{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:P6RM2TBQBCQKV6LTUB44UOTFN2","short_pith_number":"pith:P6RM2TBQ","canonical_record":{"source":{"id":"0902.3693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-21T20:35:13Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fdecf033a5300063b5da61bdaf6332922980dc96370616267bd8e168fcbbc9c9","abstract_canon_sha256":"c37e998c06d16527843dc94b85ea2e822777c0a501b041d611516fdf985cf516"},"schema_version":"1.0"},"canonical_sha256":"7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50","source":{"kind":"arxiv","id":"0902.3693","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.3693","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0902.3693v1","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.3693","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"P6RM2TBQBCQK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P6RM2TBQBCQKV6LT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P6RM2TBQ","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:P6RM2TBQBCQKV6LTUB44UOTFN2","target":"record","payload":{"canonical_record":{"source":{"id":"0902.3693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-21T20:35:13Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fdecf033a5300063b5da61bdaf6332922980dc96370616267bd8e168fcbbc9c9","abstract_canon_sha256":"c37e998c06d16527843dc94b85ea2e822777c0a501b041d611516fdf985cf516"},"schema_version":"1.0"},"canonical_sha256":"7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.641656Z","signature_b64":"Nv2Rj+HI1JxB5gUKDJC9k+S0j0r5uvFgtFjG6vHQ3pmFxJfmih39KmDKFNtAHiec57ofZqBu8tMYZrQ4xGX+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50","last_reissued_at":"2026-05-18T02:58:10.641068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.641068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.3693","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":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EK+m8Rvad9I/gb6kaDQYvhKvwnJ0Pg5oaHbKEd9IpTWCtelC2sl4CEzP2MjN/MBBYBCe2A2oiSBn8JtQNBJ0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:49:15.026409Z"},"content_sha256":"dbf5b67759474c222b5a62d8f9ddc4e402cd2cbb02b406682fca6548b414e1fd","schema_version":"1.0","event_id":"sha256:dbf5b67759474c222b5a62d8f9ddc4e402cd2cbb02b406682fca6548b414e1fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:P6RM2TBQBCQKV6LTUB44UOTFN2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On surface subgroups of doubles of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Cameron Gordon, Henry Wilton","submitted_at":"2009-02-21T20:35:13Z","abstract_excerpt":"We give several sufficient conditions for a double of a free group along a cyclic subgroup to contain a surface subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3693","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":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1lBzPdyjow1AX6MaY5KjumgeuUXSGvN/yy51X2f8xJqoxc9reO198Y/KtKxD4LNod7MLHkIwwMSdBkqiAEVXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:49:15.027116Z"},"content_sha256":"7361a55cb010ba9b3089cf28afed6cae51b6da9eadacec461d78592c92cad3be","schema_version":"1.0","event_id":"sha256:7361a55cb010ba9b3089cf28afed6cae51b6da9eadacec461d78592c92cad3be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6RM2TBQBCQKV6LTUB44UOTFN2/bundle.json","state_url":"https://pith.science/pith/P6RM2TBQBCQKV6LTUB44UOTFN2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6RM2TBQBCQKV6LTUB44UOTFN2/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":"2026-05-27T07:49:15Z","links":{"resolver":"https://pith.science/pith/P6RM2TBQBCQKV6LTUB44UOTFN2","bundle":"https://pith.science/pith/P6RM2TBQBCQKV6LTUB44UOTFN2/bundle.json","state":"https://pith.science/pith/P6RM2TBQBCQKV6LTUB44UOTFN2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6RM2TBQBCQKV6LTUB44UOTFN2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:P6RM2TBQBCQKV6LTUB44UOTFN2","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":"c37e998c06d16527843dc94b85ea2e822777c0a501b041d611516fdf985cf516","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-21T20:35:13Z","title_canon_sha256":"fdecf033a5300063b5da61bdaf6332922980dc96370616267bd8e168fcbbc9c9"},"schema_version":"1.0","source":{"id":"0902.3693","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.3693","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0902.3693v1","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.3693","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"P6RM2TBQBCQK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P6RM2TBQBCQKV6LT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P6RM2TBQ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:7361a55cb010ba9b3089cf28afed6cae51b6da9eadacec461d78592c92cad3be","target":"graph","created_at":"2026-05-18T02:58:10Z","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":"We give several sufficient conditions for a double of a free group along a cyclic subgroup to contain a surface subgroup.","authors_text":"Cameron Gordon, Henry Wilton","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-21T20:35:13Z","title":"On surface subgroups of doubles of free groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3693","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:dbf5b67759474c222b5a62d8f9ddc4e402cd2cbb02b406682fca6548b414e1fd","target":"record","created_at":"2026-05-18T02:58:10Z","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":"c37e998c06d16527843dc94b85ea2e822777c0a501b041d611516fdf985cf516","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-21T20:35:13Z","title_canon_sha256":"fdecf033a5300063b5da61bdaf6332922980dc96370616267bd8e168fcbbc9c9"},"schema_version":"1.0","source":{"id":"0902.3693","kind":"arxiv","version":1}},"canonical_sha256":"7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50","first_computed_at":"2026-05-18T02:58:10.641068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:10.641068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nv2Rj+HI1JxB5gUKDJC9k+S0j0r5uvFgtFjG6vHQ3pmFxJfmih39KmDKFNtAHiec57ofZqBu8tMYZrQ4xGX+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:10.641656Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.3693","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbf5b67759474c222b5a62d8f9ddc4e402cd2cbb02b406682fca6548b414e1fd","sha256:7361a55cb010ba9b3089cf28afed6cae51b6da9eadacec461d78592c92cad3be"],"state_sha256":"65dfb01b11a6f4b7db7833a615d5d2720b2d3892f1569a974c322e02af85cc58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHudCMGauMki0Tyr2caQK3jYZokdLFXIsZ1moAxjTG1b8iUKR0fePG5f9HJP6+k9qaxC0ReUQmynBZrbOHHwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:49:15.030825Z","bundle_sha256":"3bbf9a1bd098563022238f3503fff25acbe10bf0ff049fa4e2ac880dc186b66a"}}