54c6cc3067708de68fbe8ed","last_reissued_at":"2026-05-17T23:47:06.464133Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:06.464133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01222","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":"2026-05-17T23:47:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6VLAEtwL04+fQc87CikGrdL+/6ZFfcKj1TbpyVm4JEGlRpxCv1wtEvOF+5M0kW09cBSecY4DX7zQu0rDqt2AAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:48:07.066931Z"},"content_sha256":"6ba02755bfa7b659b51275621c0aebd92ff6ad746e5220f34161355d8cd63e20","schema_version":"1.0","event_id":"sha256:6ba02755bfa7b659b51275621c0aebd92ff6ad746e5220f34161355d8cd63e20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NBGK75N3GQ6D4EDYVU6MNWBB5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Investment with Vintage Capital:Equilibrium Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fausto Gozzi, Peter M. Kort, Silvia Faggian","submitted_at":"2019-05-03T15:25:10Z","abstract_excerpt":"The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with \\textit{vintage capital}, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time $\\tau$ but also by age $s$. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable $s$ of ages. Investments in frontier as well as non-frontier vintages are possible. Firstly a general method is developed to compute and study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01222","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":"2026-05-17T23:47:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"naZmF707JAeaKRMtSovhRRXtGfi9jl4liadKhjju/rE1oLJ/nSEQJkgHTHKxvfomzuHmSKUhB8Ruy5kXvNjCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:48:07.067328Z"},"content_sha256":"061186a6e1779a73028d8ef22f156792862d8175ae299f3e0b69da2a5b4768df","schema_version":"1.0","event_id":"sha256:061186a6e1779a73028d8ef22f156792862d8175ae299f3e0b69da2a5b4768df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y/bundle.json","state_url":"https://pith.science/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y/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":"2026-07-01T13:48:07Z","links":{"resolver":"https://pith.science/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y","bundle":"https://pith.science/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y/bundle.json","state":"https://pith.science/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBGK75N3GQ6D4EDYVU6MNWBB5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NBGK75N3GQ6D4EDYVU6MNWBB5Y","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":"81828b6ce9892d8a8ff0f101d53b19ae2331fc167ccbd49b9b59c43233e54fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-03T15:25:10Z","title_canon_sha256":"17017620fa28bc5b784a97dcef982215e5af31d2feb5040f72526041d6055d41"},"schema_version":"1.0","source":{"id":"1905.01222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01222","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01222v1","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01222","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"pith_short_12","alias_value":"NBGK75N3GQ6D","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NBGK75N3GQ6D4EDY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NBGK75N3","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:061186a6e1779a73028d8ef22f156792862d8175ae299f3e0b69da2a5b4768df","target":"graph","created_at":"2026-05-17T23:47:06Z","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":"The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with \\textit{vintage capital}, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time $\\tau$ but also by age $s$. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable $s$ of ages. Investments in frontier as well as non-frontier vintages are possible. Firstly a general method is developed to compute and study ","authors_text":"Fausto Gozzi, Peter M. Kort, Silvia Faggian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-03T15:25:10Z","title":"Optimal Investment with Vintage Capital:Equilibrium Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01222","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":"sha256:6ba02755bfa7b659b51275621c0aebd92ff6ad746e5220f34161355d8cd63e20","target":"record","created_at":"2026-05-17T23:47:06Z","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":"81828b6ce9892d8a8ff0f101d53b19ae2331fc167ccbd49b9b59c43233e54fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-03T15:25:10Z","title_canon_sha256":"17017620fa28bc5b784a97dcef982215e5af31d2feb5040f72526041d6055d41"},"schema_version":"1.0","source":{"id":"1905.01222","kind":"arxiv","version":1}},"canonical_sha256":"684caff5bb343c3e1078ad3cc6d821ee3666e9bee54c6cc3067708de68fbe8ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"684caff5bb343c3e1078ad3cc6d821ee3666e9bee54c6cc3067708de68fbe8ed","first_computed_at":"2026-05-17T23:47:06.464133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:06.464133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A8YRya73YnGS/2uy1OR1lkjrUrv4uV+Gc55x0cNVbbvXiNjPeNWiY9lwYEgCRJNDsijDrNzgcmml/d9fm+c/Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:06.464779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba02755bfa7b659b51275621c0aebd92ff6ad746e5220f34161355d8cd63e20","sha256:061186a6e1779a73028d8ef22f156792862d8175ae299f3e0b69da2a5b4768df"],"state_sha256":"dae98e4f31235a814a2e09fab2e003e1e449a92e543c5394080605eb3c455342"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HutZWHnTBHLG98x3SBCWwiWolPIDWyyDSCBiD6uUpnXItVh5vQ2Vx5+32IRaDMcTSIQT3n8PMpZdqd9RTMCIBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T13:48:07.069419Z","bundle_sha256":"233daffc0ade6dcf07b04335d3e91a1aa71413b1038bac941e9ee700eae5e2a1"}}