{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6PVPZRARILYYXNHS4ZGSPIUEUD","short_pith_number":"pith:6PVPZRAR","canonical_record":{"source":{"id":"1204.4636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-20T14:05:33Z","cross_cats_sorted":[],"title_canon_sha256":"96bf2c146a5a6e02ea96acf3fcff07d3570057c23a514256a06084ee8b29d6d2","abstract_canon_sha256":"41b608d81c709775324bd3d5a0e55942c096d635ae5b8caa239b69ee381b21eb"},"schema_version":"1.0"},"canonical_sha256":"f3eafcc41142f18bb4f2e64d27a284a0dda1eceb72e2d39c24e3e83aa1fa6525","source":{"kind":"arxiv","id":"1204.4636","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4636","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4636v1","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4636","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"6PVPZRARILYY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6PVPZRARILYYXNHS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6PVPZRAR","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6PVPZRARILYYXNHS4ZGSPIUEUD","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-20T14:05:33Z","cross_cats_sorted":[],"title_canon_sha256":"96bf2c146a5a6e02ea96acf3fcff07d3570057c23a514256a06084ee8b29d6d2","abstract_canon_sha256":"41b608d81c709775324bd3d5a0e55942c096d635ae5b8caa239b69ee381b21eb"},"schema_version":"1.0"},"canonical_sha256":"f3eafcc41142f18bb4f2e64d27a284a0dda1eceb72e2d39c24e3e83aa1fa6525","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:43.225756Z","signature_b64":"KCxsjhk/jPgB7XE5TgrsUnDhymkB9qkEcLmiCNgj5mxHLIKjbIew+qSw6BI9SPa6jOx7AlAHCak8+AsFwkaoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3eafcc41142f18bb4f2e64d27a284a0dda1eceb72e2d39c24e3e83aa1fa6525","last_reissued_at":"2026-05-18T02:41:43.225209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:43.225209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4636","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":"2026-05-18T02:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Kj5BdezDc0wZlEEwzfUz+IbO/mXsMMoSilmO04/hsa7VrnqasLMFMMyaqTx3a+o962JIvWZ7D9x7FSh9nymAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:12:48.378194Z"},"content_sha256":"56f8b540b6161691ca0596e025e0a06b32e5586379265340a96d8230021615ed","schema_version":"1.0","event_id":"sha256:56f8b540b6161691ca0596e025e0a06b32e5586379265340a96d8230021615ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6PVPZRARILYYXNHS4ZGSPIUEUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conservative Subgroup Separability For Surfaces With Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daryl Cooper, Mark D. Baker","submitted_at":"2012-04-20T14:05:33Z","abstract_excerpt":"If F is a surface with boundary, then a finitely generated subgroup without peripheral elements of G = {\\pi}_1(F) can be separated from finitely many other elements of G by a finite index subgroup of G corresponding to a finite cover F' with the same number of boundary components as F ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4636","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":"2026-05-18T02:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXKWXsLu63HtydJluNiKHqAW3qx5s4HitF2K4T+7jYlgafq4lVf1vFeWnRfooGqzkAWQelK3AVmk2sHPxP0GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:12:48.378776Z"},"content_sha256":"d2f064a149d1a92408e43a019a4df159453b3d059d91a0fc7f8c3c7a19456307","schema_version":"1.0","event_id":"sha256:d2f064a149d1a92408e43a019a4df159453b3d059d91a0fc7f8c3c7a19456307"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PVPZRARILYYXNHS4ZGSPIUEUD/bundle.json","state_url":"https://pith.science/pith/6PVPZRARILYYXNHS4ZGSPIUEUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PVPZRARILYYXNHS4ZGSPIUEUD/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":"2026-05-30T21:12:48Z","links":{"resolver":"https://pith.science/pith/6PVPZRARILYYXNHS4ZGSPIUEUD","bundle":"https://pith.science/pith/6PVPZRARILYYXNHS4ZGSPIUEUD/bundle.json","state":"https://pith.science/pith/6PVPZRARILYYXNHS4ZGSPIUEUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PVPZRARILYYXNHS4ZGSPIUEUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6PVPZRARILYYXNHS4ZGSPIUEUD","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":"41b608d81c709775324bd3d5a0e55942c096d635ae5b8caa239b69ee381b21eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-20T14:05:33Z","title_canon_sha256":"96bf2c146a5a6e02ea96acf3fcff07d3570057c23a514256a06084ee8b29d6d2"},"schema_version":"1.0","source":{"id":"1204.4636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4636","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4636v1","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4636","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"6PVPZRARILYY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6PVPZRARILYYXNHS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6PVPZRAR","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:d2f064a149d1a92408e43a019a4df159453b3d059d91a0fc7f8c3c7a19456307","target":"graph","created_at":"2026-05-18T02:41:43Z","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":"If F is a surface with boundary, then a finitely generated subgroup without peripheral elements of G = {\\pi}_1(F) can be separated from finitely many other elements of G by a finite index subgroup of G corresponding to a finite cover F' with the same number of boundary components as F .","authors_text":"Daryl Cooper, Mark D. Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-20T14:05:33Z","title":"Conservative Subgroup Separability For Surfaces With Boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4636","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":"sha256:56f8b540b6161691ca0596e025e0a06b32e5586379265340a96d8230021615ed","target":"record","created_at":"2026-05-18T02:41:43Z","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":"41b608d81c709775324bd3d5a0e55942c096d635ae5b8caa239b69ee381b21eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-20T14:05:33Z","title_canon_sha256":"96bf2c146a5a6e02ea96acf3fcff07d3570057c23a514256a06084ee8b29d6d2"},"schema_version":"1.0","source":{"id":"1204.4636","kind":"arxiv","version":1}},"canonical_sha256":"f3eafcc41142f18bb4f2e64d27a284a0dda1eceb72e2d39c24e3e83aa1fa6525","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3eafcc41142f18bb4f2e64d27a284a0dda1eceb72e2d39c24e3e83aa1fa6525","first_computed_at":"2026-05-18T02:41:43.225209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:43.225209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCxsjhk/jPgB7XE5TgrsUnDhymkB9qkEcLmiCNgj5mxHLIKjbIew+qSw6BI9SPa6jOx7AlAHCak8+AsFwkaoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:43.225756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56f8b540b6161691ca0596e025e0a06b32e5586379265340a96d8230021615ed","sha256:d2f064a149d1a92408e43a019a4df159453b3d059d91a0fc7f8c3c7a19456307"],"state_sha256":"07e4a356c32cfd8d3e29034c83d37866134c943421dd9221841b9381f0241818"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkgPNyYdmjLLUnzek7gyz5gbWdGvgQ/2EEtjzLydPj2bdBPdDf+svWAGt1bdAf2zJQI5ZVnL5uviUuUdwE0hAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:12:48.381759Z","bundle_sha256":"25bee6d2bfcbbb55bcbe878f51138acf7b51b88a7ab1e1f0ed7bfdb6d525cf24"}}