{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VWWWSEQS7QASIRWX4XAF2WXK6C","short_pith_number":"pith:VWWWSEQS","canonical_record":{"source":{"id":"1508.03989","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-17T12:00:32Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"02d28815cbe80650d4a44de0856147d66c928121848f2049ac21024ce7f386b3","abstract_canon_sha256":"d492de5632ed2b44281fb99789f3313731fd963d0ae1642b14162883c31ffbd7"},"schema_version":"1.0"},"canonical_sha256":"adad691212fc012446d7e5c05d5aeaf0b6c2dfa49094495ead90e5564ecec8d8","source":{"kind":"arxiv","id":"1508.03989","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03989","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03989v3","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03989","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"VWWWSEQS7QAS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VWWWSEQS7QASIRWX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VWWWSEQS","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VWWWSEQS7QASIRWX4XAF2WXK6C","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03989","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-17T12:00:32Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"02d28815cbe80650d4a44de0856147d66c928121848f2049ac21024ce7f386b3","abstract_canon_sha256":"d492de5632ed2b44281fb99789f3313731fd963d0ae1642b14162883c31ffbd7"},"schema_version":"1.0"},"canonical_sha256":"adad691212fc012446d7e5c05d5aeaf0b6c2dfa49094495ead90e5564ecec8d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:46.793914Z","signature_b64":"ywGzoFFhRpLVlvb7XV8avxWr7Zb0dXkhcp6QrT3RDc73iYoNfkJh6xW7Ups1EakDV5293if8JqJ0s8g6ChAhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adad691212fc012446d7e5c05d5aeaf0b6c2dfa49094495ead90e5564ecec8d8","last_reissued_at":"2026-05-18T00:38:46.793232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:46.793232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03989","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0QY+DugnlwfBfah2Ugh4vNnStr3i49ZALwr5Glb7qHr2gTYIctUxpm8ZwVsXe0W0X4Vf5hsrpCRABZ3G8ptGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:14:32.335360Z"},"content_sha256":"d48e5a66a808cc8e756e088f92210184618bf078fc20ca757d96760b770933ea","schema_version":"1.0","event_id":"sha256:d48e5a66a808cc8e756e088f92210184618bf078fc20ca757d96760b770933ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VWWWSEQS7QASIRWX4XAF2WXK6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nash equilibria of threshold type for two-player nonzero-sum games of stopping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Giorgio Ferrari, John Moriarty, Tiziano De Angelis","submitted_at":"2015-08-17T12:00:32Z","abstract_excerpt":"This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not non-singular boundary behaviour (in the sense of It\\^o and McKean (1974), p.\\ 108). We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also provide conditions sufficient for the uniqueness of the equilibrium in this class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03989","kind":"arxiv","version":3},"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":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXnr4ApIpLjbGOq6LaFFlTvlqinRy5sP5AfIyPc8V5ACSn8SDsDWVjUpfWI6AGfnVP9a88zVwSX1Z43hN5S5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:14:32.335921Z"},"content_sha256":"db1c2d399dc9300f64d48c9d283ca80d42c8ec131f2358728c49005885319069","schema_version":"1.0","event_id":"sha256:db1c2d399dc9300f64d48c9d283ca80d42c8ec131f2358728c49005885319069"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWWWSEQS7QASIRWX4XAF2WXK6C/bundle.json","state_url":"https://pith.science/pith/VWWWSEQS7QASIRWX4XAF2WXK6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWWWSEQS7QASIRWX4XAF2WXK6C/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":"2026-05-26T13:14:32Z","links":{"resolver":"https://pith.science/pith/VWWWSEQS7QASIRWX4XAF2WXK6C","bundle":"https://pith.science/pith/VWWWSEQS7QASIRWX4XAF2WXK6C/bundle.json","state":"https://pith.science/pith/VWWWSEQS7QASIRWX4XAF2WXK6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWWWSEQS7QASIRWX4XAF2WXK6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VWWWSEQS7QASIRWX4XAF2WXK6C","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":"d492de5632ed2b44281fb99789f3313731fd963d0ae1642b14162883c31ffbd7","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-17T12:00:32Z","title_canon_sha256":"02d28815cbe80650d4a44de0856147d66c928121848f2049ac21024ce7f386b3"},"schema_version":"1.0","source":{"id":"1508.03989","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03989","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03989v3","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03989","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"VWWWSEQS7QAS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VWWWSEQS7QASIRWX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VWWWSEQS","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:db1c2d399dc9300f64d48c9d283ca80d42c8ec131f2358728c49005885319069","target":"graph","created_at":"2026-05-18T00:38:46Z","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 analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not non-singular boundary behaviour (in the sense of It\\^o and McKean (1974), p.\\ 108). We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also provide conditions sufficient for the uniqueness of the equilibrium in this class.","authors_text":"Giorgio Ferrari, John Moriarty, Tiziano De Angelis","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-17T12:00:32Z","title":"Nash equilibria of threshold type for two-player nonzero-sum games of stopping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03989","kind":"arxiv","version":3},"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:d48e5a66a808cc8e756e088f92210184618bf078fc20ca757d96760b770933ea","target":"record","created_at":"2026-05-18T00:38:46Z","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":"d492de5632ed2b44281fb99789f3313731fd963d0ae1642b14162883c31ffbd7","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-17T12:00:32Z","title_canon_sha256":"02d28815cbe80650d4a44de0856147d66c928121848f2049ac21024ce7f386b3"},"schema_version":"1.0","source":{"id":"1508.03989","kind":"arxiv","version":3}},"canonical_sha256":"adad691212fc012446d7e5c05d5aeaf0b6c2dfa49094495ead90e5564ecec8d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adad691212fc012446d7e5c05d5aeaf0b6c2dfa49094495ead90e5564ecec8d8","first_computed_at":"2026-05-18T00:38:46.793232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:46.793232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywGzoFFhRpLVlvb7XV8avxWr7Zb0dXkhcp6QrT3RDc73iYoNfkJh6xW7Ups1EakDV5293if8JqJ0s8g6ChAhCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:46.793914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03989","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d48e5a66a808cc8e756e088f92210184618bf078fc20ca757d96760b770933ea","sha256:db1c2d399dc9300f64d48c9d283ca80d42c8ec131f2358728c49005885319069"],"state_sha256":"6932f256d2f583ad83e87cbfcb82bd443f98e1cdd24fc07568867c0a58af49d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJiBEl06tS4KoJZXVfqhtDngWLUuWzh+/j+2kG02HlvSGAWm9sYiZyzXi/NchNeSvbSQ5taSyBqMqzzmAelLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:14:32.338508Z","bundle_sha256":"ee5aef0d2f57811a396ee2d1b31e6323e686d6a8dfeb5469f190858f3b517202"}}