{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Y5L6HBXIOHIYSGI6HKCHJTCITB","short_pith_number":"pith:Y5L6HBXI","canonical_record":{"source":{"id":"1706.02820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-09T03:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"f355de45b768a10311ed8db3bbcc221d8078e43eb40b136636d3561af54707f4","abstract_canon_sha256":"c43e7d6bd62f488ae198c738c212ab0f13cf3f8aaad47eb9ab22bf44f456ee53"},"schema_version":"1.0"},"canonical_sha256":"c757e386e871d189191e3a8474cc4898657722d86e31b940710361c4dc35c408","source":{"kind":"arxiv","id":"1706.02820","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02820","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02820v1","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02820","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"Y5L6HBXIOHIY","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y5L6HBXIOHIYSGI6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y5L6HBXI","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Y5L6HBXIOHIYSGI6HKCHJTCITB","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-09T03:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"f355de45b768a10311ed8db3bbcc221d8078e43eb40b136636d3561af54707f4","abstract_canon_sha256":"c43e7d6bd62f488ae198c738c212ab0f13cf3f8aaad47eb9ab22bf44f456ee53"},"schema_version":"1.0"},"canonical_sha256":"c757e386e871d189191e3a8474cc4898657722d86e31b940710361c4dc35c408","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:00.227943Z","signature_b64":"8pT9bijDSOIY66Z62+HypJtxUwaEiMWHGHKn9IrauhveuPOoaZ5nUsqk6Nu0LtEg9UsQOYXuPO/ahgbCgTbcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c757e386e871d189191e3a8474cc4898657722d86e31b940710361c4dc35c408","last_reissued_at":"2026-05-17T23:56:00.227259Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:00.227259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02820","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":"2026-05-17T23:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SiJWTQP5BIPrDE8PsyCGp5mxBoBH7L9endcRdL+8RyXGWDveYCj4Bu0SoWX4a1FgYNXusov/c7NWGZQOPPACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:42:03.731462Z"},"content_sha256":"0540c972c2472a5144ab5ff8eda53414d6b6afbf06fba47235876b1b35702a12","schema_version":"1.0","event_id":"sha256:0540c972c2472a5144ab5ff8eda53414d6b6afbf06fba47235876b1b35702a12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Y5L6HBXIOHIYSGI6HKCHJTCITB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A full-twist inequality for the $\\nu^+$-invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kouki Sato","submitted_at":"2017-06-09T03:28:54Z","abstract_excerpt":"Hom and Wu introduced a knot concordance invariant called $\\nu^+$, which dominates many concordance invariants derived from Heegaard Floer homology. In this paper, we give a full-twist inequality for $\\nu^+$. By using the inequality, we extend Wu's cabling formula for $\\nu^+$ (which is proved only for particular positive cables) to all cables in the form of an inequality. In addition, we also discuss $\\nu^+$-equivalence, which is an equivalence relation on the knot concordance group. We introduce a partial order on $\\nu^+$-equivalence classes, and study its relationship to full-twists."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02820","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":"2026-05-17T23:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QXDGGWK59JMe4xchZItntRX/eSpRTlMTdTRGXR9Dpx2XA7lECyBC2OSK7iYC4mZglUjfc6SwvaUg5ShIxEv8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:42:03.731814Z"},"content_sha256":"bfb1d3b9f4f7f5b954bf0ffe6b78ba77b55d18ff2814ece1e13da91a4bb5a373","schema_version":"1.0","event_id":"sha256:bfb1d3b9f4f7f5b954bf0ffe6b78ba77b55d18ff2814ece1e13da91a4bb5a373"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB/bundle.json","state_url":"https://pith.science/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB/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":"2026-06-28T08:42:03Z","links":{"resolver":"https://pith.science/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB","bundle":"https://pith.science/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB/bundle.json","state":"https://pith.science/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5L6HBXIOHIYSGI6HKCHJTCITB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y5L6HBXIOHIYSGI6HKCHJTCITB","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":"c43e7d6bd62f488ae198c738c212ab0f13cf3f8aaad47eb9ab22bf44f456ee53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-09T03:28:54Z","title_canon_sha256":"f355de45b768a10311ed8db3bbcc221d8078e43eb40b136636d3561af54707f4"},"schema_version":"1.0","source":{"id":"1706.02820","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02820","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02820v1","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02820","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"Y5L6HBXIOHIY","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y5L6HBXIOHIYSGI6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y5L6HBXI","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:bfb1d3b9f4f7f5b954bf0ffe6b78ba77b55d18ff2814ece1e13da91a4bb5a373","target":"graph","created_at":"2026-05-17T23:56:00Z","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":"Hom and Wu introduced a knot concordance invariant called $\\nu^+$, which dominates many concordance invariants derived from Heegaard Floer homology. In this paper, we give a full-twist inequality for $\\nu^+$. By using the inequality, we extend Wu's cabling formula for $\\nu^+$ (which is proved only for particular positive cables) to all cables in the form of an inequality. In addition, we also discuss $\\nu^+$-equivalence, which is an equivalence relation on the knot concordance group. We introduce a partial order on $\\nu^+$-equivalence classes, and study its relationship to full-twists.","authors_text":"Kouki Sato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-09T03:28:54Z","title":"A full-twist inequality for the $\\nu^+$-invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02820","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":"sha256:0540c972c2472a5144ab5ff8eda53414d6b6afbf06fba47235876b1b35702a12","target":"record","created_at":"2026-05-17T23:56:00Z","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":"c43e7d6bd62f488ae198c738c212ab0f13cf3f8aaad47eb9ab22bf44f456ee53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-09T03:28:54Z","title_canon_sha256":"f355de45b768a10311ed8db3bbcc221d8078e43eb40b136636d3561af54707f4"},"schema_version":"1.0","source":{"id":"1706.02820","kind":"arxiv","version":1}},"canonical_sha256":"c757e386e871d189191e3a8474cc4898657722d86e31b940710361c4dc35c408","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c757e386e871d189191e3a8474cc4898657722d86e31b940710361c4dc35c408","first_computed_at":"2026-05-17T23:56:00.227259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:00.227259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8pT9bijDSOIY66Z62+HypJtxUwaEiMWHGHKn9IrauhveuPOoaZ5nUsqk6Nu0LtEg9UsQOYXuPO/ahgbCgTbcDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:00.227943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0540c972c2472a5144ab5ff8eda53414d6b6afbf06fba47235876b1b35702a12","sha256:bfb1d3b9f4f7f5b954bf0ffe6b78ba77b55d18ff2814ece1e13da91a4bb5a373"],"state_sha256":"d1817d97446f00c47e92f33ecae871a3340e309e3ceaf06ece23b57d8a9b0330"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XwO9Hkre2ys673ph1JC8NsNqItQPhLSfxhMV0pgpWBN0CDyi/iO9YgjZjBgB0+t7eF0Hh191zCIWQGxNyJt0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T08:42:03.733676Z","bundle_sha256":"b3c424f2b98cfcc44f2c9eaa4e385e88f5f8e11226daa16e5e9f04c3831614d7"}}