{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:O3SKAPCTIHFO2S3EPCK2EQ7IZA","short_pith_number":"pith:O3SKAPCT","schema_version":"1.0","canonical_sha256":"76e4a03c5341caed4b647895a243e8c8029b00cbe5853f8de6d59d39b56a17a0","source":{"kind":"arxiv","id":"1610.00878","version":4},"attestation_state":"computed","paper":{"title":"Reverse mathematics of the finite downwards closed subsets of $\\mathbb{N}^k$ ordered by inclusion and adjacent Ramsey for fixed dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Florian Pelupessy","submitted_at":"2016-10-04T07:33:31Z","abstract_excerpt":"We show that the well-partial orderedness of the finite downwards closed subsets of $\\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $\\omega^{\\omega^\\omega}$. This was conjectured to be the case by Hatzikiriakou and Simpson. Since we use Friedman's adjacent Ramsey theorem for fixed dimensions in the upper bound, we also give a treatment of the reverse mathematical status of that theorem."},"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":"1610.00878","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-04T07:33:31Z","cross_cats_sorted":[],"title_canon_sha256":"b8af8c6b690339e60e073d6729f0aee2d642071391bb4808bdb0f0a613573aed","abstract_canon_sha256":"ec9686effc9937c87976cb4e71311d257162a787873daf69f538e2aab4954203"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:00.807645Z","signature_b64":"G7tmgqFv86E+tJnkevcXDF5rkA9zxvKp8DvUP4Ylc/WSXOQh6s9CtQxJTZDKFugDMiQH35iMV0RYwI+t7Oe7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76e4a03c5341caed4b647895a243e8c8029b00cbe5853f8de6d59d39b56a17a0","last_reissued_at":"2026-05-18T00:09:00.806880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:00.806880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reverse mathematics of the finite downwards closed subsets of $\\mathbb{N}^k$ ordered by inclusion and adjacent Ramsey for fixed dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Florian Pelupessy","submitted_at":"2016-10-04T07:33:31Z","abstract_excerpt":"We show that the well-partial orderedness of the finite downwards closed subsets of $\\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $\\omega^{\\omega^\\omega}$. This was conjectured to be the case by Hatzikiriakou and Simpson. Since we use Friedman's adjacent Ramsey theorem for fixed dimensions in the upper bound, we also give a treatment of the reverse mathematical status of that theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00878","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.00878","created_at":"2026-05-18T00:09:00.807016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00878v4","created_at":"2026-05-18T00:09:00.807016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00878","created_at":"2026-05-18T00:09:00.807016+00:00"},{"alias_kind":"pith_short_12","alias_value":"O3SKAPCTIHFO","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"O3SKAPCTIHFO2S3E","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"O3SKAPCT","created_at":"2026-05-18T12:30:36.002864+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/O3SKAPCTIHFO2S3EPCK2EQ7IZA","json":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA.json","graph_json":"https://pith.science/api/pith-number/O3SKAPCTIHFO2S3EPCK2EQ7IZA/graph.json","events_json":"https://pith.science/api/pith-number/O3SKAPCTIHFO2S3EPCK2EQ7IZA/events.json","paper":"https://pith.science/paper/O3SKAPCT"},"agent_actions":{"view_html":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA","download_json":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA.json","view_paper":"https://pith.science/paper/O3SKAPCT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00878&json=true","fetch_graph":"https://pith.science/api/pith-number/O3SKAPCTIHFO2S3EPCK2EQ7IZA/graph.json","fetch_events":"https://pith.science/api/pith-number/O3SKAPCTIHFO2S3EPCK2EQ7IZA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA/action/storage_attestation","attest_author":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA/action/author_attestation","sign_citation":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA/action/citation_signature","submit_replication":"https://pith.science/pith/O3SKAPCTIHFO2S3EPCK2EQ7IZA/action/replication_record"}},"created_at":"2026-05-18T00:09:00.807016+00:00","updated_at":"2026-05-18T00:09:00.807016+00:00"}