{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7UHS7UXRC5YJ5O3S52VHSWQOKG","short_pith_number":"pith:7UHS7UXR","canonical_record":{"source":{"id":"1211.1423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-07T00:01:16Z","cross_cats_sorted":[],"title_canon_sha256":"5ab8544a683f1c73daa3c65cb57f1367fa75a789ed17fda2ef87fabbcc9840fd","abstract_canon_sha256":"bd697a8d7bde9bdcb9505e1ce99cf3051cf8c2df3b60f515375b426bad7ef88a"},"schema_version":"1.0"},"canonical_sha256":"fd0f2fd2f117709ebb72eeaa795a0e5198eecf96f5d7f5442655f1e897ab7d6c","source":{"kind":"arxiv","id":"1211.1423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1423","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1423v1","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1423","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"7UHS7UXRC5YJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7UHS7UXRC5YJ5O3S","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7UHS7UXR","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7UHS7UXRC5YJ5O3S52VHSWQOKG","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-07T00:01:16Z","cross_cats_sorted":[],"title_canon_sha256":"5ab8544a683f1c73daa3c65cb57f1367fa75a789ed17fda2ef87fabbcc9840fd","abstract_canon_sha256":"bd697a8d7bde9bdcb9505e1ce99cf3051cf8c2df3b60f515375b426bad7ef88a"},"schema_version":"1.0"},"canonical_sha256":"fd0f2fd2f117709ebb72eeaa795a0e5198eecf96f5d7f5442655f1e897ab7d6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:26.024922Z","signature_b64":"Vxzr6aMvX7HA+LyCWnGmW7I9Bfnt8qe5+PdLb3HmcrHUZCTn8sy+ELYL21i11MGeze0XA0U52jEvdgU+BdrCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd0f2fd2f117709ebb72eeaa795a0e5198eecf96f5d7f5442655f1e897ab7d6c","last_reissued_at":"2026-05-18T01:22:26.024274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:26.024274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1423","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":"2026-05-18T01:22:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5H8D3GrNhOcUvD4MG+E0Nbd6SarSyD60/w0NIaHZRYy0Ob0EQao/7hxnFtzk1ieVfS10pQKjWnRZv6Osdu2pAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:59:09.265281Z"},"content_sha256":"3efda5169cbdbd42bc05759fa08acf7a139b87a70d64bb22a55336f9332fe6f9","schema_version":"1.0","event_id":"sha256:3efda5169cbdbd42bc05759fa08acf7a139b87a70d64bb22a55336f9332fe6f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7UHS7UXRC5YJ5O3S52VHSWQOKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The (n)-solvable filtration of the link concordance group and Milnor's invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Carolyn Otto","submitted_at":"2012-11-07T00:01:16Z","abstract_excerpt":"We establish several new results about both the (n)-solvable filtration, F_n^m, of the set of link concordance classes and the (n)-solvable filtration of the string link concordance group. We first establish a relationship between Milnor's invariants and links, L, with certain restrictions on the 4-manifold bounded by M_L. Using this relationship, we can relate (n)-solvability of a link (or string link) with its Milnor's invariants. Specifically, we show that if a link is (n)-solvable, then its Milnor's invariants vanish for lengths up to 2^{n+2}-1. Previously, there were no known results abou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1423","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":"2026-05-18T01:22:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X000Fi1CT003Z0FLSxQWvpz8VmMFT9GerEdUT3Gdu68DTIeL/LHPzx+iXUP4XbM3LRBwK0ARBM9WVK1XGcsyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:59:09.265641Z"},"content_sha256":"baeae24daf2604719eb5bce8f3b80c034d2202009f8cb243ee1e3fa9dd37a653","schema_version":"1.0","event_id":"sha256:baeae24daf2604719eb5bce8f3b80c034d2202009f8cb243ee1e3fa9dd37a653"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG/bundle.json","state_url":"https://pith.science/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG/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":"2026-06-21T21:59:09Z","links":{"resolver":"https://pith.science/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG","bundle":"https://pith.science/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG/bundle.json","state":"https://pith.science/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UHS7UXRC5YJ5O3S52VHSWQOKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7UHS7UXRC5YJ5O3S52VHSWQOKG","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":"bd697a8d7bde9bdcb9505e1ce99cf3051cf8c2df3b60f515375b426bad7ef88a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-07T00:01:16Z","title_canon_sha256":"5ab8544a683f1c73daa3c65cb57f1367fa75a789ed17fda2ef87fabbcc9840fd"},"schema_version":"1.0","source":{"id":"1211.1423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1423","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1423v1","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1423","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"7UHS7UXRC5YJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7UHS7UXRC5YJ5O3S","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7UHS7UXR","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:baeae24daf2604719eb5bce8f3b80c034d2202009f8cb243ee1e3fa9dd37a653","target":"graph","created_at":"2026-05-18T01:22:26Z","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 establish several new results about both the (n)-solvable filtration, F_n^m, of the set of link concordance classes and the (n)-solvable filtration of the string link concordance group. We first establish a relationship between Milnor's invariants and links, L, with certain restrictions on the 4-manifold bounded by M_L. Using this relationship, we can relate (n)-solvability of a link (or string link) with its Milnor's invariants. Specifically, we show that if a link is (n)-solvable, then its Milnor's invariants vanish for lengths up to 2^{n+2}-1. Previously, there were no known results abou","authors_text":"Carolyn Otto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-07T00:01:16Z","title":"The (n)-solvable filtration of the link concordance group and Milnor's invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1423","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":"sha256:3efda5169cbdbd42bc05759fa08acf7a139b87a70d64bb22a55336f9332fe6f9","target":"record","created_at":"2026-05-18T01:22:26Z","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":"bd697a8d7bde9bdcb9505e1ce99cf3051cf8c2df3b60f515375b426bad7ef88a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-07T00:01:16Z","title_canon_sha256":"5ab8544a683f1c73daa3c65cb57f1367fa75a789ed17fda2ef87fabbcc9840fd"},"schema_version":"1.0","source":{"id":"1211.1423","kind":"arxiv","version":1}},"canonical_sha256":"fd0f2fd2f117709ebb72eeaa795a0e5198eecf96f5d7f5442655f1e897ab7d6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd0f2fd2f117709ebb72eeaa795a0e5198eecf96f5d7f5442655f1e897ab7d6c","first_computed_at":"2026-05-18T01:22:26.024274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:26.024274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vxzr6aMvX7HA+LyCWnGmW7I9Bfnt8qe5+PdLb3HmcrHUZCTn8sy+ELYL21i11MGeze0XA0U52jEvdgU+BdrCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:26.024922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3efda5169cbdbd42bc05759fa08acf7a139b87a70d64bb22a55336f9332fe6f9","sha256:baeae24daf2604719eb5bce8f3b80c034d2202009f8cb243ee1e3fa9dd37a653"],"state_sha256":"bea9873adeb60b9974ca7026d56893581cbbfb134ff6f75fc70f73f2a3b642b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bf2SOb8ktr3pN1+AoTMB/9AKmCRphkwQKKLZ9ahjYYUD4R0PfHyiVEcO2/225/EMxRbWW8HEMDwBo7HlzGLKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:59:09.267593Z","bundle_sha256":"0cb56f5ffafecadb7f85b43399b7920338024c09f9dc250acb5e9d84a43111ea"}}