{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SV4U2DKWU5RI6E5MDH5LZXNNGX","short_pith_number":"pith:SV4U2DKW","schema_version":"1.0","canonical_sha256":"95794d0d56a7628f13ac19fabcddad35c53876f35a4dd59d8bbd3522b940c7ec","source":{"kind":"arxiv","id":"1411.4481","version":2},"attestation_state":"computed","paper":{"title":"An order-theoretic characterization of the Howard-Bachmann-hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andreas Weiermann, Jeroen Van der Meeren, Michael Rathjen","submitted_at":"2014-11-17T14:07:06Z","abstract_excerpt":"In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face $\\Pi^1_1$-comprehension"},"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":"1411.4481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-17T14:07:06Z","cross_cats_sorted":[],"title_canon_sha256":"1633fb29277ad158effcf4df6c9e36e4ed90d464d1c8f434ca1c713cb24dcd6a","abstract_canon_sha256":"456e516cc5a55e258a59ac567f6a378f5e4427992763ab7061bccb07b7d1f582"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:07.722820Z","signature_b64":"2F0VADgWMX2KkqglhJxbstBrLudOSjp4J4M4opDD0dtE4HfVQLZVstVEmH10hQvwj3NVMB6dVag5img4NjfpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95794d0d56a7628f13ac19fabcddad35c53876f35a4dd59d8bbd3522b940c7ec","last_reissued_at":"2026-05-18T02:30:07.722187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:07.722187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An order-theoretic characterization of the Howard-Bachmann-hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andreas Weiermann, Jeroen Van der Meeren, Michael Rathjen","submitted_at":"2014-11-17T14:07:06Z","abstract_excerpt":"In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face $\\Pi^1_1$-comprehension"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4481","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":""},"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":"1411.4481","created_at":"2026-05-18T02:30:07.722290+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.4481v2","created_at":"2026-05-18T02:30:07.722290+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4481","created_at":"2026-05-18T02:30:07.722290+00:00"},{"alias_kind":"pith_short_12","alias_value":"SV4U2DKWU5RI","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SV4U2DKWU5RI6E5M","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SV4U2DKW","created_at":"2026-05-18T12:28:49.207871+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/SV4U2DKWU5RI6E5MDH5LZXNNGX","json":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX.json","graph_json":"https://pith.science/api/pith-number/SV4U2DKWU5RI6E5MDH5LZXNNGX/graph.json","events_json":"https://pith.science/api/pith-number/SV4U2DKWU5RI6E5MDH5LZXNNGX/events.json","paper":"https://pith.science/paper/SV4U2DKW"},"agent_actions":{"view_html":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX","download_json":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX.json","view_paper":"https://pith.science/paper/SV4U2DKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.4481&json=true","fetch_graph":"https://pith.science/api/pith-number/SV4U2DKWU5RI6E5MDH5LZXNNGX/graph.json","fetch_events":"https://pith.science/api/pith-number/SV4U2DKWU5RI6E5MDH5LZXNNGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX/action/storage_attestation","attest_author":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX/action/author_attestation","sign_citation":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX/action/citation_signature","submit_replication":"https://pith.science/pith/SV4U2DKWU5RI6E5MDH5LZXNNGX/action/replication_record"}},"created_at":"2026-05-18T02:30:07.722290+00:00","updated_at":"2026-05-18T02:30:07.722290+00:00"}