{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GD2XNJ4E3ZPMLNP4FQSCEEZIUT","short_pith_number":"pith:GD2XNJ4E","schema_version":"1.0","canonical_sha256":"30f576a784de5ec5b5fc2c24221328a4c94dc482b1f8056f07458d6f9790bce0","source":{"kind":"arxiv","id":"1605.06164","version":1},"attestation_state":"computed","paper":{"title":"The uniform content of partial and linear orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damir D. Dzhafarov, Eric P. Astor, Jacob Suggs, Reed Solomon","submitted_at":"2016-05-19T22:15:31Z","abstract_excerpt":"The principle $ADS$ asserts that every linear order on $\\omega$ has an infinite ascending or descending sequence. This has been studied extensively in the reverse mathematics literature, beginning with the work of Hirschfeldt and Shore. We introduce the principle $ADC$, which asserts that linear order has an infinite ascending or descending chain. The two are easily seen to be equivalent over the base system $RCA_0$ of second order arithmetic; they are even computably equivalent. However, we prove that $ADC$ is strictly weaker than $ADS$ under Weihrauch (uniform) reducibility. In fact, we show"},"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":"1605.06164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-05-19T22:15:31Z","cross_cats_sorted":[],"title_canon_sha256":"f395f16059f9510a343eda75397c02d6b3e7816d19ebf83c905654887b57dd7d","abstract_canon_sha256":"57a0b8d53ddd00bb231f466e96370311768ba8c00120473fde7abd098df7778d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:19.794775Z","signature_b64":"oVEinbiNR7ISa4xqhhk74lrIkYQ/7dovvfoS/Md4RMue4d6EdJ7kzFAQKfuxUJVDNEHwiwHkY76EgRF47yBuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30f576a784de5ec5b5fc2c24221328a4c94dc482b1f8056f07458d6f9790bce0","last_reissued_at":"2026-05-18T01:14:19.794228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:19.794228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The uniform content of partial and linear orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damir D. Dzhafarov, Eric P. Astor, Jacob Suggs, Reed Solomon","submitted_at":"2016-05-19T22:15:31Z","abstract_excerpt":"The principle $ADS$ asserts that every linear order on $\\omega$ has an infinite ascending or descending sequence. This has been studied extensively in the reverse mathematics literature, beginning with the work of Hirschfeldt and Shore. We introduce the principle $ADC$, which asserts that linear order has an infinite ascending or descending chain. The two are easily seen to be equivalent over the base system $RCA_0$ of second order arithmetic; they are even computably equivalent. However, we prove that $ADC$ is strictly weaker than $ADS$ under Weihrauch (uniform) reducibility. In fact, we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06164","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":""},"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":"1605.06164","created_at":"2026-05-18T01:14:19.794338+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.06164v1","created_at":"2026-05-18T01:14:19.794338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06164","created_at":"2026-05-18T01:14:19.794338+00:00"},{"alias_kind":"pith_short_12","alias_value":"GD2XNJ4E3ZPM","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GD2XNJ4E3ZPMLNP4","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GD2XNJ4E","created_at":"2026-05-18T12:30:19.053100+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/GD2XNJ4E3ZPMLNP4FQSCEEZIUT","json":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT.json","graph_json":"https://pith.science/api/pith-number/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/graph.json","events_json":"https://pith.science/api/pith-number/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/events.json","paper":"https://pith.science/paper/GD2XNJ4E"},"agent_actions":{"view_html":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT","download_json":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT.json","view_paper":"https://pith.science/paper/GD2XNJ4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.06164&json=true","fetch_graph":"https://pith.science/api/pith-number/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/graph.json","fetch_events":"https://pith.science/api/pith-number/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/action/storage_attestation","attest_author":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/action/author_attestation","sign_citation":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/action/citation_signature","submit_replication":"https://pith.science/pith/GD2XNJ4E3ZPMLNP4FQSCEEZIUT/action/replication_record"}},"created_at":"2026-05-18T01:14:19.794338+00:00","updated_at":"2026-05-18T01:14:19.794338+00:00"}