{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:JLVQHKZ32AOYKFRFBABMOBOEOT","short_pith_number":"pith:JLVQHKZ3","canonical_record":{"source":{"id":"2211.17109","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-30T15:54:51Z","cross_cats_sorted":[],"title_canon_sha256":"b2f49eff8a01a197ed2d36c48033c7be3e055fc263d3200c6a5af3eef45de872","abstract_canon_sha256":"73c5fc1d0859c273d55f586d337ae31bc55e00d12fa2073a630eb0eb2f391833"},"schema_version":"1.0"},"canonical_sha256":"4aeb03ab3bd01d8516250802c705c474f880c138356464ed8ac5933d7bcd9e8f","source":{"kind":"arxiv","id":"2211.17109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.17109","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"2211.17109v2","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.17109","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"JLVQHKZ32AOY","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"pith_short_16","alias_value":"JLVQHKZ32AOYKFRF","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"pith_short_8","alias_value":"JLVQHKZ3","created_at":"2026-07-05T09:57:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:JLVQHKZ32AOYKFRFBABMOBOEOT","target":"record","payload":{"canonical_record":{"source":{"id":"2211.17109","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-30T15:54:51Z","cross_cats_sorted":[],"title_canon_sha256":"b2f49eff8a01a197ed2d36c48033c7be3e055fc263d3200c6a5af3eef45de872","abstract_canon_sha256":"73c5fc1d0859c273d55f586d337ae31bc55e00d12fa2073a630eb0eb2f391833"},"schema_version":"1.0"},"canonical_sha256":"4aeb03ab3bd01d8516250802c705c474f880c138356464ed8ac5933d7bcd9e8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:36.613577Z","signature_b64":"F+fc1OUfic0ksZJn0DPd+OuGzhTtzlDDAPZt5QKjHcZ/c+3qrBL//DJL8f4zO9p6NefJPZ0rRnXIK6TOA0qQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aeb03ab3bd01d8516250802c705c474f880c138356464ed8ac5933d7bcd9e8f","last_reissued_at":"2026-07-05T09:57:36.613075Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:36.613075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.17109","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":"2026-07-05T09:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jN1dvG6svNA9rmokn6qRLis6Gbv0aVu3XR0tDNwMfxVmrDIbg2KR7C5Wg02iyX3et9SJVtuMx94RQ0Mbj37DAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T07:29:08.148750Z"},"content_sha256":"5befd6b6ce1a25b24d6be2a0e340f7d097c8a4e82e12e8838c970e2275ebd315","schema_version":"1.0","event_id":"sha256:5befd6b6ce1a25b24d6be2a0e340f7d097c8a4e82e12e8838c970e2275ebd315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:JLVQHKZ32AOYKFRFBABMOBOEOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twist positivity, L-space knots, and concordance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hugh Morton, Siddhi Krishna","submitted_at":"2022-11-30T15:54:51Z","abstract_excerpt":"Many well studied knots can be realized as positive braid knots where the braid word contains a positive full twist; we say that such knots are twist positive. Some important families of knots are twist positive, including torus knots, 1-bridge braids, algebraic knots, and Lorenz knots. We prove that if a knot is twist positive, the braid index appears as the third exponent in its Alexander polynomial. We provide a few applications of this result. After observing that most known examples of L-space knots are twist positive, we prove: if $K$ is a twist positive L-space knot, the braid index and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.17109","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.17109/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yj0zeqj/xcpEenwrXPw8jOiH8jDLiFieVWbI8GSkBMAlgPfMPwepvO+gmuD1hTKNaGLsZ2ZbYQ86yF1QnLVPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T07:29:08.149326Z"},"content_sha256":"def9a3de2eb62d7b8b7d5862b8a9e233195f195a3ae3bcb60bbfc642313b3e6e","schema_version":"1.0","event_id":"sha256:def9a3de2eb62d7b8b7d5862b8a9e233195f195a3ae3bcb60bbfc642313b3e6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JLVQHKZ32AOYKFRFBABMOBOEOT/bundle.json","state_url":"https://pith.science/pith/JLVQHKZ32AOYKFRFBABMOBOEOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JLVQHKZ32AOYKFRFBABMOBOEOT/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":"2026-08-22T07:29:08Z","links":{"resolver":"https://pith.science/pith/JLVQHKZ32AOYKFRFBABMOBOEOT","bundle":"https://pith.science/pith/JLVQHKZ32AOYKFRFBABMOBOEOT/bundle.json","state":"https://pith.science/pith/JLVQHKZ32AOYKFRFBABMOBOEOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JLVQHKZ32AOYKFRFBABMOBOEOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JLVQHKZ32AOYKFRFBABMOBOEOT","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":"73c5fc1d0859c273d55f586d337ae31bc55e00d12fa2073a630eb0eb2f391833","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-30T15:54:51Z","title_canon_sha256":"b2f49eff8a01a197ed2d36c48033c7be3e055fc263d3200c6a5af3eef45de872"},"schema_version":"1.0","source":{"id":"2211.17109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.17109","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"2211.17109v2","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.17109","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"JLVQHKZ32AOY","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"pith_short_16","alias_value":"JLVQHKZ32AOYKFRF","created_at":"2026-07-05T09:57:36Z"},{"alias_kind":"pith_short_8","alias_value":"JLVQHKZ3","created_at":"2026-07-05T09:57:36Z"}],"graph_snapshots":[{"event_id":"sha256:def9a3de2eb62d7b8b7d5862b8a9e233195f195a3ae3bcb60bbfc642313b3e6e","target":"graph","created_at":"2026-07-05T09:57:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.17109/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many well studied knots can be realized as positive braid knots where the braid word contains a positive full twist; we say that such knots are twist positive. Some important families of knots are twist positive, including torus knots, 1-bridge braids, algebraic knots, and Lorenz knots. We prove that if a knot is twist positive, the braid index appears as the third exponent in its Alexander polynomial. We provide a few applications of this result. After observing that most known examples of L-space knots are twist positive, we prove: if $K$ is a twist positive L-space knot, the braid index and","authors_text":"Hugh Morton, Siddhi Krishna","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-30T15:54:51Z","title":"Twist positivity, L-space knots, and concordance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.17109","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":"sha256:5befd6b6ce1a25b24d6be2a0e340f7d097c8a4e82e12e8838c970e2275ebd315","target":"record","created_at":"2026-07-05T09:57:36Z","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":"73c5fc1d0859c273d55f586d337ae31bc55e00d12fa2073a630eb0eb2f391833","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-11-30T15:54:51Z","title_canon_sha256":"b2f49eff8a01a197ed2d36c48033c7be3e055fc263d3200c6a5af3eef45de872"},"schema_version":"1.0","source":{"id":"2211.17109","kind":"arxiv","version":2}},"canonical_sha256":"4aeb03ab3bd01d8516250802c705c474f880c138356464ed8ac5933d7bcd9e8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aeb03ab3bd01d8516250802c705c474f880c138356464ed8ac5933d7bcd9e8f","first_computed_at":"2026-07-05T09:57:36.613075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:36.613075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+fc1OUfic0ksZJn0DPd+OuGzhTtzlDDAPZt5QKjHcZ/c+3qrBL//DJL8f4zO9p6NefJPZ0rRnXIK6TOA0qQAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:36.613577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.17109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5befd6b6ce1a25b24d6be2a0e340f7d097c8a4e82e12e8838c970e2275ebd315","sha256:def9a3de2eb62d7b8b7d5862b8a9e233195f195a3ae3bcb60bbfc642313b3e6e"],"state_sha256":"ab14e7ccfacabb34ba6fbe7dbe80ee24dd8b42d575ff1078a7e9909dd303b5ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Olcp6Raogj5qnsKcdjSD8Li2kpCcUDUbWRsOHIiW5PpiZZjHaot+52WnwHfh66qRauyDPAS+0V8Ca/3P71FuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T07:29:08.153218Z","bundle_sha256":"242696a63a70cba513b8b3c65095681014c4e9f2ce5ccce0b125f68c4be92523"}}