{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2ZCHOAOYTB6QHWJITZAKGOW5UJ","short_pith_number":"pith:2ZCHOAOY","canonical_record":{"source":{"id":"1406.5573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-21T03:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"0f0b929b69b7bdb492348147aa3c642caece59c22304710890d6e3d51e7397eb","abstract_canon_sha256":"bed2cddba03daae3647691520b70b102922e0044c0404ec01673c5441763c492"},"schema_version":"1.0"},"canonical_sha256":"d6447701d8987d03d9289e40a33adda26e24aee9ef8689f5337217f358542dd6","source":{"kind":"arxiv","id":"1406.5573","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5573","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5573v2","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5573","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"2ZCHOAOYTB6Q","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2ZCHOAOYTB6QHWJI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2ZCHOAOY","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2ZCHOAOYTB6QHWJITZAKGOW5UJ","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-21T03:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"0f0b929b69b7bdb492348147aa3c642caece59c22304710890d6e3d51e7397eb","abstract_canon_sha256":"bed2cddba03daae3647691520b70b102922e0044c0404ec01673c5441763c492"},"schema_version":"1.0"},"canonical_sha256":"d6447701d8987d03d9289e40a33adda26e24aee9ef8689f5337217f358542dd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:09.233068Z","signature_b64":"spmpEcZ8wAUxROpWdP9WOyVA1/v/eNWQ/4B1TnMCoqIiupTmGArokfpxIrgaaIRlSJiR565nDPPa0YOy81k4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6447701d8987d03d9289e40a33adda26e24aee9ef8689f5337217f358542dd6","last_reissued_at":"2026-05-18T00:19:09.232550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:09.232550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5573","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":"2026-05-18T00:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F7y1lY29aSrxDpF2RIWPLDHAMZIT9TqUMFOUogA2QFoLlVapjA6HUyVOaYwzfZcJ5wFvAK6sjRxDJCnwSFf9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T07:46:53.294106Z"},"content_sha256":"92968c4c83baac4b51f3bf79ec592cf9f38c979b62e04ed32f8dced9d69b3d03","schema_version":"1.0","event_id":"sha256:92968c4c83baac4b51f3bf79ec592cf9f38c979b62e04ed32f8dced9d69b3d03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2ZCHOAOYTB6QHWJITZAKGOW5UJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local moves on knots and products of knots II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiji Ogasa, Louis H. Kauffman","submitted_at":"2014-06-21T03:30:34Z","abstract_excerpt":"We use the terms, knot product and local move, as defined in the text of the paper. Let $n$ be an integer$\\geqq3$. Let $\\mathcal S_n$ be the set of simple spherical $n$-knots in $S^{n+2}$. Let $m$ be an integer$\\geqq4$. We prove that the map $j:\\mathcal S_{2m}\\to\\mathcal S_{2m+4}$ is bijective, where $j(K)=K\\otimes$Hopf, and Hopf denotes the Hopf link.\n  Let $J$ and $K$ be 1-links in $S^3$. Suppose that $J$ is obtained from $K$ by a single pass-move, which is a local-move on 1-links. Let $k$ be a positive integer. Let $P\\otimes^kQ$ denote the knot product $P\\otimes\\underbrace{Q\\otimes...\\otime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5573","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":""},"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":"2026-05-18T00:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzY8/THhC6UH++xM9p01jk9uH8lXr+qnsZcEFWuVH7OkxvMwSQn3MY6GGFrtiLBS8qiJCRE84+On2Z2C/aOQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T07:46:53.294798Z"},"content_sha256":"a9a1206a6f55ff6462ec48353abbadf7c1e1c90ed5036c0dbd3fc1202b834ade","schema_version":"1.0","event_id":"sha256:a9a1206a6f55ff6462ec48353abbadf7c1e1c90ed5036c0dbd3fc1202b834ade"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ/bundle.json","state_url":"https://pith.science/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ/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":"2026-06-06T07:46:53Z","links":{"resolver":"https://pith.science/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ","bundle":"https://pith.science/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ/bundle.json","state":"https://pith.science/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZCHOAOYTB6QHWJITZAKGOW5UJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2ZCHOAOYTB6QHWJITZAKGOW5UJ","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":"bed2cddba03daae3647691520b70b102922e0044c0404ec01673c5441763c492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-21T03:30:34Z","title_canon_sha256":"0f0b929b69b7bdb492348147aa3c642caece59c22304710890d6e3d51e7397eb"},"schema_version":"1.0","source":{"id":"1406.5573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5573","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5573v2","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5573","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"2ZCHOAOYTB6Q","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2ZCHOAOYTB6QHWJI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2ZCHOAOY","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:a9a1206a6f55ff6462ec48353abbadf7c1e1c90ed5036c0dbd3fc1202b834ade","target":"graph","created_at":"2026-05-18T00:19:09Z","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 use the terms, knot product and local move, as defined in the text of the paper. Let $n$ be an integer$\\geqq3$. Let $\\mathcal S_n$ be the set of simple spherical $n$-knots in $S^{n+2}$. Let $m$ be an integer$\\geqq4$. We prove that the map $j:\\mathcal S_{2m}\\to\\mathcal S_{2m+4}$ is bijective, where $j(K)=K\\otimes$Hopf, and Hopf denotes the Hopf link.\n  Let $J$ and $K$ be 1-links in $S^3$. Suppose that $J$ is obtained from $K$ by a single pass-move, which is a local-move on 1-links. Let $k$ be a positive integer. Let $P\\otimes^kQ$ denote the knot product $P\\otimes\\underbrace{Q\\otimes...\\otime","authors_text":"Eiji Ogasa, Louis H. Kauffman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-21T03:30:34Z","title":"Local moves on knots and products of knots II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5573","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":"sha256:92968c4c83baac4b51f3bf79ec592cf9f38c979b62e04ed32f8dced9d69b3d03","target":"record","created_at":"2026-05-18T00:19:09Z","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":"bed2cddba03daae3647691520b70b102922e0044c0404ec01673c5441763c492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-21T03:30:34Z","title_canon_sha256":"0f0b929b69b7bdb492348147aa3c642caece59c22304710890d6e3d51e7397eb"},"schema_version":"1.0","source":{"id":"1406.5573","kind":"arxiv","version":2}},"canonical_sha256":"d6447701d8987d03d9289e40a33adda26e24aee9ef8689f5337217f358542dd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6447701d8987d03d9289e40a33adda26e24aee9ef8689f5337217f358542dd6","first_computed_at":"2026-05-18T00:19:09.232550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:09.232550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"spmpEcZ8wAUxROpWdP9WOyVA1/v/eNWQ/4B1TnMCoqIiupTmGArokfpxIrgaaIRlSJiR565nDPPa0YOy81k4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:09.233068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92968c4c83baac4b51f3bf79ec592cf9f38c979b62e04ed32f8dced9d69b3d03","sha256:a9a1206a6f55ff6462ec48353abbadf7c1e1c90ed5036c0dbd3fc1202b834ade"],"state_sha256":"e0dbaf14f0d82d5c11b10facb27e4f8456b551f0717db0227afb7d026764f28f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BxpAqLbW1/Cs8hDFlUVgNpx4VfVsfH6F8drSxZJzjEglhF9cpuFTOCMn1lJY1b+Tye9GsXIYlovw7CzHBzP/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T07:46:53.298696Z","bundle_sha256":"28e22b0ee39c3b644b2bfe05c3389282c0891a062cbf40a2dd4498377af4eacd"}}