{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BFLMHPY4Q2LHEL4ZIK46KEIRNG","short_pith_number":"pith:BFLMHPY4","canonical_record":{"source":{"id":"2311.17363","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-29T05:23:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"72d265a15d5a31b49a6b6b2a7b703076c829d51e05cbda9343b0cd10a7ae3876","abstract_canon_sha256":"8d4a6ffc66e79525812dcaf4079faaa1384cb6a4b7c4fe631f79dd43ebfa68a2"},"schema_version":"1.0"},"canonical_sha256":"0956c3bf1c8696722f9942b9e51111699cc5ecf8c95e7c74bbbed27d39c4ac46","source":{"kind":"arxiv","id":"2311.17363","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.17363","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"2311.17363v2","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.17363","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"BFLMHPY4Q2LH","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_16","alias_value":"BFLMHPY4Q2LHEL4Z","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_8","alias_value":"BFLMHPY4","created_at":"2026-07-05T09:24:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BFLMHPY4Q2LHEL4ZIK46KEIRNG","target":"record","payload":{"canonical_record":{"source":{"id":"2311.17363","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-29T05:23:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"72d265a15d5a31b49a6b6b2a7b703076c829d51e05cbda9343b0cd10a7ae3876","abstract_canon_sha256":"8d4a6ffc66e79525812dcaf4079faaa1384cb6a4b7c4fe631f79dd43ebfa68a2"},"schema_version":"1.0"},"canonical_sha256":"0956c3bf1c8696722f9942b9e51111699cc5ecf8c95e7c74bbbed27d39c4ac46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:24:31.947326Z","signature_b64":"NT1AGE6y3+m2WuVDQBJJx2mSaXP/WQrzMRNPybv7W7LXR0LEO7l47poVpBbZcUnf0RYPNwBR2DW2ES6ii3Y9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0956c3bf1c8696722f9942b9e51111699cc5ecf8c95e7c74bbbed27d39c4ac46","last_reissued_at":"2026-07-05T09:24:31.946800Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:24:31.946800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.17363","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":"2026-07-05T09:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ik5KQAhaGBquEh/X4WAyRT3ioqXQWRpo2T87ZerwkNxDR/OKhornVZCP+uTZkRc3lzpoyySyhIwQluqaXqhmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:34:18.855103Z"},"content_sha256":"c9f7cdaef4457ca7750744588f9aeeb1eae596fba47de67335c8cf3c4bc27735","schema_version":"1.0","event_id":"sha256:c9f7cdaef4457ca7750744588f9aeeb1eae596fba47de67335c8cf3c4bc27735"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BFLMHPY4Q2LHEL4ZIK46KEIRNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Principal hierarchy of Frobenius manifolds with rational and trigonometric superpotentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shilin Ma","submitted_at":"2023-11-29T05:23:56Z","abstract_excerpt":"In this paper, we construct the principal hierarchies for Frobenius manifolds with rational and trigonometric superpotentials, as well as their almost dualities. We demonstrate that in both cases, submanifolds with even superpotentials form natural Frobenius submanifolds, and their principal hierarchies can be obtained as restrictions of the principal hierarchies for the original Frobenius manifolds. Furthermore, we introduce a natural rank-1 extension for each of these Frobenius manifolds, providing solutions to the associated open WDVV equations. The principal hierarchy for each extension is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17363","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/2311.17363/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":"2026-07-05T09:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+j+Y6kgjq9UaSvXfe3IynivbEgqNaxAC9cZeKR31HFvw+EwbG41f2JXovrLRGDm5e4mhA1A73NuvfpdcB3CCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:34:18.855577Z"},"content_sha256":"7349af65024133b9ced17d6d6eb807cb525b75692d5b577e79048236d6e7b1f0","schema_version":"1.0","event_id":"sha256:7349af65024133b9ced17d6d6eb807cb525b75692d5b577e79048236d6e7b1f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG/bundle.json","state_url":"https://pith.science/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG/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":"2026-08-06T16:34:18Z","links":{"resolver":"https://pith.science/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG","bundle":"https://pith.science/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG/bundle.json","state":"https://pith.science/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFLMHPY4Q2LHEL4ZIK46KEIRNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BFLMHPY4Q2LHEL4ZIK46KEIRNG","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":"8d4a6ffc66e79525812dcaf4079faaa1384cb6a4b7c4fe631f79dd43ebfa68a2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-29T05:23:56Z","title_canon_sha256":"72d265a15d5a31b49a6b6b2a7b703076c829d51e05cbda9343b0cd10a7ae3876"},"schema_version":"1.0","source":{"id":"2311.17363","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.17363","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"2311.17363v2","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.17363","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"BFLMHPY4Q2LH","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_16","alias_value":"BFLMHPY4Q2LHEL4Z","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_8","alias_value":"BFLMHPY4","created_at":"2026-07-05T09:24:31Z"}],"graph_snapshots":[{"event_id":"sha256:7349af65024133b9ced17d6d6eb807cb525b75692d5b577e79048236d6e7b1f0","target":"graph","created_at":"2026-07-05T09:24:31Z","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/2311.17363/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we construct the principal hierarchies for Frobenius manifolds with rational and trigonometric superpotentials, as well as their almost dualities. We demonstrate that in both cases, submanifolds with even superpotentials form natural Frobenius submanifolds, and their principal hierarchies can be obtained as restrictions of the principal hierarchies for the original Frobenius manifolds. Furthermore, we introduce a natural rank-1 extension for each of these Frobenius manifolds, providing solutions to the associated open WDVV equations. The principal hierarchy for each extension is","authors_text":"Shilin Ma","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-29T05:23:56Z","title":"Principal hierarchy of Frobenius manifolds with rational and trigonometric superpotentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17363","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:c9f7cdaef4457ca7750744588f9aeeb1eae596fba47de67335c8cf3c4bc27735","target":"record","created_at":"2026-07-05T09:24:31Z","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":"8d4a6ffc66e79525812dcaf4079faaa1384cb6a4b7c4fe631f79dd43ebfa68a2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-29T05:23:56Z","title_canon_sha256":"72d265a15d5a31b49a6b6b2a7b703076c829d51e05cbda9343b0cd10a7ae3876"},"schema_version":"1.0","source":{"id":"2311.17363","kind":"arxiv","version":2}},"canonical_sha256":"0956c3bf1c8696722f9942b9e51111699cc5ecf8c95e7c74bbbed27d39c4ac46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0956c3bf1c8696722f9942b9e51111699cc5ecf8c95e7c74bbbed27d39c4ac46","first_computed_at":"2026-07-05T09:24:31.946800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:24:31.946800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NT1AGE6y3+m2WuVDQBJJx2mSaXP/WQrzMRNPybv7W7LXR0LEO7l47poVpBbZcUnf0RYPNwBR2DW2ES6ii3Y9DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:24:31.947326Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.17363","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9f7cdaef4457ca7750744588f9aeeb1eae596fba47de67335c8cf3c4bc27735","sha256:7349af65024133b9ced17d6d6eb807cb525b75692d5b577e79048236d6e7b1f0"],"state_sha256":"eea0e63e3dbbcb93c36d3ff8d285621715e975ce2f08830beed0e486f6038896"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/WNi+LG394NiUmurh0l6LjMGwdKpyJZW0CzL6DYp6Phx1tA4Pq9716HuK6YLaG9Nc0WKh7dFFKoUwpZ2IpsaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T16:34:18.859951Z","bundle_sha256":"26d2b8e3f69960be7c62e5f6b38dac47bd3c7698358630fcab0b0933b2f85d8e"}}