{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:G5BN5YDDTGM4VMB5WEHY4REMVV","short_pith_number":"pith:G5BN5YDD","canonical_record":{"source":{"id":"2606.18214","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T17:44:18Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"28dc660a1ba23fb58452b48dc23da93475c7c3e82207d28c8922307839b0d0f4","abstract_canon_sha256":"310cca820e6320e23bd88bdaa86754b4979f5da04784c583ed2a5bfd0cc4b5d5"},"schema_version":"1.0"},"canonical_sha256":"3742dee0639999cab03db10f8e448cad425967e352b8ca43f805226260b3fbe6","source":{"kind":"arxiv","id":"2606.18214","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18214","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18214v1","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18214","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"pith_short_12","alias_value":"G5BN5YDDTGM4","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"pith_short_16","alias_value":"G5BN5YDDTGM4VMB5","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"pith_short_8","alias_value":"G5BN5YDD","created_at":"2026-06-19T16:10:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:G5BN5YDDTGM4VMB5WEHY4REMVV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18214","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T17:44:18Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"28dc660a1ba23fb58452b48dc23da93475c7c3e82207d28c8922307839b0d0f4","abstract_canon_sha256":"310cca820e6320e23bd88bdaa86754b4979f5da04784c583ed2a5bfd0cc4b5d5"},"schema_version":"1.0"},"canonical_sha256":"3742dee0639999cab03db10f8e448cad425967e352b8ca43f805226260b3fbe6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:51.241979Z","signature_b64":"7DnbXhIpbiKNXKOswisMuqKVGsndWxylHw4fWFLC73qE4q88GGDidgBoMEgsnunP7oTq82L2TG18Q7FBu9UYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3742dee0639999cab03db10f8e448cad425967e352b8ca43f805226260b3fbe6","last_reissued_at":"2026-06-19T16:10:51.241603Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:51.241603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18214","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":"2026-06-19T16:10:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PlTZpSMErdXcXw06GldtKvp8Hq6b2Z0tV4ElS8EPN2u3OmPAWdn780gdD3Aav1fFF8WQyaHhiPxebpHvMFcnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:11:35.827514Z"},"content_sha256":"5984cf89e927f8fd78cfabf90965a6d0069d774cc1d08a1f800063b95f7a0a3f","schema_version":"1.0","event_id":"sha256:5984cf89e927f8fd78cfabf90965a6d0069d774cc1d08a1f800063b95f7a0a3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:G5BN5YDDTGM4VMB5WEHY4REMVV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time and Killed Resolvents in Reflected Optimal Stopping with a Max Payoff","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Louis Shuo Wang, Ye Liang","submitted_at":"2026-06-16T17:44:18Z","abstract_excerpt":"We study infinite-horizon optimal stopping for normally reflected two-dimensional diffusions in the positive quadrant with max payoff \\(G(x_1,x_2)=x_1\\vee\\alpha x_2\\). The non-smooth payoff produces a singular stopping-gain measure on the kink set \\(\\Delta=\\{x_1=\\alpha x_2\\}\\). We prove $\\displaystyle \\Gamma^\\Delta(dx)\n  =\n  -\\frac{n^\\top a(x)n}{2\\sqrt{1+\\alpha^2}}\\,\\sigma_\\Delta(dx)$, with $n=(1,-\\alpha)$, so the diagonal component is non-positive and strictly negative under local ellipticity. This implies that every interior kink point lies in the continuation region. We further show that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18214","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18214/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-19T16:10:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2s8gtSYrka4gWZBsWjLU59Vh66QzSlAcL662ra8+CIUBjTEabixp+HmI01laUIwZYZlpolaD0fqAtOS70tG8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:11:35.827881Z"},"content_sha256":"96a1eff33349e4f6a518c51889d47dfbd38c1f0831224794d748ed559eb125b5","schema_version":"1.0","event_id":"sha256:96a1eff33349e4f6a518c51889d47dfbd38c1f0831224794d748ed559eb125b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5BN5YDDTGM4VMB5WEHY4REMVV/bundle.json","state_url":"https://pith.science/pith/G5BN5YDDTGM4VMB5WEHY4REMVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5BN5YDDTGM4VMB5WEHY4REMVV/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":"2026-06-28T11:11:35Z","links":{"resolver":"https://pith.science/pith/G5BN5YDDTGM4VMB5WEHY4REMVV","bundle":"https://pith.science/pith/G5BN5YDDTGM4VMB5WEHY4REMVV/bundle.json","state":"https://pith.science/pith/G5BN5YDDTGM4VMB5WEHY4REMVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5BN5YDDTGM4VMB5WEHY4REMVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:G5BN5YDDTGM4VMB5WEHY4REMVV","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":"310cca820e6320e23bd88bdaa86754b4979f5da04784c583ed2a5bfd0cc4b5d5","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T17:44:18Z","title_canon_sha256":"28dc660a1ba23fb58452b48dc23da93475c7c3e82207d28c8922307839b0d0f4"},"schema_version":"1.0","source":{"id":"2606.18214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18214","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18214v1","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18214","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"pith_short_12","alias_value":"G5BN5YDDTGM4","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"pith_short_16","alias_value":"G5BN5YDDTGM4VMB5","created_at":"2026-06-19T16:10:51Z"},{"alias_kind":"pith_short_8","alias_value":"G5BN5YDD","created_at":"2026-06-19T16:10:51Z"}],"graph_snapshots":[{"event_id":"sha256:96a1eff33349e4f6a518c51889d47dfbd38c1f0831224794d748ed559eb125b5","target":"graph","created_at":"2026-06-19T16:10:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.18214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study infinite-horizon optimal stopping for normally reflected two-dimensional diffusions in the positive quadrant with max payoff \\(G(x_1,x_2)=x_1\\vee\\alpha x_2\\). The non-smooth payoff produces a singular stopping-gain measure on the kink set \\(\\Delta=\\{x_1=\\alpha x_2\\}\\). We prove $\\displaystyle \\Gamma^\\Delta(dx)\n  =\n  -\\frac{n^\\top a(x)n}{2\\sqrt{1+\\alpha^2}}\\,\\sigma_\\Delta(dx)$, with $n=(1,-\\alpha)$, so the diagonal component is non-positive and strictly negative under local ellipticity. This implies that every interior kink point lies in the continuation region. We further show that th","authors_text":"Louis Shuo Wang, Ye Liang","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T17:44:18Z","title":"Time and Killed Resolvents in Reflected Optimal Stopping with a Max Payoff"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18214","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":"sha256:5984cf89e927f8fd78cfabf90965a6d0069d774cc1d08a1f800063b95f7a0a3f","target":"record","created_at":"2026-06-19T16:10:51Z","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":"310cca820e6320e23bd88bdaa86754b4979f5da04784c583ed2a5bfd0cc4b5d5","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T17:44:18Z","title_canon_sha256":"28dc660a1ba23fb58452b48dc23da93475c7c3e82207d28c8922307839b0d0f4"},"schema_version":"1.0","source":{"id":"2606.18214","kind":"arxiv","version":1}},"canonical_sha256":"3742dee0639999cab03db10f8e448cad425967e352b8ca43f805226260b3fbe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3742dee0639999cab03db10f8e448cad425967e352b8ca43f805226260b3fbe6","first_computed_at":"2026-06-19T16:10:51.241603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:51.241603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7DnbXhIpbiKNXKOswisMuqKVGsndWxylHw4fWFLC73qE4q88GGDidgBoMEgsnunP7oTq82L2TG18Q7FBu9UYCg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:51.241979Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5984cf89e927f8fd78cfabf90965a6d0069d774cc1d08a1f800063b95f7a0a3f","sha256:96a1eff33349e4f6a518c51889d47dfbd38c1f0831224794d748ed559eb125b5"],"state_sha256":"54c97375ad7a3c4d9c90df57b1d481ab713d18b4c025c7d03825bf77ee66ed2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yqjkxqu3v7OF0lzLHOZMmWboW/15lI0MzvO9HvpkLIlOvO02Hp6AzjJi4vy2UaRW8oDFHLGS7PrvgV0XMTgVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T11:11:35.830098Z","bundle_sha256":"3c146bc687aa75566d0563e5d5d1322805326c9bdd8b4fd83cc0f265a021fc39"}}