{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UO7GIX4OGUYYTQ36VQGV3H6A3V","short_pith_number":"pith:UO7GIX4O","schema_version":"1.0","canonical_sha256":"a3be645f8e353189c37eac0d5d9fc0dd594fdb68df99d41c96f1da6e3be67c57","source":{"kind":"arxiv","id":"1812.09413","version":4},"attestation_state":"computed","paper":{"title":"Algorithmic aspects of immersibility and embeddability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"Fedor Manin, Shmuel Weinberger","submitted_at":"2018-12-21T23:34:29Z","abstract_excerpt":"We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\\mathbf{Diff}$ or $\\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\\mathbb{R}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in $\\mathbb{R}^n$ is undecidable when $n-m$ is even and $11m \\geq 10n+1$."},"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":"1812.09413","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-12-21T23:34:29Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"40684b8eff15854dd705e9357c39cda5670e60cfae7b581e6d4438a1164a35f1","abstract_canon_sha256":"c26ec6dff551e4db5b5e736bbca83667d34f2ef72432aa72d244ab344076a441"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:22:35.242831Z","signature_b64":"/8zvMf/Sq7wUlSuSUDbwldmsAreZpn5nrkvKKf/r09CN7REJ2PqplHwcYDfFLC+F6MphDE6DVFOA0rp5+f07DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3be645f8e353189c37eac0d5d9fc0dd594fdb68df99d41c96f1da6e3be67c57","last_reissued_at":"2026-07-05T09:22:35.242297Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:22:35.242297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithmic aspects of immersibility and embeddability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"Fedor Manin, Shmuel Weinberger","submitted_at":"2018-12-21T23:34:29Z","abstract_excerpt":"We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\\mathbf{Diff}$ or $\\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\\mathbb{R}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in $\\mathbb{R}^n$ is undecidable when $n-m$ is even and $11m \\geq 10n+1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09413","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1812.09413/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":"1812.09413","created_at":"2026-07-05T09:22:35.242376+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.09413v4","created_at":"2026-07-05T09:22:35.242376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09413","created_at":"2026-07-05T09:22:35.242376+00:00"},{"alias_kind":"pith_short_12","alias_value":"UO7GIX4OGUYY","created_at":"2026-07-05T09:22:35.242376+00:00"},{"alias_kind":"pith_short_16","alias_value":"UO7GIX4OGUYYTQ36","created_at":"2026-07-05T09:22:35.242376+00:00"},{"alias_kind":"pith_short_8","alias_value":"UO7GIX4O","created_at":"2026-07-05T09:22:35.242376+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/UO7GIX4OGUYYTQ36VQGV3H6A3V","json":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V.json","graph_json":"https://pith.science/api/pith-number/UO7GIX4OGUYYTQ36VQGV3H6A3V/graph.json","events_json":"https://pith.science/api/pith-number/UO7GIX4OGUYYTQ36VQGV3H6A3V/events.json","paper":"https://pith.science/paper/UO7GIX4O"},"agent_actions":{"view_html":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V","download_json":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V.json","view_paper":"https://pith.science/paper/UO7GIX4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.09413&json=true","fetch_graph":"https://pith.science/api/pith-number/UO7GIX4OGUYYTQ36VQGV3H6A3V/graph.json","fetch_events":"https://pith.science/api/pith-number/UO7GIX4OGUYYTQ36VQGV3H6A3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V/action/storage_attestation","attest_author":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V/action/author_attestation","sign_citation":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V/action/citation_signature","submit_replication":"https://pith.science/pith/UO7GIX4OGUYYTQ36VQGV3H6A3V/action/replication_record"}},"created_at":"2026-07-05T09:22:35.242376+00:00","updated_at":"2026-07-05T09:22:35.242376+00:00"}