{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NGUDLYQZ4A355LFSBUO4BICN2L","short_pith_number":"pith:NGUDLYQZ","canonical_record":{"source":{"id":"1803.03496","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-09T13:09:46Z","cross_cats_sorted":[],"title_canon_sha256":"538555d08fab5a07a1f5aaa809b9ef643560b2ffd27e7123d36b481fddac4775","abstract_canon_sha256":"784bd2f33de892f1485eaef91af2c09fbd89912280940f5ee358ef62bf0653cf"},"schema_version":"1.0"},"canonical_sha256":"69a835e219e037deacb20d1dc0a04dd2f0b527d9daf449a4f0a19e467445fbf0","source":{"kind":"arxiv","id":"1803.03496","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03496","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03496v3","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03496","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"NGUDLYQZ4A35","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NGUDLYQZ4A355LFS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NGUDLYQZ","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NGUDLYQZ4A355LFSBUO4BICN2L","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03496","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-09T13:09:46Z","cross_cats_sorted":[],"title_canon_sha256":"538555d08fab5a07a1f5aaa809b9ef643560b2ffd27e7123d36b481fddac4775","abstract_canon_sha256":"784bd2f33de892f1485eaef91af2c09fbd89912280940f5ee358ef62bf0653cf"},"schema_version":"1.0"},"canonical_sha256":"69a835e219e037deacb20d1dc0a04dd2f0b527d9daf449a4f0a19e467445fbf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:21.647559Z","signature_b64":"LTLOEIVjZGwMWKaylBb2tSEtjEm4IadQU1Xo5bn0cMd2jti6wy8s4YTzkyjT+/2McbJJXfPk+gt8DTz570ZQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69a835e219e037deacb20d1dc0a04dd2f0b527d9daf449a4f0a19e467445fbf0","last_reissued_at":"2026-05-18T00:14:21.646912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:21.646912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03496","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2uzFFH21diGjUNvAGhjUiLix/ewQ1j8/pmXKrGOTUkdqoi19kHwSqTVAYE4tg/MxQTD4NRF1aiDVWSF5+wfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:12:37.592746Z"},"content_sha256":"6e6e86ee5fba775ab2af02962ca307d55a53b832974550b4f98cc37c97de243f","schema_version":"1.0","event_id":"sha256:6e6e86ee5fba775ab2af02962ca307d55a53b832974550b4f98cc37c97de243f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NGUDLYQZ4A355LFSBUO4BICN2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intersectional pairs of $n$-knots, local moves of $n$-knots, and their associated invariants of $n$-knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiji Ogasa","submitted_at":"2018-03-09T13:09:46Z","abstract_excerpt":"Let $n$ be an integer$\\geqq0$. Let $S^{n+2}_1$ (respectively, $S^{n+2}_2$) be the $(n+2)$-sphere embedded in the $(n+4)$-sphere $S^{n+4}$. Let $S^{n+2}_1$ and $S^{n+2}_2$ intersect transversely. Suppose that the smooth submanifold, $S^{n+2}_1 \\cap S^{n+2}_2$ in $S^{n+2}_i$ is PL homeomophic to the $n$-sphere. Then $S^{n+2}_1$ and $S^{n+2}_2$ in $S^{n+2}_i$ is an $n$-knot $K_i$. We say that the pair $(K_1,K_2)$ of n-knots is realizable.\n  We consider the following problem in this paper. Let $A_1$ and $A_2$ be n-knots. Is the pair $(A_1,A_2)$ of $n$-knots realizable?\n  We give a complete charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03496","kind":"arxiv","version":3},"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":"2026-05-18T00:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urRFONnG4HezFw8yiJku+jn/WVbOZQ50pZhbijHVORzNcbN9wB40BLSaSABolMJ5QK/aX8UuEpu17NpavuXYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:12:37.593120Z"},"content_sha256":"b47542c245b6741cf5833bc6aaca211cd5937065b9732040a80268f86d5edb22","schema_version":"1.0","event_id":"sha256:b47542c245b6741cf5833bc6aaca211cd5937065b9732040a80268f86d5edb22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGUDLYQZ4A355LFSBUO4BICN2L/bundle.json","state_url":"https://pith.science/pith/NGUDLYQZ4A355LFSBUO4BICN2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGUDLYQZ4A355LFSBUO4BICN2L/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":"2026-05-27T10:12:37Z","links":{"resolver":"https://pith.science/pith/NGUDLYQZ4A355LFSBUO4BICN2L","bundle":"https://pith.science/pith/NGUDLYQZ4A355LFSBUO4BICN2L/bundle.json","state":"https://pith.science/pith/NGUDLYQZ4A355LFSBUO4BICN2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGUDLYQZ4A355LFSBUO4BICN2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NGUDLYQZ4A355LFSBUO4BICN2L","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":"784bd2f33de892f1485eaef91af2c09fbd89912280940f5ee358ef62bf0653cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-09T13:09:46Z","title_canon_sha256":"538555d08fab5a07a1f5aaa809b9ef643560b2ffd27e7123d36b481fddac4775"},"schema_version":"1.0","source":{"id":"1803.03496","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03496","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03496v3","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03496","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"NGUDLYQZ4A35","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NGUDLYQZ4A355LFS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NGUDLYQZ","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:b47542c245b6741cf5833bc6aaca211cd5937065b9732040a80268f86d5edb22","target":"graph","created_at":"2026-05-18T00:14:21Z","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":"Let $n$ be an integer$\\geqq0$. Let $S^{n+2}_1$ (respectively, $S^{n+2}_2$) be the $(n+2)$-sphere embedded in the $(n+4)$-sphere $S^{n+4}$. Let $S^{n+2}_1$ and $S^{n+2}_2$ intersect transversely. Suppose that the smooth submanifold, $S^{n+2}_1 \\cap S^{n+2}_2$ in $S^{n+2}_i$ is PL homeomophic to the $n$-sphere. Then $S^{n+2}_1$ and $S^{n+2}_2$ in $S^{n+2}_i$ is an $n$-knot $K_i$. We say that the pair $(K_1,K_2)$ of n-knots is realizable.\n  We consider the following problem in this paper. Let $A_1$ and $A_2$ be n-knots. Is the pair $(A_1,A_2)$ of $n$-knots realizable?\n  We give a complete charact","authors_text":"Eiji Ogasa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-09T13:09:46Z","title":"Intersectional pairs of $n$-knots, local moves of $n$-knots, and their associated invariants of $n$-knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03496","kind":"arxiv","version":3},"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":"sha256:6e6e86ee5fba775ab2af02962ca307d55a53b832974550b4f98cc37c97de243f","target":"record","created_at":"2026-05-18T00:14:21Z","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":"784bd2f33de892f1485eaef91af2c09fbd89912280940f5ee358ef62bf0653cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-09T13:09:46Z","title_canon_sha256":"538555d08fab5a07a1f5aaa809b9ef643560b2ffd27e7123d36b481fddac4775"},"schema_version":"1.0","source":{"id":"1803.03496","kind":"arxiv","version":3}},"canonical_sha256":"69a835e219e037deacb20d1dc0a04dd2f0b527d9daf449a4f0a19e467445fbf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69a835e219e037deacb20d1dc0a04dd2f0b527d9daf449a4f0a19e467445fbf0","first_computed_at":"2026-05-18T00:14:21.646912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:21.646912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LTLOEIVjZGwMWKaylBb2tSEtjEm4IadQU1Xo5bn0cMd2jti6wy8s4YTzkyjT+/2McbJJXfPk+gt8DTz570ZQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:21.647559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03496","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e6e86ee5fba775ab2af02962ca307d55a53b832974550b4f98cc37c97de243f","sha256:b47542c245b6741cf5833bc6aaca211cd5937065b9732040a80268f86d5edb22"],"state_sha256":"fcc68eed28a0b7d4ee251de75c350c066654e2be543c59bbada563456085c80d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bPiiDIdOAGqFmRf5UdLhftlQmRbwgSGJvaTo9VU6ITjZc8Az798iX9JiVPQ3MUCzGQbHkcBjIzmJglA4MYlBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:12:37.595706Z","bundle_sha256":"41a1875b73416afc942c97c15344709b377789e060b4adb76c92d3e5379bf06b"}}