{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3JXAMWSO23I7WFTGBC2LSUB7S5","short_pith_number":"pith:3JXAMWSO","canonical_record":{"source":{"id":"2506.11883","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.plasm-ph","submitted_at":"2025-06-13T15:33:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"fefbca0dccc799fb68fcd794238472a7ec1e6e6ae72c1d8d8eb40903acf7d8ed","abstract_canon_sha256":"bf0ec4d2737f615247135a82ef0e61519fb6c40893b7611a228f5de9b5561359"},"schema_version":"1.0"},"canonical_sha256":"da6e065a4ed6d1fb166608b4b9503f976d1167201c6dab7aeac05f74b34aa5db","source":{"kind":"arxiv","id":"2506.11883","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11883","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11883v2","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11883","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"3JXAMWSO23I7","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"pith_short_16","alias_value":"3JXAMWSO23I7WFTG","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"pith_short_8","alias_value":"3JXAMWSO","created_at":"2026-07-05T11:25:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3JXAMWSO23I7WFTGBC2LSUB7S5","target":"record","payload":{"canonical_record":{"source":{"id":"2506.11883","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.plasm-ph","submitted_at":"2025-06-13T15:33:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"fefbca0dccc799fb68fcd794238472a7ec1e6e6ae72c1d8d8eb40903acf7d8ed","abstract_canon_sha256":"bf0ec4d2737f615247135a82ef0e61519fb6c40893b7611a228f5de9b5561359"},"schema_version":"1.0"},"canonical_sha256":"da6e065a4ed6d1fb166608b4b9503f976d1167201c6dab7aeac05f74b34aa5db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:46.045103Z","signature_b64":"tqXnGBlWvIYFNumJloS+JJRiWeD5aucjXb4/ELAtJ3S2bLfSxUQNBfSe+IJP1ky+7G6grQsRYFj5XKDuewz2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da6e065a4ed6d1fb166608b4b9503f976d1167201c6dab7aeac05f74b34aa5db","last_reissued_at":"2026-07-05T11:25:46.044460Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:46.044460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.11883","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":"2026-07-05T11:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJrEKxiVAw032BWQNRZGyIhrlYqJiVOp89MX1vVsGSkWNKik47ETMTcJhYkNzIK9KaISrRE4KwgBRHWV6zuxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:34:23.438215Z"},"content_sha256":"85ab585a75388deb78633ca8c649f2e0d9d1f7eeccf3cae3cc72b5e3d5d327e6","schema_version":"1.0","event_id":"sha256:85ab585a75388deb78633ca8c649f2e0d9d1f7eeccf3cae3cc72b5e3d5d327e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3JXAMWSO23I7WFTGBC2LSUB7S5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surfaces with Klein bottle topology occur in fusion reactor fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"physics.plasm-ph","authors_text":"Christopher Berg Smiet","submitted_at":"2025-06-13T15:33:09Z","abstract_excerpt":"Magnetic confinement fusion devices, such as tokamaks and stellarators, are designed such that magnetic field lines lie in magnetic surfaces that form a foliation of nested genus-1 tori. The Poincar\\'e-Hopf index theorem implies that only surfaces with genus 1 allow for vector fields that lie tangent to the surface and are smooth and nowhere-vanishing. It is often implicitly assumed that magnetic surfaces are always toroidal. This paper we show that surfaces with the topology of an immersed Klein bottle (the only other genus-1 compact surface) can also occur in fusion reactor fields.\n  These s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11883","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/2506.11883/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":"2026-07-05T11:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktA/vhHuhohT7dtuTBoxS1Cp23QXibfZd+A7+Dt4JBYwdgF7CXV0+GNrulf47EJAiRSn/9a2inQUtDM/G4WdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:34:23.440065Z"},"content_sha256":"118555df3b1743973dcb961c3a05596fca885b69919d6810d6cee8271cb1c481","schema_version":"1.0","event_id":"sha256:118555df3b1743973dcb961c3a05596fca885b69919d6810d6cee8271cb1c481"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JXAMWSO23I7WFTGBC2LSUB7S5/bundle.json","state_url":"https://pith.science/pith/3JXAMWSO23I7WFTGBC2LSUB7S5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JXAMWSO23I7WFTGBC2LSUB7S5/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":"2026-08-08T18:34:23Z","links":{"resolver":"https://pith.science/pith/3JXAMWSO23I7WFTGBC2LSUB7S5","bundle":"https://pith.science/pith/3JXAMWSO23I7WFTGBC2LSUB7S5/bundle.json","state":"https://pith.science/pith/3JXAMWSO23I7WFTGBC2LSUB7S5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JXAMWSO23I7WFTGBC2LSUB7S5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3JXAMWSO23I7WFTGBC2LSUB7S5","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":"bf0ec4d2737f615247135a82ef0e61519fb6c40893b7611a228f5de9b5561359","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.plasm-ph","submitted_at":"2025-06-13T15:33:09Z","title_canon_sha256":"fefbca0dccc799fb68fcd794238472a7ec1e6e6ae72c1d8d8eb40903acf7d8ed"},"schema_version":"1.0","source":{"id":"2506.11883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11883","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11883v2","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11883","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"3JXAMWSO23I7","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"pith_short_16","alias_value":"3JXAMWSO23I7WFTG","created_at":"2026-07-05T11:25:46Z"},{"alias_kind":"pith_short_8","alias_value":"3JXAMWSO","created_at":"2026-07-05T11:25:46Z"}],"graph_snapshots":[{"event_id":"sha256:118555df3b1743973dcb961c3a05596fca885b69919d6810d6cee8271cb1c481","target":"graph","created_at":"2026-07-05T11:25:46Z","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/2506.11883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Magnetic confinement fusion devices, such as tokamaks and stellarators, are designed such that magnetic field lines lie in magnetic surfaces that form a foliation of nested genus-1 tori. The Poincar\\'e-Hopf index theorem implies that only surfaces with genus 1 allow for vector fields that lie tangent to the surface and are smooth and nowhere-vanishing. It is often implicitly assumed that magnetic surfaces are always toroidal. This paper we show that surfaces with the topology of an immersed Klein bottle (the only other genus-1 compact surface) can also occur in fusion reactor fields.\n  These s","authors_text":"Christopher Berg Smiet","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.plasm-ph","submitted_at":"2025-06-13T15:33:09Z","title":"Surfaces with Klein bottle topology occur in fusion reactor fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11883","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":"sha256:85ab585a75388deb78633ca8c649f2e0d9d1f7eeccf3cae3cc72b5e3d5d327e6","target":"record","created_at":"2026-07-05T11:25:46Z","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":"bf0ec4d2737f615247135a82ef0e61519fb6c40893b7611a228f5de9b5561359","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.plasm-ph","submitted_at":"2025-06-13T15:33:09Z","title_canon_sha256":"fefbca0dccc799fb68fcd794238472a7ec1e6e6ae72c1d8d8eb40903acf7d8ed"},"schema_version":"1.0","source":{"id":"2506.11883","kind":"arxiv","version":2}},"canonical_sha256":"da6e065a4ed6d1fb166608b4b9503f976d1167201c6dab7aeac05f74b34aa5db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da6e065a4ed6d1fb166608b4b9503f976d1167201c6dab7aeac05f74b34aa5db","first_computed_at":"2026-07-05T11:25:46.044460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:46.044460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tqXnGBlWvIYFNumJloS+JJRiWeD5aucjXb4/ELAtJ3S2bLfSxUQNBfSe+IJP1ky+7G6grQsRYFj5XKDuewz2Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:46.045103Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85ab585a75388deb78633ca8c649f2e0d9d1f7eeccf3cae3cc72b5e3d5d327e6","sha256:118555df3b1743973dcb961c3a05596fca885b69919d6810d6cee8271cb1c481"],"state_sha256":"92f07d3c99fa1af64b9aa9443c646b623767ed864bf748aece963bf7d59bec44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DcdEgeGuOsdSV1DJq6vRI9vcEZVcs+f5Vd0Td8PHDT5gBfNKEXne2eTK1amTuIR2aP9KcpKZjJ+fq8BVWlhEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:34:23.449637Z","bundle_sha256":"e4fc04e13a8c3a548506e458ae173048416cdad88fee17161fd65f722da28ac9"}}