{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KAP2IYC7UOKCHOJLGHJVVXZ4GY","short_pith_number":"pith:KAP2IYC7","canonical_record":{"source":{"id":"2606.01749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-06-01T06:12:09Z","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"title_canon_sha256":"4fa0b7d21b75b5af1558339216be328b115074b69d4ae5846aac71241ac84958","abstract_canon_sha256":"00cb0df87426ef789376cdecf00a11e17baf5ed99931088f3b3f629d804b4fd7"},"schema_version":"1.0"},"canonical_sha256":"501fa4605fa39423b92b31d35adf3c363c663cf4d0aee32b1990e939acf2dd91","source":{"kind":"arxiv","id":"2606.01749","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01749","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01749v1","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01749","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"KAP2IYC7UOKC","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"KAP2IYC7UOKCHOJL","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"KAP2IYC7","created_at":"2026-06-02T02:04:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KAP2IYC7UOKCHOJLGHJVVXZ4GY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-06-01T06:12:09Z","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"title_canon_sha256":"4fa0b7d21b75b5af1558339216be328b115074b69d4ae5846aac71241ac84958","abstract_canon_sha256":"00cb0df87426ef789376cdecf00a11e17baf5ed99931088f3b3f629d804b4fd7"},"schema_version":"1.0"},"canonical_sha256":"501fa4605fa39423b92b31d35adf3c363c663cf4d0aee32b1990e939acf2dd91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:55.673768Z","signature_b64":"2vCPXSjPk0p2lHBskR9bAU6pQIoc1+preZtxf0AShdqpakre6Tl2xaJEzrGqoElVoMmw63yosPDMxKMtSobsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501fa4605fa39423b92b31d35adf3c363c663cf4d0aee32b1990e939acf2dd91","last_reissued_at":"2026-06-02T02:04:55.673406Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:55.673406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01749","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":"2026-06-02T02:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/B7sS0cr+SfK6r4z46elxxKmxgCs5bcR6DWFyOJl7uCTq8ekBoOKImxOFGPL0nLlVwB1NHbvyQQkzj55iC5SCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:27:06.044470Z"},"content_sha256":"9baec47753a41e25d3993d23a82c476caa83d09aa7e523cacafe2cac0afcfccb","schema_version":"1.0","event_id":"sha256:9baec47753a41e25d3993d23a82c476caa83d09aa7e523cacafe2cac0afcfccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KAP2IYC7UOKCHOJLGHJVVXZ4GY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a Floer theory for Mars I -- Twisted Zeeman systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DS","math.MP"],"primary_cat":"math.SG","authors_text":"Joa Weber, Urs Frauenfelder","submitted_at":"2026-06-01T06:12:09Z","abstract_excerpt":"In this article we study periodic orbits of an electron attracted by a proton subject to Lorentz, electric, and Euler forces where each of them is allowed to depend periodically on time. This setup is motivated by the elliptic restricted three-body-problem where the Lorentz force corresponds to Coriolis force, the Coulomb force is replaced by the gravitational force, and the electric force of an external source is a combination of centrifugal forces and gravitational forces of other bodies. This is a singular version of a Euler-Hamilton system as discussed in [FW26b]. The singularity is due to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01749","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01749/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":"2026-06-02T02:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NiKsx+em/SzOm1Mombt9QxBKlkqNA6P8FmS/YMHz/D6eemdIFutjRkBjbQXd7cx2rAS1YBZvjJbroq9sdil9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:27:06.044976Z"},"content_sha256":"4d83aa2535e083eeccdf911fe4610884a75e1f8a1d198f64be2b9c09004557bf","schema_version":"1.0","event_id":"sha256:4d83aa2535e083eeccdf911fe4610884a75e1f8a1d198f64be2b9c09004557bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY/bundle.json","state_url":"https://pith.science/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY/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":"2026-08-03T18:27:06Z","links":{"resolver":"https://pith.science/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY","bundle":"https://pith.science/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY/bundle.json","state":"https://pith.science/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAP2IYC7UOKCHOJLGHJVVXZ4GY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KAP2IYC7UOKCHOJLGHJVVXZ4GY","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":"00cb0df87426ef789376cdecf00a11e17baf5ed99931088f3b3f629d804b4fd7","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-06-01T06:12:09Z","title_canon_sha256":"4fa0b7d21b75b5af1558339216be328b115074b69d4ae5846aac71241ac84958"},"schema_version":"1.0","source":{"id":"2606.01749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01749","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01749v1","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01749","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"KAP2IYC7UOKC","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"KAP2IYC7UOKCHOJL","created_at":"2026-06-02T02:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"KAP2IYC7","created_at":"2026-06-02T02:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:4d83aa2535e083eeccdf911fe4610884a75e1f8a1d198f64be2b9c09004557bf","target":"graph","created_at":"2026-06-02T02:04:55Z","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/2606.01749/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we study periodic orbits of an electron attracted by a proton subject to Lorentz, electric, and Euler forces where each of them is allowed to depend periodically on time. This setup is motivated by the elliptic restricted three-body-problem where the Lorentz force corresponds to Coriolis force, the Coulomb force is replaced by the gravitational force, and the electric force of an external source is a combination of centrifugal forces and gravitational forces of other bodies. This is a singular version of a Euler-Hamilton system as discussed in [FW26b]. The singularity is due to","authors_text":"Joa Weber, Urs Frauenfelder","cross_cats":["math-ph","math.AP","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-06-01T06:12:09Z","title":"Towards a Floer theory for Mars I -- Twisted Zeeman systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01749","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":"sha256:9baec47753a41e25d3993d23a82c476caa83d09aa7e523cacafe2cac0afcfccb","target":"record","created_at":"2026-06-02T02:04:55Z","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":"00cb0df87426ef789376cdecf00a11e17baf5ed99931088f3b3f629d804b4fd7","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-06-01T06:12:09Z","title_canon_sha256":"4fa0b7d21b75b5af1558339216be328b115074b69d4ae5846aac71241ac84958"},"schema_version":"1.0","source":{"id":"2606.01749","kind":"arxiv","version":1}},"canonical_sha256":"501fa4605fa39423b92b31d35adf3c363c663cf4d0aee32b1990e939acf2dd91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"501fa4605fa39423b92b31d35adf3c363c663cf4d0aee32b1990e939acf2dd91","first_computed_at":"2026-06-02T02:04:55.673406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:55.673406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2vCPXSjPk0p2lHBskR9bAU6pQIoc1+preZtxf0AShdqpakre6Tl2xaJEzrGqoElVoMmw63yosPDMxKMtSobsBg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:55.673768Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9baec47753a41e25d3993d23a82c476caa83d09aa7e523cacafe2cac0afcfccb","sha256:4d83aa2535e083eeccdf911fe4610884a75e1f8a1d198f64be2b9c09004557bf"],"state_sha256":"942073fdb6ef1e66035bec58a81a3d4b96861504cdbc06c313e5dff47c5d298c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fETOBuOWkKSj82svjNwB0PtdJ2RoTHEnoeki3CN5XduayNYn7c2G4SF1IqpMcDDDl3rnO4ZE2j96CWIh68C8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:27:06.051604Z","bundle_sha256":"084eb86f847c61a2960802b8ac3951b3b4ca616f0ba2172988f4e784051bf469"}}