{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VOAS2VT3N4DQHZM6QN5XC2IWU6","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":"529e37aadf554e8425cf18c8f93d8ab3cf4ecc618dca0e51adc75ab1dd94fdd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:17:00Z","title_canon_sha256":"fa74349606c2c9f778d18a6fe0bb4138464ff2139bd7e8eefed1bbc5db713620"},"schema_version":"1.0","source":{"id":"1108.4477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4477","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4477v2","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4477","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"VOAS2VT3N4DQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VOAS2VT3N4DQHZM6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VOAS2VT3","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:26878ad8604917ab4f722b870b5925a04cd4269d6d9ca7069aa09f84694ca8ee","target":"graph","created_at":"2026-05-18T04:12:54Z","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 give an explicit construction of linearly independent families of knots arbitrarily deep in the (n)-solvable filtration of the knot concordance group using the \\rho^1-invariant. A difference between previous constructions of infinite rank subgroups in the concordance group and ours is that the deepest infecting knots in the construction we present are allowed to have vanishing Tristram-Levine signatures.","authors_text":"Christopher William Davis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:17:00Z","title":"Linear Independence of Knots Arising from Iterated Infection Without the Use of Tristram Levine Signatures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4477","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:fa0e9ca79e4ad0cd9ccae54f23f98b33b70fd94bef06485352ed4bc58e863835","target":"record","created_at":"2026-05-18T04:12:54Z","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":"529e37aadf554e8425cf18c8f93d8ab3cf4ecc618dca0e51adc75ab1dd94fdd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-23T02:17:00Z","title_canon_sha256":"fa74349606c2c9f778d18a6fe0bb4138464ff2139bd7e8eefed1bbc5db713620"},"schema_version":"1.0","source":{"id":"1108.4477","kind":"arxiv","version":2}},"canonical_sha256":"ab812d567b6f0703e59e837b716916a788e25d55e1c47b4fa705ccfabc8a86e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab812d567b6f0703e59e837b716916a788e25d55e1c47b4fa705ccfabc8a86e4","first_computed_at":"2026-05-18T04:12:54.302498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:54.302498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sakTg+1ZSbbZM4E0UI0gTQIoiMKPPo9O69E4nqUHbVkJX4wtn38wyxguZq7SIJwwLkYS6yAEzjtHzC77EQ4jAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:54.303085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa0e9ca79e4ad0cd9ccae54f23f98b33b70fd94bef06485352ed4bc58e863835","sha256:26878ad8604917ab4f722b870b5925a04cd4269d6d9ca7069aa09f84694ca8ee"],"state_sha256":"adee38b162b56ecd9f5cbef7169b66a9677dd5d5b86b6a9385a4aad09e444028"}