{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GLDVJGPUBMSG3L5WAJIRODDWYD","short_pith_number":"pith:GLDVJGPU","canonical_record":{"source":{"id":"1112.3432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-15T06:38:26Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b2f3757ef5aa15b359c71dd615132781b9b657b77c621767e074f8a4157ac0d7","abstract_canon_sha256":"ce377979339c82534ea66b03652f98798cd218241ef303b75946dbd6bcc05494"},"schema_version":"1.0"},"canonical_sha256":"32c75499f40b246dafb60251170c76c0f459c741299d4e15ab872a9b6ee37417","source":{"kind":"arxiv","id":"1112.3432","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3432","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3432v1","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3432","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"GLDVJGPUBMSG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLDVJGPUBMSG3L5W","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLDVJGPU","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GLDVJGPUBMSG3L5WAJIRODDWYD","target":"record","payload":{"canonical_record":{"source":{"id":"1112.3432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-15T06:38:26Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b2f3757ef5aa15b359c71dd615132781b9b657b77c621767e074f8a4157ac0d7","abstract_canon_sha256":"ce377979339c82534ea66b03652f98798cd218241ef303b75946dbd6bcc05494"},"schema_version":"1.0"},"canonical_sha256":"32c75499f40b246dafb60251170c76c0f459c741299d4e15ab872a9b6ee37417","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:18.615903Z","signature_b64":"bxHx/ywW6/vu8OUjVenuY375YYscAX6op8ernP4QEorLwkmjkHouFC30UVZ2wZNCrRYtrjouGIGvjwr5v8qTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32c75499f40b246dafb60251170c76c0f459c741299d4e15ab872a9b6ee37417","last_reissued_at":"2026-05-18T04:06:18.615298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:18.615298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.3432","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":"2026-05-18T04:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Thx6sPg2ZcTl/J0P5PsPrCPOV8u2dNTWoLlgSfTE8LokbfNJ2HrgDpvljIfC6D26S+fvSf4f5S96Unv0qxoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:09:27.969917Z"},"content_sha256":"f1ef77bb8b01f2035f745bcf9006299bc518aec4256f04df1d2f0976b0e58b2f","schema_version":"1.0","event_id":"sha256:f1ef77bb8b01f2035f745bcf9006299bc518aec4256f04df1d2f0976b0e58b2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GLDVJGPUBMSG3L5WAJIRODDWYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd(k,r) at most 10","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Delu Tian, Haiyan Guan, Shenglin Zhou","submitted_at":"2011-12-15T06:38:26Z","abstract_excerpt":"This paper is a further contribution to the classification of line-transitive finite linear spaces. We prove that if S is a non-trivial finite linear space with the Fang-Li parameter gcd(k,r) is 9 or 10, the automorphism group G of S is line-transitive and point-imprimitive, then S is the Desarguesian projective plane PG(2,9)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3432","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":""},"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":"2026-05-18T04:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RoTxkGIBXOTGYANoJsES1e5xCMj5tYTHP3dFVK+RkRInomAcy2EMMOXwoOmmxyp2KItd8dMzrjUCq+eBUZy8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:09:27.970518Z"},"content_sha256":"143e2b01cfcff67dffd81c63bbae57d428111fc6a742dac1ce4ad97cdeb515aa","schema_version":"1.0","event_id":"sha256:143e2b01cfcff67dffd81c63bbae57d428111fc6a742dac1ce4ad97cdeb515aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLDVJGPUBMSG3L5WAJIRODDWYD/bundle.json","state_url":"https://pith.science/pith/GLDVJGPUBMSG3L5WAJIRODDWYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLDVJGPUBMSG3L5WAJIRODDWYD/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":"2026-05-30T21:09:27Z","links":{"resolver":"https://pith.science/pith/GLDVJGPUBMSG3L5WAJIRODDWYD","bundle":"https://pith.science/pith/GLDVJGPUBMSG3L5WAJIRODDWYD/bundle.json","state":"https://pith.science/pith/GLDVJGPUBMSG3L5WAJIRODDWYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLDVJGPUBMSG3L5WAJIRODDWYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GLDVJGPUBMSG3L5WAJIRODDWYD","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":"ce377979339c82534ea66b03652f98798cd218241ef303b75946dbd6bcc05494","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-15T06:38:26Z","title_canon_sha256":"b2f3757ef5aa15b359c71dd615132781b9b657b77c621767e074f8a4157ac0d7"},"schema_version":"1.0","source":{"id":"1112.3432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3432","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3432v1","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3432","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"GLDVJGPUBMSG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLDVJGPUBMSG3L5W","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLDVJGPU","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:143e2b01cfcff67dffd81c63bbae57d428111fc6a742dac1ce4ad97cdeb515aa","target":"graph","created_at":"2026-05-18T04:06:18Z","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":"This paper is a further contribution to the classification of line-transitive finite linear spaces. We prove that if S is a non-trivial finite linear space with the Fang-Li parameter gcd(k,r) is 9 or 10, the automorphism group G of S is line-transitive and point-imprimitive, then S is the Desarguesian projective plane PG(2,9).","authors_text":"Delu Tian, Haiyan Guan, Shenglin Zhou","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-15T06:38:26Z","title":"Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd(k,r) at most 10"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3432","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:f1ef77bb8b01f2035f745bcf9006299bc518aec4256f04df1d2f0976b0e58b2f","target":"record","created_at":"2026-05-18T04:06:18Z","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":"ce377979339c82534ea66b03652f98798cd218241ef303b75946dbd6bcc05494","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-15T06:38:26Z","title_canon_sha256":"b2f3757ef5aa15b359c71dd615132781b9b657b77c621767e074f8a4157ac0d7"},"schema_version":"1.0","source":{"id":"1112.3432","kind":"arxiv","version":1}},"canonical_sha256":"32c75499f40b246dafb60251170c76c0f459c741299d4e15ab872a9b6ee37417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32c75499f40b246dafb60251170c76c0f459c741299d4e15ab872a9b6ee37417","first_computed_at":"2026-05-18T04:06:18.615298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:18.615298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bxHx/ywW6/vu8OUjVenuY375YYscAX6op8ernP4QEorLwkmjkHouFC30UVZ2wZNCrRYtrjouGIGvjwr5v8qTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:18.615903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1ef77bb8b01f2035f745bcf9006299bc518aec4256f04df1d2f0976b0e58b2f","sha256:143e2b01cfcff67dffd81c63bbae57d428111fc6a742dac1ce4ad97cdeb515aa"],"state_sha256":"5cdfacb1cc5637bebc214c225a97e53cdcb4849f3007d10f21ae21b0fdc830ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmnjUtcd4wFFRY/08C0sVBz/OKabOZSwSAVCY8H9S/7BInRvl2NQGcdXcxdZt+dli3Thf2JGhM19hp0qlUPsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:09:27.972659Z","bundle_sha256":"7a9066154179351c19ada6341ce3c821dd4f86446545e4a6c8175f99fb24fcf6"}}