{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:6DFMUJX7KCQ6YHFXJDQUIDV7PL","short_pith_number":"pith:6DFMUJX7","schema_version":"1.0","canonical_sha256":"f0caca26ff50a1ec1cb748e1440ebf7ae3811ce88c819c8681e03fa8fa0906b5","source":{"kind":"arxiv","id":"2103.15728","version":2},"attestation_state":"computed","paper":{"title":"Trees and stationary reflection at double successors of regular cardinals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Maxwell Levine, Thomas Gilton, \\v{S}\\'arka Stejskalov\\'a","submitted_at":"2021-03-29T16:16:27Z","abstract_excerpt":"We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals $\\kappa$, updating some classical constructions in the process. This includes models of $\\mathsf{CSR}(\\kappa^{++})\\wedge \\mathsf{TP}(\\kappa^{++})$ (both with and without $\\mathsf{AP}(\\kappa^{++})$) and models of the conjunctions $\\mathsf{SR}(\\kappa^{++}) \\wedge \\mathsf{wTP}(\\kappa^{++}) \\wedge \\mathsf{AP}(\\kappa^{++})$ and $\\neg \\mathsf{AP}(\\kappa^{++}) \\wedge \\mathsf{SR}(\\kappa^{++})$ (the latter was originally obtained in joint work by Krueger and the first author \\c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2103.15728","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2021-03-29T16:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"ce0ba6f677264f1491e846641f5e46ac71381b7b1a0f12a4cba59456dcf3e3e3","abstract_canon_sha256":"cdcd0d09948b2dd1c3f7a99ee7c6a85869205184608e13ef39db5d752d89b4a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:28:56.753604Z","signature_b64":"tPCMApVEqlR9YUOPMKTC3UWblWaZ+V3ZlnECL0EK07UKcfeVOem07fPHYCI1IpjIpLWNvmYPH7+8EvzkB8XmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0caca26ff50a1ec1cb748e1440ebf7ae3811ce88c819c8681e03fa8fa0906b5","last_reissued_at":"2026-07-05T02:28:56.753165Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:28:56.753165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trees and stationary reflection at double successors of regular cardinals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Maxwell Levine, Thomas Gilton, \\v{S}\\'arka Stejskalov\\'a","submitted_at":"2021-03-29T16:16:27Z","abstract_excerpt":"We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals $\\kappa$, updating some classical constructions in the process. This includes models of $\\mathsf{CSR}(\\kappa^{++})\\wedge \\mathsf{TP}(\\kappa^{++})$ (both with and without $\\mathsf{AP}(\\kappa^{++})$) and models of the conjunctions $\\mathsf{SR}(\\kappa^{++}) \\wedge \\mathsf{wTP}(\\kappa^{++}) \\wedge \\mathsf{AP}(\\kappa^{++})$ and $\\neg \\mathsf{AP}(\\kappa^{++}) \\wedge \\mathsf{SR}(\\kappa^{++})$ (the latter was originally obtained in joint work by Krueger and the first author \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15728","kind":"arxiv","version":2},"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/2103.15728/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2103.15728","created_at":"2026-07-05T02:28:56.753221+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.15728v2","created_at":"2026-07-05T02:28:56.753221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.15728","created_at":"2026-07-05T02:28:56.753221+00:00"},{"alias_kind":"pith_short_12","alias_value":"6DFMUJX7KCQ6","created_at":"2026-07-05T02:28:56.753221+00:00"},{"alias_kind":"pith_short_16","alias_value":"6DFMUJX7KCQ6YHFX","created_at":"2026-07-05T02:28:56.753221+00:00"},{"alias_kind":"pith_short_8","alias_value":"6DFMUJX7","created_at":"2026-07-05T02:28:56.753221+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL","json":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL.json","graph_json":"https://pith.science/api/pith-number/6DFMUJX7KCQ6YHFXJDQUIDV7PL/graph.json","events_json":"https://pith.science/api/pith-number/6DFMUJX7KCQ6YHFXJDQUIDV7PL/events.json","paper":"https://pith.science/paper/6DFMUJX7"},"agent_actions":{"view_html":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL","download_json":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL.json","view_paper":"https://pith.science/paper/6DFMUJX7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.15728&json=true","fetch_graph":"https://pith.science/api/pith-number/6DFMUJX7KCQ6YHFXJDQUIDV7PL/graph.json","fetch_events":"https://pith.science/api/pith-number/6DFMUJX7KCQ6YHFXJDQUIDV7PL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL/action/storage_attestation","attest_author":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL/action/author_attestation","sign_citation":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL/action/citation_signature","submit_replication":"https://pith.science/pith/6DFMUJX7KCQ6YHFXJDQUIDV7PL/action/replication_record"}},"created_at":"2026-07-05T02:28:56.753221+00:00","updated_at":"2026-07-05T02:28:56.753221+00:00"}