{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:O3QMGNA2LGAZW4JQ7I73WEKD7W","short_pith_number":"pith:O3QMGNA2","canonical_record":{"source":{"id":"1708.07661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2017-08-25T09:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"fd4b9060f3bf9d99dd7f2e5bec56068535f89bb4b6961c54c014b6da190e5e1e","abstract_canon_sha256":"ef28ce256a3e738f600b7779201502312fa5fcfc8d7bbf8c3e813a155ec7765e"},"schema_version":"1.0"},"canonical_sha256":"76e0c3341a59819b7130fa3fbb1143fdbb7bf73f71242ebab3cc9e2fee0edeff","source":{"kind":"arxiv","id":"1708.07661","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07661","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07661v1","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07661","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"O3QMGNA2LGAZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O3QMGNA2LGAZW4JQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O3QMGNA2","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:O3QMGNA2LGAZW4JQ7I73WEKD7W","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2017-08-25T09:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"fd4b9060f3bf9d99dd7f2e5bec56068535f89bb4b6961c54c014b6da190e5e1e","abstract_canon_sha256":"ef28ce256a3e738f600b7779201502312fa5fcfc8d7bbf8c3e813a155ec7765e"},"schema_version":"1.0"},"canonical_sha256":"76e0c3341a59819b7130fa3fbb1143fdbb7bf73f71242ebab3cc9e2fee0edeff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:42.445102Z","signature_b64":"Yzk/0v/arSE5uq+awNYdX1CvGMwa6GXAtI3zH4asU1SzAjgu0ziqGT/Omfi6SJeHAdO/SqXjwWD9NzVADUjMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76e0c3341a59819b7130fa3fbb1143fdbb7bf73f71242ebab3cc9e2fee0edeff","last_reissued_at":"2026-05-18T00:36:42.444465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:42.444465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07661","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":"2026-05-18T00:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NGepeSDdPWelK90ctZ24phlEWfA9fPXaRexr+pol7VxSy9IXwwHfokuCm8+ub/MwLq337u9qklY0mtJ/yTC3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:16:10.534262Z"},"content_sha256":"62ef551b53fd4f6fb1fdc6163b21bad0513061e87a96f9f423fe45ad4291fcbf","schema_version":"1.0","event_id":"sha256:62ef551b53fd4f6fb1fdc6163b21bad0513061e87a96f9f423fe45ad4291fcbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:O3QMGNA2LGAZW4JQ7I73WEKD7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic trading under integer constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Paul Kr\\\"uhner, Stefan Gerhold","submitted_at":"2017-08-25T09:18:05Z","abstract_excerpt":"In this paper we investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces and rational asset prices this has little effect on the core of the theory of no-arbitrage pricing. For price processes not restricted to the rational numbers, a novel theory of integer arbitrage free pricing and hedging emerges. We establish an FTAP, involving a set of absolutely continuous martingale measures satisfying an additional property. The set of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07661","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":"2026-05-18T00:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29BWrRcH4+b/Vrwst+F8tcF/8tQDlQjIp/RmlMNLbBQDy6E0ic0f2mJlw9bTN0OPvox7wPGZ91+Pgql7a2onAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:16:10.534618Z"},"content_sha256":"503c451b47dd1feda2bb8e59dc6d58b04ea5379a7ef0d86ae724cdc07518f82a","schema_version":"1.0","event_id":"sha256:503c451b47dd1feda2bb8e59dc6d58b04ea5379a7ef0d86ae724cdc07518f82a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W/bundle.json","state_url":"https://pith.science/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W/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":"2026-06-03T03:16:10Z","links":{"resolver":"https://pith.science/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W","bundle":"https://pith.science/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W/bundle.json","state":"https://pith.science/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O3QMGNA2LGAZW4JQ7I73WEKD7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O3QMGNA2LGAZW4JQ7I73WEKD7W","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":"ef28ce256a3e738f600b7779201502312fa5fcfc8d7bbf8c3e813a155ec7765e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2017-08-25T09:18:05Z","title_canon_sha256":"fd4b9060f3bf9d99dd7f2e5bec56068535f89bb4b6961c54c014b6da190e5e1e"},"schema_version":"1.0","source":{"id":"1708.07661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07661","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07661v1","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07661","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"O3QMGNA2LGAZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O3QMGNA2LGAZW4JQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O3QMGNA2","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:503c451b47dd1feda2bb8e59dc6d58b04ea5379a7ef0d86ae724cdc07518f82a","target":"graph","created_at":"2026-05-18T00:36:42Z","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":"In this paper we investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces and rational asset prices this has little effect on the core of the theory of no-arbitrage pricing. For price processes not restricted to the rational numbers, a novel theory of integer arbitrage free pricing and hedging emerges. We establish an FTAP, involving a set of absolutely continuous martingale measures satisfying an additional property. The set of p","authors_text":"Paul Kr\\\"uhner, Stefan Gerhold","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2017-08-25T09:18:05Z","title":"Dynamic trading under integer constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07661","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":"sha256:62ef551b53fd4f6fb1fdc6163b21bad0513061e87a96f9f423fe45ad4291fcbf","target":"record","created_at":"2026-05-18T00:36:42Z","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":"ef28ce256a3e738f600b7779201502312fa5fcfc8d7bbf8c3e813a155ec7765e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2017-08-25T09:18:05Z","title_canon_sha256":"fd4b9060f3bf9d99dd7f2e5bec56068535f89bb4b6961c54c014b6da190e5e1e"},"schema_version":"1.0","source":{"id":"1708.07661","kind":"arxiv","version":1}},"canonical_sha256":"76e0c3341a59819b7130fa3fbb1143fdbb7bf73f71242ebab3cc9e2fee0edeff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76e0c3341a59819b7130fa3fbb1143fdbb7bf73f71242ebab3cc9e2fee0edeff","first_computed_at":"2026-05-18T00:36:42.444465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:42.444465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yzk/0v/arSE5uq+awNYdX1CvGMwa6GXAtI3zH4asU1SzAjgu0ziqGT/Omfi6SJeHAdO/SqXjwWD9NzVADUjMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:42.445102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62ef551b53fd4f6fb1fdc6163b21bad0513061e87a96f9f423fe45ad4291fcbf","sha256:503c451b47dd1feda2bb8e59dc6d58b04ea5379a7ef0d86ae724cdc07518f82a"],"state_sha256":"908e4357b6101a15fc18748d97dc849c9052a81fac7324987949866aa05d2c8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQvi6iihRcr3iSIhUDOWCyynhKLQJoaGXSfzmuNJPcQ4KFLQeWq4tYdi6KhCrRF5QnwDIKwezDnp6WcsnLA6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:16:10.536724Z","bundle_sha256":"5e002668bf5af270d1541e2aace7a45eae5512ac74eb47b7b3b35d10c20da686"}}