{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Z7UKNCZ5ACBDWJVI3TXITPLVGR","short_pith_number":"pith:Z7UKNCZ5","canonical_record":{"source":{"id":"2606.03583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-02T12:51:18Z","cross_cats_sorted":["math.AP","math.GT"],"title_canon_sha256":"18083d7505e7477f4bef04939f95228ca3dab414a072f2815e70450573528bda","abstract_canon_sha256":"0ea651cf5ec660ee4a933ff799726af5da654b9688e8d41b9a28497009074d7b"},"schema_version":"1.0"},"canonical_sha256":"cfe8a68b3d00823b26a8dcee89bd753443f57583e9fe8c6cd2608fb5444e82f6","source":{"kind":"arxiv","id":"2606.03583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03583","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03583v1","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03583","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z7UKNCZ5ACBD","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"Z7UKNCZ5ACBDWJVI","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"Z7UKNCZ5","created_at":"2026-06-03T01:06:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Z7UKNCZ5ACBDWJVI3TXITPLVGR","target":"record","payload":{"canonical_record":{"source":{"id":"2606.03583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-02T12:51:18Z","cross_cats_sorted":["math.AP","math.GT"],"title_canon_sha256":"18083d7505e7477f4bef04939f95228ca3dab414a072f2815e70450573528bda","abstract_canon_sha256":"0ea651cf5ec660ee4a933ff799726af5da654b9688e8d41b9a28497009074d7b"},"schema_version":"1.0"},"canonical_sha256":"cfe8a68b3d00823b26a8dcee89bd753443f57583e9fe8c6cd2608fb5444e82f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:06:01.437602Z","signature_b64":"FCcQUi29qOF/VMbq0pe1GXaA8etcSpcdtKgHsnL6WtdtnBpIqmbwdVoCvIC0jUFIK0+MiCbCCQwvJFRxh5YUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfe8a68b3d00823b26a8dcee89bd753443f57583e9fe8c6cd2608fb5444e82f6","last_reissued_at":"2026-06-03T01:06:01.437227Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:06:01.437227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.03583","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T01:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zHUF7Lhdp1CE/EFslSx4WXYXG3B+7oHSdQXu/cYlSNstAU4MzeCreTxavK7NbRm1kEEhjm8F+gVTybkTDDIkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:03:11.726121Z"},"content_sha256":"dcfaee038081cef15bc968cdc29f86a58e76fae6888b7e81fbe66f2c100ffcf5","schema_version":"1.0","event_id":"sha256:dcfaee038081cef15bc968cdc29f86a58e76fae6888b7e81fbe66f2c100ffcf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Z7UKNCZ5ACBDWJVI3TXITPLVGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed minimal surfaces of index one in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Andr\\'e Neves, Fernando C. Marques","submitted_at":"2026-06-02T12:51:18Z","abstract_excerpt":"In this paper we prove that an $(n+1)$-manifold, compactly $n$-enlargeable, where $3\\leq (n+1)\\leq 7$, has connected, immersed Morse index one, closed minimal hypersurfaces with unbounded volumes for bumpy metrics. We prove that in the three-dimensional case the hypersurfaces are geometrically distinct using cyclic coverings of manifolds with boundary. The proof extends to $(n+1)$-fiberings. We prove a scalar curvature rigidity theorem for area-nonincreasing maps of three-dimensional manifolds. The case of stable surfaces is also discussed by using cohomology classes and incompressible surface"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03583","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03583/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T01:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hpHd47al3D2Mm/hm9io8T7/iPx3aBcgb2CN5T7ER+NL4zpe+jc60RLsSohioRX/PhL71QnJ1KkGaC+1m/n+MBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:03:11.726515Z"},"content_sha256":"4ad7209df60d79c0bdba58b6e3450cbc193574bb7d866f0a4fb21ae2a4075d3e","schema_version":"1.0","event_id":"sha256:4ad7209df60d79c0bdba58b6e3450cbc193574bb7d866f0a4fb21ae2a4075d3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR/bundle.json","state_url":"https://pith.science/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR/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":"2026-06-04T22:03:11Z","links":{"resolver":"https://pith.science/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR","bundle":"https://pith.science/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR/bundle.json","state":"https://pith.science/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7UKNCZ5ACBDWJVI3TXITPLVGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z7UKNCZ5ACBDWJVI3TXITPLVGR","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":"0ea651cf5ec660ee4a933ff799726af5da654b9688e8d41b9a28497009074d7b","cross_cats_sorted":["math.AP","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-02T12:51:18Z","title_canon_sha256":"18083d7505e7477f4bef04939f95228ca3dab414a072f2815e70450573528bda"},"schema_version":"1.0","source":{"id":"2606.03583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03583","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03583v1","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03583","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z7UKNCZ5ACBD","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"Z7UKNCZ5ACBDWJVI","created_at":"2026-06-03T01:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"Z7UKNCZ5","created_at":"2026-06-03T01:06:01Z"}],"graph_snapshots":[{"event_id":"sha256:4ad7209df60d79c0bdba58b6e3450cbc193574bb7d866f0a4fb21ae2a4075d3e","target":"graph","created_at":"2026-06-03T01:06:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.03583/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we prove that an $(n+1)$-manifold, compactly $n$-enlargeable, where $3\\leq (n+1)\\leq 7$, has connected, immersed Morse index one, closed minimal hypersurfaces with unbounded volumes for bumpy metrics. We prove that in the three-dimensional case the hypersurfaces are geometrically distinct using cyclic coverings of manifolds with boundary. The proof extends to $(n+1)$-fiberings. We prove a scalar curvature rigidity theorem for area-nonincreasing maps of three-dimensional manifolds. The case of stable surfaces is also discussed by using cohomology classes and incompressible surface","authors_text":"Andr\\'e Neves, Fernando C. Marques","cross_cats":["math.AP","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-02T12:51:18Z","title":"Closed minimal surfaces of index one in Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03583","kind":"arxiv","version":1},"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:dcfaee038081cef15bc968cdc29f86a58e76fae6888b7e81fbe66f2c100ffcf5","target":"record","created_at":"2026-06-03T01:06:01Z","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":"0ea651cf5ec660ee4a933ff799726af5da654b9688e8d41b9a28497009074d7b","cross_cats_sorted":["math.AP","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-02T12:51:18Z","title_canon_sha256":"18083d7505e7477f4bef04939f95228ca3dab414a072f2815e70450573528bda"},"schema_version":"1.0","source":{"id":"2606.03583","kind":"arxiv","version":1}},"canonical_sha256":"cfe8a68b3d00823b26a8dcee89bd753443f57583e9fe8c6cd2608fb5444e82f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfe8a68b3d00823b26a8dcee89bd753443f57583e9fe8c6cd2608fb5444e82f6","first_computed_at":"2026-06-03T01:06:01.437227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:06:01.437227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCcQUi29qOF/VMbq0pe1GXaA8etcSpcdtKgHsnL6WtdtnBpIqmbwdVoCvIC0jUFIK0+MiCbCCQwvJFRxh5YUCg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:06:01.437602Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcfaee038081cef15bc968cdc29f86a58e76fae6888b7e81fbe66f2c100ffcf5","sha256:4ad7209df60d79c0bdba58b6e3450cbc193574bb7d866f0a4fb21ae2a4075d3e"],"state_sha256":"f2337759fc7ce345ec41e221d8b9b10316bfca87686c0ad5d816e3e6e4c7f8b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xw/qxQm+KhXjiJB7PGvqgRrHaaRcAVx5U1vMTFTW7TCx722aNWcFspIOyxRWgyIcti0VBO09LxWuI+4ZtwEGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:03:11.728574Z","bundle_sha256":"007bd598735a206b1bca78d1d39a8371c4a3b90f2781269856a9460cdab90f85"}}