{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BBB6MN7KJMBMN2CAGENFRN7Q5Z","short_pith_number":"pith:BBB6MN7K","canonical_record":{"source":{"id":"1108.4476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:15:05Z","cross_cats_sorted":[],"title_canon_sha256":"e600ab4d5a23548f6c79bd35d180fec86338cd4980db3b061317da002a11dd8d","abstract_canon_sha256":"84b1d2fe07822470e85529413b75444a3f299434d00740c88e4fb77e66f076eb"},"schema_version":"1.0"},"canonical_sha256":"0843e637ea4b02c6e840311a58b7f0ee4640ca3fd198dc5de58a5b64451150ec","source":{"kind":"arxiv","id":"1108.4476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4476","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4476v1","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4476","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"BBB6MN7KJMBM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BBB6MN7KJMBMN2CA","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BBB6MN7K","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BBB6MN7KJMBMN2CAGENFRN7Q5Z","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:15:05Z","cross_cats_sorted":[],"title_canon_sha256":"e600ab4d5a23548f6c79bd35d180fec86338cd4980db3b061317da002a11dd8d","abstract_canon_sha256":"84b1d2fe07822470e85529413b75444a3f299434d00740c88e4fb77e66f076eb"},"schema_version":"1.0"},"canonical_sha256":"0843e637ea4b02c6e840311a58b7f0ee4640ca3fd198dc5de58a5b64451150ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:54.500484Z","signature_b64":"g0Ntqzva2SNmnb9tLk/rruwtrJwNB9vM5/Zob2eCNj2xwAdfOslY1u0wD9Aaf5I23GJs21GdrLBsK8hkuV4SCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0843e637ea4b02c6e840311a58b7f0ee4640ca3fd198dc5de58a5b64451150ec","last_reissued_at":"2026-05-18T04:14:54.499775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:54.499775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4476","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":"2026-05-18T04:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oEXAN3Pu5XV+HU4OA1qdk5QHG6ZFh1e5sOxxU8M9ou85X2WfbaZfhbaF51VgxFXh3E4FTRAdCb9FuhTwVK3FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:24:24.864133Z"},"content_sha256":"1e201ffc5c47d86b3923741c4d4ab28f92e2aa1a771a99ecdc789295d13c43f3","schema_version":"1.0","event_id":"sha256:1e201ffc5c47d86b3923741c4d4ab28f92e2aa1a771a99ecdc789295d13c43f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BBB6MN7KJMBMN2CAGENFRN7Q5Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concordance properties of parallel links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniel Ruberman, Saso Strle","submitted_at":"2011-08-23T02:15:05Z","abstract_excerpt":"We investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant to a split link, then many smooth concordance invariants of K must vanish, including the tau and s-invariants, and suitably normalized d-invariants of surgeries on K. We also investigate the (2,2m) cables P_m(K), and find obstructions to smooth concordance to the sum of the (2,2m) torus link and a split link."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4476","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":"2026-05-18T04:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCJMOsYUIBiCQeNutWO7iqnTYNsNKArCQdZZ/gXLcoFBpBKl7b6oDm4Sxok61ERY9pYtfjprgmja1OLNx2AqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:24:24.864816Z"},"content_sha256":"f71828aa2f3b5bdb8480ed10862c11a899241381a14fd1874cbd3f0d285bbb08","schema_version":"1.0","event_id":"sha256:f71828aa2f3b5bdb8480ed10862c11a899241381a14fd1874cbd3f0d285bbb08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z/bundle.json","state_url":"https://pith.science/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z/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":"2026-05-27T06:24:24Z","links":{"resolver":"https://pith.science/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z","bundle":"https://pith.science/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z/bundle.json","state":"https://pith.science/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBB6MN7KJMBMN2CAGENFRN7Q5Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BBB6MN7KJMBMN2CAGENFRN7Q5Z","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":"84b1d2fe07822470e85529413b75444a3f299434d00740c88e4fb77e66f076eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:15:05Z","title_canon_sha256":"e600ab4d5a23548f6c79bd35d180fec86338cd4980db3b061317da002a11dd8d"},"schema_version":"1.0","source":{"id":"1108.4476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4476","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4476v1","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4476","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"BBB6MN7KJMBM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BBB6MN7KJMBMN2CA","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BBB6MN7K","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:f71828aa2f3b5bdb8480ed10862c11a899241381a14fd1874cbd3f0d285bbb08","target":"graph","created_at":"2026-05-18T04:14:54Z","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 investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant to a split link, then many smooth concordance invariants of K must vanish, including the tau and s-invariants, and suitably normalized d-invariants of surgeries on K. We also investigate the (2,2m) cables P_m(K), and find obstructions to smooth concordance to the sum of the (2,2m) torus link and a split link.","authors_text":"Daniel Ruberman, Saso Strle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:15:05Z","title":"Concordance properties of parallel links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4476","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":"sha256:1e201ffc5c47d86b3923741c4d4ab28f92e2aa1a771a99ecdc789295d13c43f3","target":"record","created_at":"2026-05-18T04:14:54Z","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":"84b1d2fe07822470e85529413b75444a3f299434d00740c88e4fb77e66f076eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:15:05Z","title_canon_sha256":"e600ab4d5a23548f6c79bd35d180fec86338cd4980db3b061317da002a11dd8d"},"schema_version":"1.0","source":{"id":"1108.4476","kind":"arxiv","version":1}},"canonical_sha256":"0843e637ea4b02c6e840311a58b7f0ee4640ca3fd198dc5de58a5b64451150ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0843e637ea4b02c6e840311a58b7f0ee4640ca3fd198dc5de58a5b64451150ec","first_computed_at":"2026-05-18T04:14:54.499775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:54.499775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g0Ntqzva2SNmnb9tLk/rruwtrJwNB9vM5/Zob2eCNj2xwAdfOslY1u0wD9Aaf5I23GJs21GdrLBsK8hkuV4SCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:54.500484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e201ffc5c47d86b3923741c4d4ab28f92e2aa1a771a99ecdc789295d13c43f3","sha256:f71828aa2f3b5bdb8480ed10862c11a899241381a14fd1874cbd3f0d285bbb08"],"state_sha256":"dfb59f37868aed238b81d216777f22a74d470ccc6916dddd23bf2d15600cf5db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGXIRLWu/YW9/ADplzcsxcYqfvBs/u/3A+s7OA2QXllzlDrsXmFuVDPPH6InOsrnEcy2Ghgbru13g8WmmnaQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:24:24.868059Z","bundle_sha256":"53e526a591cd5daf4792c3ee263bec7c3c2f2224ab653e593858e416d4f4cd61"}}