{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:33XBRWO6OSH6DU6ZTJNQC7QKIQ","short_pith_number":"pith:33XBRWO6","canonical_record":{"source":{"id":"1312.0823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-03T13:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"9824d28edd945907a1205e8f8f1e0aa841e48a52862aaab9c8396608b00b8033","abstract_canon_sha256":"b2b084ee1d6ee0910aec50097e119f9cb59b2af71a6f14fe0fa6345273ea742b"},"schema_version":"1.0"},"canonical_sha256":"deee18d9de748fe1d3d99a5b017e0a44110c7ec5e9f560f55dbeefdde619a726","source":{"kind":"arxiv","id":"1312.0823","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0823","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0823v2","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0823","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"33XBRWO6OSH6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"33XBRWO6OSH6DU6Z","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"33XBRWO6","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:33XBRWO6OSH6DU6ZTJNQC7QKIQ","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-03T13:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"9824d28edd945907a1205e8f8f1e0aa841e48a52862aaab9c8396608b00b8033","abstract_canon_sha256":"b2b084ee1d6ee0910aec50097e119f9cb59b2af71a6f14fe0fa6345273ea742b"},"schema_version":"1.0"},"canonical_sha256":"deee18d9de748fe1d3d99a5b017e0a44110c7ec5e9f560f55dbeefdde619a726","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:38.256978Z","signature_b64":"6SdS4peeK1TdJROYCJSwn0KxkobuR1ZqnlqMYQtMJzwsPU9LY1iGoCqFew/1lcE44ea9h5bZ3H5Tn1Xzrg95AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deee18d9de748fe1d3d99a5b017e0a44110c7ec5e9f560f55dbeefdde619a726","last_reissued_at":"2026-05-18T01:12:38.256577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:38.256577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0823","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75/7yb1mYK8jrzj4DMR7zPQhq61z82UGoYltCHgPoFn6bvqgydSqG+DoSm5Wk1R9Pfv8EIW60xWSbK37w3n0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:10:12.249431Z"},"content_sha256":"b738b0b4677b2d2d87d0a6abca2d6800ca0f81d546b521035553163472e64a40","schema_version":"1.0","event_id":"sha256:b738b0b4677b2d2d87d0a6abca2d6800ca0f81d546b521035553163472e64a40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:33XBRWO6OSH6DU6ZTJNQC7QKIQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sutured Floer homology, fibrations, and taut depth one foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andr\\'as Juh\\'asz, Irida Altman, Stefan Friedl","submitted_at":"2013-12-03T13:54:29Z","abstract_excerpt":"For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibered classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured manifold $(M,\\gamma)$ detects which classes in $H^1(M)$ admit a taut depth one foliation such that the only compact leaves are the components of $R(\\gamma)$. The latter had been proved earlier by the first author under the extra assumption that $H_2(M)=0$. The main technical result is that we can obtain an extremal $\\text{Spin}^c$-structure $\\mathfrak{s}$ (i.e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0823","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kwchUC9IJmkAdDKKpR/izWIxeTmoSNVfZWeyNVcRWncTnPHKuL0zVQpHxdbePnO5C/TIWR8MJJdwtBaE2aGKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:10:12.250084Z"},"content_sha256":"3f35898ffc1e5f871b5508b79d33acf5f303c6626f4e5efac9a9e660300b02ac","schema_version":"1.0","event_id":"sha256:3f35898ffc1e5f871b5508b79d33acf5f303c6626f4e5efac9a9e660300b02ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ/bundle.json","state_url":"https://pith.science/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T18:10:12Z","links":{"resolver":"https://pith.science/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ","bundle":"https://pith.science/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ/bundle.json","state":"https://pith.science/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33XBRWO6OSH6DU6ZTJNQC7QKIQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:33XBRWO6OSH6DU6ZTJNQC7QKIQ","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":"b2b084ee1d6ee0910aec50097e119f9cb59b2af71a6f14fe0fa6345273ea742b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-03T13:54:29Z","title_canon_sha256":"9824d28edd945907a1205e8f8f1e0aa841e48a52862aaab9c8396608b00b8033"},"schema_version":"1.0","source":{"id":"1312.0823","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0823","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0823v2","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0823","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"33XBRWO6OSH6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"33XBRWO6OSH6DU6Z","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"33XBRWO6","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:3f35898ffc1e5f871b5508b79d33acf5f303c6626f4e5efac9a9e660300b02ac","target":"graph","created_at":"2026-05-18T01:12:38Z","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":"For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibered classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured manifold $(M,\\gamma)$ detects which classes in $H^1(M)$ admit a taut depth one foliation such that the only compact leaves are the components of $R(\\gamma)$. The latter had been proved earlier by the first author under the extra assumption that $H_2(M)=0$. The main technical result is that we can obtain an extremal $\\text{Spin}^c$-structure $\\mathfrak{s}$ (i.e","authors_text":"Andr\\'as Juh\\'asz, Irida Altman, Stefan Friedl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-03T13:54:29Z","title":"Sutured Floer homology, fibrations, and taut depth one foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0823","kind":"arxiv","version":2},"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:b738b0b4677b2d2d87d0a6abca2d6800ca0f81d546b521035553163472e64a40","target":"record","created_at":"2026-05-18T01:12:38Z","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":"b2b084ee1d6ee0910aec50097e119f9cb59b2af71a6f14fe0fa6345273ea742b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-03T13:54:29Z","title_canon_sha256":"9824d28edd945907a1205e8f8f1e0aa841e48a52862aaab9c8396608b00b8033"},"schema_version":"1.0","source":{"id":"1312.0823","kind":"arxiv","version":2}},"canonical_sha256":"deee18d9de748fe1d3d99a5b017e0a44110c7ec5e9f560f55dbeefdde619a726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deee18d9de748fe1d3d99a5b017e0a44110c7ec5e9f560f55dbeefdde619a726","first_computed_at":"2026-05-18T01:12:38.256577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:38.256577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6SdS4peeK1TdJROYCJSwn0KxkobuR1ZqnlqMYQtMJzwsPU9LY1iGoCqFew/1lcE44ea9h5bZ3H5Tn1Xzrg95AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:38.256978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0823","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b738b0b4677b2d2d87d0a6abca2d6800ca0f81d546b521035553163472e64a40","sha256:3f35898ffc1e5f871b5508b79d33acf5f303c6626f4e5efac9a9e660300b02ac"],"state_sha256":"6229b59eb930000fdd160953307bd0f08088c741864ecf482114ab56c605e5d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVcgBsLRlig/BXXGZ5r6LSvUT5HxicVc25VMue7qaWmHy189781sunrrXq8C1fWZbh/1mY+hYHt6GZ50o2vuDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:10:12.253259Z","bundle_sha256":"b15e731162f6eda09ace854b384cc311b51030a0ea3435f607b95c5afe611e7c"}}