{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QO5Q3O47UO3XSOYY3G7Y6TONZO","short_pith_number":"pith:QO5Q3O47","canonical_record":{"source":{"id":"1409.5225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-18T08:26:56Z","cross_cats_sorted":[],"title_canon_sha256":"d72e12a57ccf5a560c7b900e019655a0c256317fe2ad731e3369b59a44475034","abstract_canon_sha256":"ed2408c2eac34a7de5ea5731d9d4ac6bdb53d2004ef18e80f9bfe5e2cc730a5e"},"schema_version":"1.0"},"canonical_sha256":"83bb0dbb9fa3b7793b18d9bf8f4dcdcbb11ff22053e50ca94c312ff1484dd774","source":{"kind":"arxiv","id":"1409.5225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5225","created_at":"2026-05-18T02:42:30Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5225v1","created_at":"2026-05-18T02:42:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5225","created_at":"2026-05-18T02:42:30Z"},{"alias_kind":"pith_short_12","alias_value":"QO5Q3O47UO3X","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QO5Q3O47UO3XSOYY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QO5Q3O47","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QO5Q3O47UO3XSOYY3G7Y6TONZO","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-18T08:26:56Z","cross_cats_sorted":[],"title_canon_sha256":"d72e12a57ccf5a560c7b900e019655a0c256317fe2ad731e3369b59a44475034","abstract_canon_sha256":"ed2408c2eac34a7de5ea5731d9d4ac6bdb53d2004ef18e80f9bfe5e2cc730a5e"},"schema_version":"1.0"},"canonical_sha256":"83bb0dbb9fa3b7793b18d9bf8f4dcdcbb11ff22053e50ca94c312ff1484dd774","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:30.290026Z","signature_b64":"QrlhbVC+GLU8Xft+a24LjJ0YcMRNyywqGomORxz9NG3do5vF9NZ+8VNNsx3UuTvgp9u5uymAUaFitjAu2FGnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83bb0dbb9fa3b7793b18d9bf8f4dcdcbb11ff22053e50ca94c312ff1484dd774","last_reissued_at":"2026-05-18T02:42:30.289267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:30.289267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5225","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":"2026-05-18T02:42:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNnmA6xWv9QXIjXtiesXulP9EwzSmfOPixKw0JJbWr13OVpb+e3XKlIdOL2ckbbTuct12tpHWpfdf2tCYafVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T06:57:23.248925Z"},"content_sha256":"fb1eb92699f1a16e4ee7f9a5e9770de62c8e41b34daf5d619f02ce517e33bd90","schema_version":"1.0","event_id":"sha256:fb1eb92699f1a16e4ee7f9a5e9770de62c8e41b34daf5d619f02ce517e33bd90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QO5Q3O47UO3XSOYY3G7Y6TONZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete-Time Dynamic Noncooperative Game Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Philipp Hungerl\\\"ander","submitted_at":"2014-09-18T08:26:56Z","abstract_excerpt":"Dynamic noncooperative game theory is a field of mathematics and economics in which a lot of research is being carried out at present featuring a great number of applications in many different areas of economics and management science like capital accumulation and investments, R&D and technological innovations, macroeconomics, microeconomics, pricing and advertising decisions in marketing, natural resource extraction, pollution control.\n  The aim of this diploma thesis is to correct some results for discrete-time affine-quadratic dynamic games of prespecified fixed duration with open-loop and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5225","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":"2026-05-18T02:42:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"of0FPnkwTD37k89uURJcph7IdtmMFrx3Cb6xvQuDaV8GB6vuH6gCkEDN+T3wBe/N3iUJKZS+myEXwM7DxofsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T06:57:23.249262Z"},"content_sha256":"45c4f4c7e39b5dbaf2491e612cba940f02168d679d714663d410372f18e143a1","schema_version":"1.0","event_id":"sha256:45c4f4c7e39b5dbaf2491e612cba940f02168d679d714663d410372f18e143a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO/bundle.json","state_url":"https://pith.science/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO/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":"2026-07-03T06:57:23Z","links":{"resolver":"https://pith.science/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO","bundle":"https://pith.science/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO/bundle.json","state":"https://pith.science/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QO5Q3O47UO3XSOYY3G7Y6TONZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QO5Q3O47UO3XSOYY3G7Y6TONZO","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":"ed2408c2eac34a7de5ea5731d9d4ac6bdb53d2004ef18e80f9bfe5e2cc730a5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-18T08:26:56Z","title_canon_sha256":"d72e12a57ccf5a560c7b900e019655a0c256317fe2ad731e3369b59a44475034"},"schema_version":"1.0","source":{"id":"1409.5225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5225","created_at":"2026-05-18T02:42:30Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5225v1","created_at":"2026-05-18T02:42:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5225","created_at":"2026-05-18T02:42:30Z"},{"alias_kind":"pith_short_12","alias_value":"QO5Q3O47UO3X","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QO5Q3O47UO3XSOYY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QO5Q3O47","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:45c4f4c7e39b5dbaf2491e612cba940f02168d679d714663d410372f18e143a1","target":"graph","created_at":"2026-05-18T02:42:30Z","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":"Dynamic noncooperative game theory is a field of mathematics and economics in which a lot of research is being carried out at present featuring a great number of applications in many different areas of economics and management science like capital accumulation and investments, R&D and technological innovations, macroeconomics, microeconomics, pricing and advertising decisions in marketing, natural resource extraction, pollution control.\n  The aim of this diploma thesis is to correct some results for discrete-time affine-quadratic dynamic games of prespecified fixed duration with open-loop and ","authors_text":"Philipp Hungerl\\\"ander","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-18T08:26:56Z","title":"Discrete-Time Dynamic Noncooperative Game Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5225","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:fb1eb92699f1a16e4ee7f9a5e9770de62c8e41b34daf5d619f02ce517e33bd90","target":"record","created_at":"2026-05-18T02:42:30Z","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":"ed2408c2eac34a7de5ea5731d9d4ac6bdb53d2004ef18e80f9bfe5e2cc730a5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-18T08:26:56Z","title_canon_sha256":"d72e12a57ccf5a560c7b900e019655a0c256317fe2ad731e3369b59a44475034"},"schema_version":"1.0","source":{"id":"1409.5225","kind":"arxiv","version":1}},"canonical_sha256":"83bb0dbb9fa3b7793b18d9bf8f4dcdcbb11ff22053e50ca94c312ff1484dd774","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83bb0dbb9fa3b7793b18d9bf8f4dcdcbb11ff22053e50ca94c312ff1484dd774","first_computed_at":"2026-05-18T02:42:30.289267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:30.289267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QrlhbVC+GLU8Xft+a24LjJ0YcMRNyywqGomORxz9NG3do5vF9NZ+8VNNsx3UuTvgp9u5uymAUaFitjAu2FGnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:30.290026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb1eb92699f1a16e4ee7f9a5e9770de62c8e41b34daf5d619f02ce517e33bd90","sha256:45c4f4c7e39b5dbaf2491e612cba940f02168d679d714663d410372f18e143a1"],"state_sha256":"74146d0cfcc0a5654651cb8369919aa3de9894cf9031e6b7864ffbfa908316fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rbSwrBFlSoru8DlC0t2JARkmdb/I8FGuhpTW20qJjI7SR6BCdAKR4xO3AL04z+JQVXPJ8vo00PCgHF4qo0eRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T06:57:23.251120Z","bundle_sha256":"fe832730f1c71a4692a8c8395445f1efcdedf4a9613e1bb24a08eddd657ba5d1"}}