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We show that if $\\phi$ is \"sufficiently complicated\" then any incompressible or strongly irreducible surface in $M_\\phi$ can be isotoped to be disjoint from $T$. It follows that every Heegaard splitting of a 3-manifold admitting a \"sufficiently complicated\" JSJ decomposition is an amalgamation of Heegaard splittings of the components of the JSJ decomp"},"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":"0911.5078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-11-27T20:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"657981de21d9d67c19eff907910f94b1d858e7f5c9d9bb7a3b5b9efe64e1aeac","abstract_canon_sha256":"7eb5131726d6f397cce687e652022a7c271cdd9d322b4733c57b83adb8b87815"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:46.096188Z","signature_b64":"urDlJK8jGDuMg+Y23hXtMymwPcKbYwn34qVh23PFzlJK1xAiMl1i3Gv6+foVVXa62mdlf6xZhiQCPVll2SR4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"976b982802d6889ba082b2c607d9116e97423099499fe57d5a0676753ba5d17a","last_reissued_at":"2026-05-18T02:24:46.095598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:46.095598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heegaard structure respects complicated JSJ decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Bachman, Eric Sedgwick, Ryan Derby-Talbot","submitted_at":"2009-11-27T20:53:57Z","abstract_excerpt":"Let $M$ be a 3-manifold with torus boundary components $T_1$ and $T_2$. 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It follows that every Heegaard splitting of a 3-manifold admitting a \"sufficiently complicated\" JSJ decomposition is an amalgamation of Heegaard splittings of the components of the JSJ decomp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5078","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":"0911.5078","created_at":"2026-05-18T02:24:46.095679+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.5078v2","created_at":"2026-05-18T02:24:46.095679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.5078","created_at":"2026-05-18T02:24:46.095679+00:00"},{"alias_kind":"pith_short_12","alias_value":"S5VZQKAC22EJ","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"S5VZQKAC22EJXIEC","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"S5VZQKAC","created_at":"2026-05-18T12:26:01.383474+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/S5VZQKAC22EJXIECWLDAPWIRN2","json":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2.json","graph_json":"https://pith.science/api/pith-number/S5VZQKAC22EJXIECWLDAPWIRN2/graph.json","events_json":"https://pith.science/api/pith-number/S5VZQKAC22EJXIECWLDAPWIRN2/events.json","paper":"https://pith.science/paper/S5VZQKAC"},"agent_actions":{"view_html":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2","download_json":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2.json","view_paper":"https://pith.science/paper/S5VZQKAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.5078&json=true","fetch_graph":"https://pith.science/api/pith-number/S5VZQKAC22EJXIECWLDAPWIRN2/graph.json","fetch_events":"https://pith.science/api/pith-number/S5VZQKAC22EJXIECWLDAPWIRN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2/action/storage_attestation","attest_author":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2/action/author_attestation","sign_citation":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2/action/citation_signature","submit_replication":"https://pith.science/pith/S5VZQKAC22EJXIECWLDAPWIRN2/action/replication_record"}},"created_at":"2026-05-18T02:24:46.095679+00:00","updated_at":"2026-05-18T02:24:46.095679+00:00"}