{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NPQEKCGZL3RQC55QIO6PBEB22Z","short_pith_number":"pith:NPQEKCGZ","canonical_record":{"source":{"id":"1807.06849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-18T10:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"6cdf4f45bd133c047459677d6851156e6b3e3523f6afbcdae5ec3b8d76ca3d74","abstract_canon_sha256":"c6bc2345203c3ddbaf62caeb5edc840d3170f2e6f1d2dd87ecbd85384a42b340"},"schema_version":"1.0"},"canonical_sha256":"6be04508d95ee30177b043bcf0903ad6544996779468dd62dcdadb1081def630","source":{"kind":"arxiv","id":"1807.06849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06849","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06849v2","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06849","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"NPQEKCGZL3RQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NPQEKCGZL3RQC55Q","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NPQEKCGZ","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NPQEKCGZL3RQC55QIO6PBEB22Z","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-18T10:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"6cdf4f45bd133c047459677d6851156e6b3e3523f6afbcdae5ec3b8d76ca3d74","abstract_canon_sha256":"c6bc2345203c3ddbaf62caeb5edc840d3170f2e6f1d2dd87ecbd85384a42b340"},"schema_version":"1.0"},"canonical_sha256":"6be04508d95ee30177b043bcf0903ad6544996779468dd62dcdadb1081def630","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:08.294499Z","signature_b64":"VMxL6JeAlbsA7BGRdZb32eqPSLMiaRuA8E0rArY5Ct7JMewK6kqK3FRh1aWVzTf1HmT7J0haCWXOYcMZLfmDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6be04508d95ee30177b043bcf0903ad6544996779468dd62dcdadb1081def630","last_reissued_at":"2026-05-18T00:00:08.294059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:08.294059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06849","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":"2026-05-18T00:00:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0zYEgthc4pGr/Ul7tD/n8S8FLw9Vik8HyPnuzwywE7ZvFR2vJWMbc4ikWr71uCs/r/8pMCbWKK76ToaplBVMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:43:43.384652Z"},"content_sha256":"fff7ba9552dcf6b3325bee2635dbd7e0b5eb940f22cf8a806cd927f67664c71d","schema_version":"1.0","event_id":"sha256:fff7ba9552dcf6b3325bee2635dbd7e0b5eb940f22cf8a806cd927f67664c71d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NPQEKCGZL3RQC55QIO6PBEB22Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vanishing theorems for the cohomology groups of free boundary hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abra\\~ao Mendes, Feliciano Vit\\'orio, Marcos P. Cavalcante","submitted_at":"2018-07-18T10:30:59Z","abstract_excerpt":"In this paper, we prove that there exists a universal constant $C$, depending only on positive integers $n\\geq 3$ and $p\\leq n-1$, such that if $M^n$ is a compact free boundary submanifold of dimension $n$ immersed in the Euclidean unit ball $\\mathbb{B}^{n+k}$ whose size of the traceless second fundamental form is less than $C$, then the $p$th cohomology group of $M^n$ vanishes. Also, employing a different technique, we obtain a rigidity result for compact free boundary surfaces minimally immersed in the unit ball $\\mathbb{B}^{2+k}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06849","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":"2026-05-18T00:00:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qt79Rf39xT3kivHvoCc/x6ihXfIRQYrkeOvf8sIc3qaEgC/t8D0aBU6MxAod3J4olLOKWvSqXTCfrC0m/aKuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:43:43.385419Z"},"content_sha256":"0325aff072dae370d1c9de137b397549147a5710f79392e43251a6fbdc69389c","schema_version":"1.0","event_id":"sha256:0325aff072dae370d1c9de137b397549147a5710f79392e43251a6fbdc69389c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPQEKCGZL3RQC55QIO6PBEB22Z/bundle.json","state_url":"https://pith.science/pith/NPQEKCGZL3RQC55QIO6PBEB22Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPQEKCGZL3RQC55QIO6PBEB22Z/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":"2026-06-10T11:43:43Z","links":{"resolver":"https://pith.science/pith/NPQEKCGZL3RQC55QIO6PBEB22Z","bundle":"https://pith.science/pith/NPQEKCGZL3RQC55QIO6PBEB22Z/bundle.json","state":"https://pith.science/pith/NPQEKCGZL3RQC55QIO6PBEB22Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPQEKCGZL3RQC55QIO6PBEB22Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NPQEKCGZL3RQC55QIO6PBEB22Z","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":"c6bc2345203c3ddbaf62caeb5edc840d3170f2e6f1d2dd87ecbd85384a42b340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-18T10:30:59Z","title_canon_sha256":"6cdf4f45bd133c047459677d6851156e6b3e3523f6afbcdae5ec3b8d76ca3d74"},"schema_version":"1.0","source":{"id":"1807.06849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06849","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06849v2","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06849","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"NPQEKCGZL3RQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NPQEKCGZL3RQC55Q","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NPQEKCGZ","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:0325aff072dae370d1c9de137b397549147a5710f79392e43251a6fbdc69389c","target":"graph","created_at":"2026-05-18T00:00:08Z","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":"In this paper, we prove that there exists a universal constant $C$, depending only on positive integers $n\\geq 3$ and $p\\leq n-1$, such that if $M^n$ is a compact free boundary submanifold of dimension $n$ immersed in the Euclidean unit ball $\\mathbb{B}^{n+k}$ whose size of the traceless second fundamental form is less than $C$, then the $p$th cohomology group of $M^n$ vanishes. Also, employing a different technique, we obtain a rigidity result for compact free boundary surfaces minimally immersed in the unit ball $\\mathbb{B}^{2+k}$.","authors_text":"Abra\\~ao Mendes, Feliciano Vit\\'orio, Marcos P. Cavalcante","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-18T10:30:59Z","title":"Vanishing theorems for the cohomology groups of free boundary hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06849","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:fff7ba9552dcf6b3325bee2635dbd7e0b5eb940f22cf8a806cd927f67664c71d","target":"record","created_at":"2026-05-18T00:00:08Z","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":"c6bc2345203c3ddbaf62caeb5edc840d3170f2e6f1d2dd87ecbd85384a42b340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-18T10:30:59Z","title_canon_sha256":"6cdf4f45bd133c047459677d6851156e6b3e3523f6afbcdae5ec3b8d76ca3d74"},"schema_version":"1.0","source":{"id":"1807.06849","kind":"arxiv","version":2}},"canonical_sha256":"6be04508d95ee30177b043bcf0903ad6544996779468dd62dcdadb1081def630","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6be04508d95ee30177b043bcf0903ad6544996779468dd62dcdadb1081def630","first_computed_at":"2026-05-18T00:00:08.294059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:08.294059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VMxL6JeAlbsA7BGRdZb32eqPSLMiaRuA8E0rArY5Ct7JMewK6kqK3FRh1aWVzTf1HmT7J0haCWXOYcMZLfmDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:08.294499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff7ba9552dcf6b3325bee2635dbd7e0b5eb940f22cf8a806cd927f67664c71d","sha256:0325aff072dae370d1c9de137b397549147a5710f79392e43251a6fbdc69389c"],"state_sha256":"e3ef3ed7d239bb41f438fb6a2bb176603301922208846c944bbf579ac078d8d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5nOoI1KrFY4+pflb6mjr/MMEsj7J5KSPaCHlNMdkIer8qRMrCKb2rQsaq5Bz0J3qC4YHteXNwmoS3WB5/avAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:43:43.389415Z","bundle_sha256":"2159abf439dac63316a84528a3cf54ad64433da01896a6a6322245bd5656c1e9"}}