{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U4BNDP4JRPTPMFWVIXUV7VOFGG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6c73f98fb43c29f0c1d37c1f43428b3dd041dd1460531c75a720b7716bb129ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-04T11:13:14Z","title_canon_sha256":"feaafb26c97bc3180b055f3c3874f1e55691d38cba6be6d0f34646cee585209e"},"schema_version":"1.0","source":{"id":"1612.01100","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01100","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01100v3","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01100","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"U4BNDP4JRPTP","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U4BNDP4JRPTPMFWV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U4BNDP4J","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:4afe13fd7b7046e4cb4f9ed91a23715c7392fb238ae576ed9fc91558b8714c21","target":"graph","created_at":"2026-05-18T00:27:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $N$ (resp., $U$) be a manifold (resp., an open subset of $\\mathbb{R}^m$). Let $f:N\\to U$ and $F:U\\to \\mathbb{R}^\\ell$ be an immersion and a $C^{\\infty}$ mapping, respectively. Generally, the composition $F\\circ f$ does not necessarily yield a mapping transverse to a given subfiber-bundle of $J^1(N,\\mathbb{R}^\\ell)$. Nevertheless, in this paper, for any $\\mathcal{A}^1$-invariant fiber, we show that composing generic linearly perturbed mappings of $F$ and the given immersion $f$ yields a mapping transverse to the subfiber-bundle of $J^1(N,\\mathbb{R}^\\ell)$ with the given fiber. Moreover, we ","authors_text":"Shunsuke Ichiki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-04T11:13:14Z","title":"Composing generic linearly perturbed mappings and immersions/injections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01100","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c11dbb69686b092012f7292c42a77eeb87898bcaceba8d612652242e1bb770ea","target":"record","created_at":"2026-05-18T00:27:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6c73f98fb43c29f0c1d37c1f43428b3dd041dd1460531c75a720b7716bb129ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-04T11:13:14Z","title_canon_sha256":"feaafb26c97bc3180b055f3c3874f1e55691d38cba6be6d0f34646cee585209e"},"schema_version":"1.0","source":{"id":"1612.01100","kind":"arxiv","version":3}},"canonical_sha256":"a702d1bf898be6f616d545e95fd5c531b4183e35834c372e374b15c4f27ae5f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a702d1bf898be6f616d545e95fd5c531b4183e35834c372e374b15c4f27ae5f3","first_computed_at":"2026-05-18T00:27:21.995792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:21.995792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G/ZsR7fBYhBr3sbVy2Wsb8cWxHgFW6fUWw7IMrfPSzpx9elzWXwXOsMtpU+4UIE75G6sCjF1eUeOEc1RU2HfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:21.996431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01100","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c11dbb69686b092012f7292c42a77eeb87898bcaceba8d612652242e1bb770ea","sha256:4afe13fd7b7046e4cb4f9ed91a23715c7392fb238ae576ed9fc91558b8714c21"],"state_sha256":"4c0c11d4e6d3308321e538fa359922fe7654eaad273fb2486e5dd4a072117d9d"}