{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FPTDSROIYSTQLTYTDRC73G3XGP","short_pith_number":"pith:FPTDSROI","canonical_record":{"source":{"id":"2607.28863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T22:03:06Z","cross_cats_sorted":[],"title_canon_sha256":"37c957300812e1726be9bfe8b069cb431de4effc1adbb278422f7056398f9147","abstract_canon_sha256":"66b0166671834445fc77f4194bed555015db1c023eedc64ba14db9afb64f79df"},"schema_version":"1.0"},"canonical_sha256":"2be63945c8c4a705cf131c45fd9b7733f99e957628ee49cc4879537672f6d04b","source":{"kind":"arxiv","id":"2607.28863","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28863","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28863v1","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28863","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"FPTDSROIYSTQ","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_16","alias_value":"FPTDSROIYSTQLTYT","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_8","alias_value":"FPTDSROI","created_at":"2026-08-03T01:17:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FPTDSROIYSTQLTYTDRC73G3XGP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.28863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T22:03:06Z","cross_cats_sorted":[],"title_canon_sha256":"37c957300812e1726be9bfe8b069cb431de4effc1adbb278422f7056398f9147","abstract_canon_sha256":"66b0166671834445fc77f4194bed555015db1c023eedc64ba14db9afb64f79df"},"schema_version":"1.0"},"canonical_sha256":"2be63945c8c4a705cf131c45fd9b7733f99e957628ee49cc4879537672f6d04b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:17:14.216963Z","signature_b64":"f9/sX2fCpgIn2tD+Ts96DqdAojHlmuIWAeMWwyhXfIQn11teieics+F/zOjB5olN00gjjOwpHuiMkNbKIvQSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2be63945c8c4a705cf131c45fd9b7733f99e957628ee49cc4879537672f6d04b","last_reissued_at":"2026-08-03T01:17:14.215383Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:17:14.215383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.28863","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":"2026-08-03T01:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLKdCxqWjHtdrNktCu08xf0p6rFlWIknxWrd81vZe+ruXu1AczB1BmE/5Kkm35WuqIuEfTQSOm2I5Ar0euPTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:04:38.032931Z"},"content_sha256":"e57c55fed0aeba879bcad95669c22953de744d7ae9ebde1c3c174a5b27ba4bac","schema_version":"1.0","event_id":"sha256:e57c55fed0aeba879bcad95669c22953de744d7ae9ebde1c3c174a5b27ba4bac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FPTDSROIYSTQLTYTDRC73G3XGP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On transversality in flag manifolds and linearity of amalgams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Konstantinos Tsouvalas, Sami Douba","submitted_at":"2026-07-30T22:03:06Z","abstract_excerpt":"We show that the fundamental group of the double of a complete negatively curved locally symmetric manifold along a closed geodesic is linear. More generally, we establish linearity of doubles of torsion-free transverse subgroups (also known in the literature as regular antipodal subgroups) of semisimple Lie groups along biproximal maximal cyclic subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28863","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/2607.28863/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":"2026-08-03T01:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n15Nq9OFa3MqLG6MhjdPr1tvXIuG7F8UCsptP7oHq5VDdHEBegIlY6p7Xap3SydeRR5IK5dMbAfJD7UZXWMcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:04:38.033707Z"},"content_sha256":"54dac8c659b394e38c0bdf574a04e2149f2a2b4b96bae2f852bc65d41f6b8f20","schema_version":"1.0","event_id":"sha256:54dac8c659b394e38c0bdf574a04e2149f2a2b4b96bae2f852bc65d41f6b8f20"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:FPTDSROIYSTQLTYTDRC73G3XGP","target":"integrity","payload":{"note":"Identifier '10.1093/plms/s3-55' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"Gehring, F. W. and Martin, G. J. , TITLE =. Proc. London Math. Soc. (3) , FJOURNAL =. 1987 , NUMBER =. doi:10.1093/plms/s3-55\\_2.331 , URL =","arxiv_id":"2607.28863","detector":"doi_compliance","evidence":{"doi":"10.1093/plms/s3-55","arxiv_id":null,"ref_index":3,"raw_excerpt":"Gehring, F. W. and Martin, G. J. , TITLE =. Proc. London Math. Soc. (3) , FJOURNAL =. 1987 , NUMBER =. doi:10.1093/plms/s3-55\\_2.331 , URL =","parse_status":"well_formed","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"],"resolution_status":"hard_miss"},"severity":"critical","ref_index":3,"audited_at":"2026-08-03T01:48:23.228566Z","event_type":"pith.integrity.v1","detected_doi":"10.1093/plms/s3-55","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"621f6aed2674dd13ec411c0e13355b10271aa1c09900f06446b6b6e6dc6acb8c","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17517,"payload_sha256":"6da3360ef7a8550bbb77a82ee5923069e596b23043d06dde322fe9f427b336d8","signature_b64":"A7VMd+Im5eKGKbBIbacnQHVfGlufpK7kVKZ8g/d53OV3x/N9KF2O6hHFeKCGVcfH+JhkIso1g5FnoHLO3Of4CA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-03T01:48:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5EzwNAI3R2rmo/YJD44Gb6+0dISqifC4thx4M078GL3QsZHDJwKHZkn3ntbwXbcdFdLCRnu6IEiEinGvBjdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:04:38.037079Z"},"content_sha256":"2faae6aac94b6a49165dd1ce353c14567849acddbcf92a251b71677968d7d6eb","schema_version":"1.0","event_id":"sha256:2faae6aac94b6a49165dd1ce353c14567849acddbcf92a251b71677968d7d6eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPTDSROIYSTQLTYTDRC73G3XGP/bundle.json","state_url":"https://pith.science/pith/FPTDSROIYSTQLTYTDRC73G3XGP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPTDSROIYSTQLTYTDRC73G3XGP/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":"2026-08-10T00:04:38Z","links":{"resolver":"https://pith.science/pith/FPTDSROIYSTQLTYTDRC73G3XGP","bundle":"https://pith.science/pith/FPTDSROIYSTQLTYTDRC73G3XGP/bundle.json","state":"https://pith.science/pith/FPTDSROIYSTQLTYTDRC73G3XGP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPTDSROIYSTQLTYTDRC73G3XGP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FPTDSROIYSTQLTYTDRC73G3XGP","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"66b0166671834445fc77f4194bed555015db1c023eedc64ba14db9afb64f79df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T22:03:06Z","title_canon_sha256":"37c957300812e1726be9bfe8b069cb431de4effc1adbb278422f7056398f9147"},"schema_version":"1.0","source":{"id":"2607.28863","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28863","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28863v1","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28863","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"FPTDSROIYSTQ","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_16","alias_value":"FPTDSROIYSTQLTYT","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_8","alias_value":"FPTDSROI","created_at":"2026-08-03T01:17:14Z"}],"graph_snapshots":[{"event_id":"sha256:54dac8c659b394e38c0bdf574a04e2149f2a2b4b96bae2f852bc65d41f6b8f20","target":"graph","created_at":"2026-08-03T01:17:14Z","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/2607.28863/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the fundamental group of the double of a complete negatively curved locally symmetric manifold along a closed geodesic is linear. More generally, we establish linearity of doubles of torsion-free transverse subgroups (also known in the literature as regular antipodal subgroups) of semisimple Lie groups along biproximal maximal cyclic subgroups.","authors_text":"Konstantinos Tsouvalas, Sami Douba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T22:03:06Z","title":"On transversality in flag manifolds and linearity of amalgams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28863","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:e57c55fed0aeba879bcad95669c22953de744d7ae9ebde1c3c174a5b27ba4bac","target":"record","created_at":"2026-08-03T01:17:14Z","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":"66b0166671834445fc77f4194bed555015db1c023eedc64ba14db9afb64f79df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T22:03:06Z","title_canon_sha256":"37c957300812e1726be9bfe8b069cb431de4effc1adbb278422f7056398f9147"},"schema_version":"1.0","source":{"id":"2607.28863","kind":"arxiv","version":1}},"canonical_sha256":"2be63945c8c4a705cf131c45fd9b7733f99e957628ee49cc4879537672f6d04b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2be63945c8c4a705cf131c45fd9b7733f99e957628ee49cc4879537672f6d04b","first_computed_at":"2026-08-03T01:17:14.215383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:17:14.215383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9/sX2fCpgIn2tD+Ts96DqdAojHlmuIWAeMWwyhXfIQn11teieics+F/zOjB5olN00gjjOwpHuiMkNbKIvQSAQ==","signature_status":"signed_v1","signed_at":"2026-08-03T01:17:14.216963Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28863","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e57c55fed0aeba879bcad95669c22953de744d7ae9ebde1c3c174a5b27ba4bac","sha256:54dac8c659b394e38c0bdf574a04e2149f2a2b4b96bae2f852bc65d41f6b8f20","sha256:2faae6aac94b6a49165dd1ce353c14567849acddbcf92a251b71677968d7d6eb"],"state_sha256":"2d0e85e6ac5ad69b8c467fd87fba4a24ae23d575ac5167ea60a31813428122ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TA2FamXjfQvXoAfb1aEzUDrGwxDPRHkKDbMCnRZQQS5lFHnUdsKE/0q+I0gV7OoZ+1NW0HST1fcHx4YY48meBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T00:04:38.040515Z","bundle_sha256":"9a4e5316e09f99f9e239db16b50f0e5b6835df4fb5da01e183c4d6d7ca67ffc6"}}