{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:N2B2SD7KCNNDSOW3IUU53ARLRO","short_pith_number":"pith:N2B2SD7K","canonical_record":{"source":{"id":"1212.6628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-29T13:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"be43e0a692babf80c414f2da8dc1e9304e6f2898ad3883e24172dd38cc5ccaf6","abstract_canon_sha256":"9ed400070d47b296c0a92655f7e1e7b26bc9746e5dfd7a8d25e508f773438206"},"schema_version":"1.0"},"canonical_sha256":"6e83a90fea135a393adb4529dd822b8bb9106abc7cd6bdcec398895adcbd9262","source":{"kind":"arxiv","id":"1212.6628","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6628","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6628v2","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6628","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"N2B2SD7KCNND","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N2B2SD7KCNNDSOW3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N2B2SD7K","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:N2B2SD7KCNNDSOW3IUU53ARLRO","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-29T13:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"be43e0a692babf80c414f2da8dc1e9304e6f2898ad3883e24172dd38cc5ccaf6","abstract_canon_sha256":"9ed400070d47b296c0a92655f7e1e7b26bc9746e5dfd7a8d25e508f773438206"},"schema_version":"1.0"},"canonical_sha256":"6e83a90fea135a393adb4529dd822b8bb9106abc7cd6bdcec398895adcbd9262","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:41.947332Z","signature_b64":"doAu4JwwaK4k9atb7P9F8yQu8iHeGRMFv9Od0h9v3ZVzvfAHqC5dPhpIOI+o75+Fow8LVGjdtvNS65IVFsi7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e83a90fea135a393adb4529dd822b8bb9106abc7cd6bdcec398895adcbd9262","last_reissued_at":"2026-05-18T01:04:41.946824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:41.946824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6628","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hud14/qhem1AoJKStqRIrVlqG1oHxvmhpi3703rvXsV1Fnd9ppo+UP2pKNrNLALyUCg1vYieiUhIhBxLV6fWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:18:45.905765Z"},"content_sha256":"a24a1ecf27441704422bd74e787b4bc0ca2a4e520d6d138d1b35f22f3ff7b9ae","schema_version":"1.0","event_id":"sha256:a24a1ecf27441704422bd74e787b4bc0ca2a4e520d6d138d1b35f22f3ff7b9ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:N2B2SD7KCNNDSOW3IUU53ARLRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topologically slice knots of smooth concordance order two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Charles Livingston, Matthew Hedden, Se-Goo Kim","submitted_at":"2012-12-29T13:44:20Z","abstract_excerpt":"The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman's work on topological surgery and Donaldson's gauge theoretic approach to 4-manifolds. Here, as an application of Ozsvath and Szabo's Heegaard-Floer theory, we show the existence of an infinite subgroup of the smooth concordance group generated by topologically slice knots of concordance order two. In addition, no nontrivial element in this subgroup can be represented by a knot with Alexander polynomial one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6628","kind":"arxiv","version":2},"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":"2026-05-18T01:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"++GkzjaXRsMKp0bMvRvADp5MRKgUEqdN0RpWp8EQ8PpvAyA7VOWPnLwWvP6cjVQILOnb4Fk7wq3ykpRDVkJFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:18:45.906115Z"},"content_sha256":"1c8d95438689acf807ad3212a612f19c083af4b49db4ac81df65ac477184e786","schema_version":"1.0","event_id":"sha256:1c8d95438689acf807ad3212a612f19c083af4b49db4ac81df65ac477184e786"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2B2SD7KCNNDSOW3IUU53ARLRO/bundle.json","state_url":"https://pith.science/pith/N2B2SD7KCNNDSOW3IUU53ARLRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2B2SD7KCNNDSOW3IUU53ARLRO/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":"2026-05-31T12:18:45Z","links":{"resolver":"https://pith.science/pith/N2B2SD7KCNNDSOW3IUU53ARLRO","bundle":"https://pith.science/pith/N2B2SD7KCNNDSOW3IUU53ARLRO/bundle.json","state":"https://pith.science/pith/N2B2SD7KCNNDSOW3IUU53ARLRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2B2SD7KCNNDSOW3IUU53ARLRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N2B2SD7KCNNDSOW3IUU53ARLRO","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":"9ed400070d47b296c0a92655f7e1e7b26bc9746e5dfd7a8d25e508f773438206","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-29T13:44:20Z","title_canon_sha256":"be43e0a692babf80c414f2da8dc1e9304e6f2898ad3883e24172dd38cc5ccaf6"},"schema_version":"1.0","source":{"id":"1212.6628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6628","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6628v2","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6628","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"N2B2SD7KCNND","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N2B2SD7KCNNDSOW3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N2B2SD7K","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:1c8d95438689acf807ad3212a612f19c083af4b49db4ac81df65ac477184e786","target":"graph","created_at":"2026-05-18T01:04:41Z","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":"The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman's work on topological surgery and Donaldson's gauge theoretic approach to 4-manifolds. Here, as an application of Ozsvath and Szabo's Heegaard-Floer theory, we show the existence of an infinite subgroup of the smooth concordance group generated by topologically slice knots of concordance order two. In addition, no nontrivial element in this subgroup can be represented by a knot with Alexander polynomial one.","authors_text":"Charles Livingston, Matthew Hedden, Se-Goo Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-29T13:44:20Z","title":"Topologically slice knots of smooth concordance order two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6628","kind":"arxiv","version":2},"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:a24a1ecf27441704422bd74e787b4bc0ca2a4e520d6d138d1b35f22f3ff7b9ae","target":"record","created_at":"2026-05-18T01:04:41Z","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":"9ed400070d47b296c0a92655f7e1e7b26bc9746e5dfd7a8d25e508f773438206","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-29T13:44:20Z","title_canon_sha256":"be43e0a692babf80c414f2da8dc1e9304e6f2898ad3883e24172dd38cc5ccaf6"},"schema_version":"1.0","source":{"id":"1212.6628","kind":"arxiv","version":2}},"canonical_sha256":"6e83a90fea135a393adb4529dd822b8bb9106abc7cd6bdcec398895adcbd9262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e83a90fea135a393adb4529dd822b8bb9106abc7cd6bdcec398895adcbd9262","first_computed_at":"2026-05-18T01:04:41.946824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:41.946824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"doAu4JwwaK4k9atb7P9F8yQu8iHeGRMFv9Od0h9v3ZVzvfAHqC5dPhpIOI+o75+Fow8LVGjdtvNS65IVFsi7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:41.947332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a24a1ecf27441704422bd74e787b4bc0ca2a4e520d6d138d1b35f22f3ff7b9ae","sha256:1c8d95438689acf807ad3212a612f19c083af4b49db4ac81df65ac477184e786"],"state_sha256":"5f9b08d55cfbba2cf4dbc7318e52640adac16481b07dd3b5134ecc2c826a3847"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ByXWUCdZclmU6i/27SsEmZ5loAKrTzqqVelEbx9HAsR6EFt/jTbTG1pVYRBgnb9AwR6DXeqWf86GHFnwZ8EcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:18:45.908332Z","bundle_sha256":"8a313fd4ee52650f7878003246094b5b12a907786c41ea4ca7a132bba2150fe0"}}