{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XKBA2K2GN5DHEJBJQNN6JJYVKB","short_pith_number":"pith:XKBA2K2G","canonical_record":{"source":{"id":"1304.3011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-10T16:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"ad6396cc9be7a2225c4a421c65c525ccd4ef35222efeca3f3362b887ed31d2dd","abstract_canon_sha256":"e942e6a2dcf6f3fe68bd144d2cdf4c34e925901c554bfdda9a2f0f45aad6aa98"},"schema_version":"1.0"},"canonical_sha256":"ba820d2b466f46722429835be4a7155044985f1eb618b8358aa07fbacb27a092","source":{"kind":"arxiv","id":"1304.3011","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3011","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3011v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3011","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"XKBA2K2GN5DH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XKBA2K2GN5DHEJBJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XKBA2K2G","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XKBA2K2GN5DHEJBJQNN6JJYVKB","target":"record","payload":{"canonical_record":{"source":{"id":"1304.3011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-10T16:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"ad6396cc9be7a2225c4a421c65c525ccd4ef35222efeca3f3362b887ed31d2dd","abstract_canon_sha256":"e942e6a2dcf6f3fe68bd144d2cdf4c34e925901c554bfdda9a2f0f45aad6aa98"},"schema_version":"1.0"},"canonical_sha256":"ba820d2b466f46722429835be4a7155044985f1eb618b8358aa07fbacb27a092","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.886190Z","signature_b64":"flHBPVoUQIDNtyBszJ3D8NH2mu1FfvH9CgmWPHuPfQRUKKEcLE2Adj6rMRlcqYqnZvMeIcFurEoyPM7E9RZvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba820d2b466f46722429835be4a7155044985f1eb618b8358aa07fbacb27a092","last_reissued_at":"2026-05-18T00:44:29.885534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.885534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.3011","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":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDxNWDD6BSkx0j4QfmfZMeiEvnyIhFdlmlOWjll+bse/Fvz+SR8OzMz2uJGgBFa/qKfLg+llb3H8c4cQPvUGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:23:16.595849Z"},"content_sha256":"52129ce7d97d9c4648eb4efa02d8b4eb2d017de13e7636fcd29da9ff99ffba63","schema_version":"1.0","event_id":"sha256:52129ce7d97d9c4648eb4efa02d8b4eb2d017de13e7636fcd29da9ff99ffba63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XKBA2K2GN5DHEJBJQNN6JJYVKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splittings of von Neumann rho-invariants of knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Se-Goo Kim, Taehee Kim","submitted_at":"2013-04-10T16:05:41Z","abstract_excerpt":"We give a sufficient condition under which vanishing property of Cochran-Orr-Teichner knot concordance obstructions splits under connected sum. The condition is described in terms of self-annihilating submodules with respect to higher-order Blanchfield linking forms. This extends results of Levine and the authors on distinguishing knots with coprime Alexander polynomials up to concordance. As an application, we show that the knots constructed by Cochran, Orr and Teichner as the first examples of nonslice knots with vanishing Casson-Gordon invariants are not concordant to any knot of genus one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3011","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":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5j2Fxa/06ymiiT05DkXN+kADClmAGTKCpSuMkvPDf8cSvYUEsJhzFVB5/JibuH70DAPu0aU6SgSaD2BBwYOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:23:16.596498Z"},"content_sha256":"720b27b691e09a5779fa966eb88e66756d5b9fc30154394b4d62f8840e7da9f0","schema_version":"1.0","event_id":"sha256:720b27b691e09a5779fa966eb88e66756d5b9fc30154394b4d62f8840e7da9f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB/bundle.json","state_url":"https://pith.science/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB/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":"2026-05-28T15:23:16Z","links":{"resolver":"https://pith.science/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB","bundle":"https://pith.science/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB/bundle.json","state":"https://pith.science/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKBA2K2GN5DHEJBJQNN6JJYVKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XKBA2K2GN5DHEJBJQNN6JJYVKB","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":"e942e6a2dcf6f3fe68bd144d2cdf4c34e925901c554bfdda9a2f0f45aad6aa98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-10T16:05:41Z","title_canon_sha256":"ad6396cc9be7a2225c4a421c65c525ccd4ef35222efeca3f3362b887ed31d2dd"},"schema_version":"1.0","source":{"id":"1304.3011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3011","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3011v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3011","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"XKBA2K2GN5DH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XKBA2K2GN5DHEJBJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XKBA2K2G","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:720b27b691e09a5779fa966eb88e66756d5b9fc30154394b4d62f8840e7da9f0","target":"graph","created_at":"2026-05-18T00:44:29Z","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 a sufficient condition under which vanishing property of Cochran-Orr-Teichner knot concordance obstructions splits under connected sum. The condition is described in terms of self-annihilating submodules with respect to higher-order Blanchfield linking forms. This extends results of Levine and the authors on distinguishing knots with coprime Alexander polynomials up to concordance. As an application, we show that the knots constructed by Cochran, Orr and Teichner as the first examples of nonslice knots with vanishing Casson-Gordon invariants are not concordant to any knot of genus one.","authors_text":"Se-Goo Kim, Taehee Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-10T16:05:41Z","title":"Splittings of von Neumann rho-invariants of knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3011","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":"sha256:52129ce7d97d9c4648eb4efa02d8b4eb2d017de13e7636fcd29da9ff99ffba63","target":"record","created_at":"2026-05-18T00:44:29Z","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":"e942e6a2dcf6f3fe68bd144d2cdf4c34e925901c554bfdda9a2f0f45aad6aa98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-10T16:05:41Z","title_canon_sha256":"ad6396cc9be7a2225c4a421c65c525ccd4ef35222efeca3f3362b887ed31d2dd"},"schema_version":"1.0","source":{"id":"1304.3011","kind":"arxiv","version":1}},"canonical_sha256":"ba820d2b466f46722429835be4a7155044985f1eb618b8358aa07fbacb27a092","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba820d2b466f46722429835be4a7155044985f1eb618b8358aa07fbacb27a092","first_computed_at":"2026-05-18T00:44:29.885534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:29.885534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flHBPVoUQIDNtyBszJ3D8NH2mu1FfvH9CgmWPHuPfQRUKKEcLE2Adj6rMRlcqYqnZvMeIcFurEoyPM7E9RZvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:29.886190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52129ce7d97d9c4648eb4efa02d8b4eb2d017de13e7636fcd29da9ff99ffba63","sha256:720b27b691e09a5779fa966eb88e66756d5b9fc30154394b4d62f8840e7da9f0"],"state_sha256":"19ba4f32fadda91b98a5ca76e88c1458c1e4723552a35f053cfb29626b882603"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2O0chkB+J8t/Xi5bfWs+Pxxc3DdEjyF9al9xsnQAqPPr8BEiI9RtwKH34oNrh4Vi5pjKBqoWUbbDkfZ2uRCRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:23:16.599643Z","bundle_sha256":"e81aafd69be7439632bd7c017471066ba9fc438a2729d265f49d9efe88eba208"}}