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Let also $\\mathcal{O}_f(f,X)$ be a connected component of $\\mathcal{O}(f,X)$ which contains $f.$ In the case when Kronrod-Reeb graph of $f$ is a tree we obtain the full description of $\\pi_1\\mathcal{O}_f(f).$\n  This result also holds for more general class of smooth functions $f:T^2\\to \\mathbb{R}$ which have the following property: for each critical point $z$ of $f$ the germ $f$ of $z$ "},"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":"1804.08966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-24T11:46:51Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"acd4ea9a9903abf29100f9946c6e977194b85bb2cd3d647617a0888ca4443174","abstract_canon_sha256":"25a77e5a353dfd975d873ae23f38489f6510fd72a3bd3648f0534cf96a0c88c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:36.766337Z","signature_b64":"pQ4BV97rQ2mwwrtNKl0VUXheCy6Vd6zdpm3tLKKduYezOgc1z/dPMHTcYxCx9BjinlAAOKU566RJnx879HCBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e8aa4e2c6f031757c479cd5e4d37efb20ffa3027373168ef82d3f3441d7111b","last_reissued_at":"2026-05-18T00:17:36.765706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:36.765706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformations of smooth function on $2$-torus whose KR-graph is a tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Bohdan Feshchenko","submitted_at":"2018-04-24T11:46:51Z","abstract_excerpt":"Let $f:T^2\\to \\mathbb{R}$ be Morse function on $2$-torus $T^2,$ and $\\mathcal{O}(f)$ be the orbit of $f$ with respect to the right action of the group of diffeomorphisms $\\mathcal{D}(T^2)$ on $C^{\\infty}(T^2)$. Let also $\\mathcal{O}_f(f,X)$ be a connected component of $\\mathcal{O}(f,X)$ which contains $f.$ In the case when Kronrod-Reeb graph of $f$ is a tree we obtain the full description of $\\pi_1\\mathcal{O}_f(f).$\n  This result also holds for more general class of smooth functions $f:T^2\\to \\mathbb{R}$ which have the following property: for each critical point $z$ of $f$ the germ $f$ of $z$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08966","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":"1804.08966","created_at":"2026-05-18T00:17:36.765784+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.08966v1","created_at":"2026-05-18T00:17:36.765784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08966","created_at":"2026-05-18T00:17:36.765784+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2FKJYWG6AYX","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2FKJYWG6AYXK7CH","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2FKJYWG","created_at":"2026-05-18T12:32:22.470017+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/F2FKJYWG6AYXK7CHTTK6JU367M","json":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M.json","graph_json":"https://pith.science/api/pith-number/F2FKJYWG6AYXK7CHTTK6JU367M/graph.json","events_json":"https://pith.science/api/pith-number/F2FKJYWG6AYXK7CHTTK6JU367M/events.json","paper":"https://pith.science/paper/F2FKJYWG"},"agent_actions":{"view_html":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M","download_json":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M.json","view_paper":"https://pith.science/paper/F2FKJYWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.08966&json=true","fetch_graph":"https://pith.science/api/pith-number/F2FKJYWG6AYXK7CHTTK6JU367M/graph.json","fetch_events":"https://pith.science/api/pith-number/F2FKJYWG6AYXK7CHTTK6JU367M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M/action/storage_attestation","attest_author":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M/action/author_attestation","sign_citation":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M/action/citation_signature","submit_replication":"https://pith.science/pith/F2FKJYWG6AYXK7CHTTK6JU367M/action/replication_record"}},"created_at":"2026-05-18T00:17:36.765784+00:00","updated_at":"2026-05-18T00:17:36.765784+00:00"}