{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:P7BQAYRPB5C3UP3GIKCI43CV5O","short_pith_number":"pith:P7BQAYRP","canonical_record":{"source":{"id":"1205.5990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-27T17:52:14Z","cross_cats_sorted":["math.AG","math.MP"],"title_canon_sha256":"9ec0a4c08f3d5b825fa4e6ae3c935d16470506af22b235ba10f100406fc9d05d","abstract_canon_sha256":"5a0481d6bb94cfa55ce4472acc28bfe6753bb0eae239c0aafd0ec115cc1d0311"},"schema_version":"1.0"},"canonical_sha256":"7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117","source":{"kind":"arxiv","id":"1205.5990","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5990","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5990v2","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5990","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"P7BQAYRPB5C3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P7BQAYRPB5C3UP3G","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P7BQAYRP","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:P7BQAYRPB5C3UP3GIKCI43CV5O","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-27T17:52:14Z","cross_cats_sorted":["math.AG","math.MP"],"title_canon_sha256":"9ec0a4c08f3d5b825fa4e6ae3c935d16470506af22b235ba10f100406fc9d05d","abstract_canon_sha256":"5a0481d6bb94cfa55ce4472acc28bfe6753bb0eae239c0aafd0ec115cc1d0311"},"schema_version":"1.0"},"canonical_sha256":"7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:16.761752Z","signature_b64":"bNF4tq0rqOfguwJzoWbsAc+6C4j8vIOzL7QIl0KSz6nEZ6pkKV1cbpSZc4DuhMl5T3D9WXkRNERRk3ggpM1zCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117","last_reissued_at":"2026-05-18T01:57:16.761161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:16.761161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5990","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":"2026-05-18T01:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKfR74xRAsDuzBCRdJ0I9KdASPRhP1yalVlfu2Vte4ggoQip5G9GqmIrF96EKmVUcT3hb4Je9z3WVeMwFZjECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:35:59.616394Z"},"content_sha256":"97ea1dd73efdcdeafc648782b7298df2f0ef395b9e11dfc2f1360c6acf958df4","schema_version":"1.0","event_id":"sha256:97ea1dd73efdcdeafc648782b7298df2f0ef395b9e11dfc2f1360c6acf958df4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:P7BQAYRPB5C3UP3GIKCI43CV5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Genus Two Free Energies for Semisimple Frobenius Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP"],"primary_cat":"math-ph","authors_text":"Boris Dubrovin, Si-Qi Liu, Youjin Zhang","submitted_at":"2012-05-27T17:52:14Z","abstract_excerpt":"We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called \"genus two G-function\". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5990","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":"2026-05-18T01:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGfHwm45pBneduntZnXwWqER28pxePY+nV7GY6jk5GLTVvMLT+QeMNBGV8u1DOikMnvGn2E/xqjCKkn43fUFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:35:59.616740Z"},"content_sha256":"00b0ad5550180c8096d6821ca8277d26fd4a002a3603394bcb280f15233b53b8","schema_version":"1.0","event_id":"sha256:00b0ad5550180c8096d6821ca8277d26fd4a002a3603394bcb280f15233b53b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7BQAYRPB5C3UP3GIKCI43CV5O/bundle.json","state_url":"https://pith.science/pith/P7BQAYRPB5C3UP3GIKCI43CV5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7BQAYRPB5C3UP3GIKCI43CV5O/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":"2026-06-03T15:35:59Z","links":{"resolver":"https://pith.science/pith/P7BQAYRPB5C3UP3GIKCI43CV5O","bundle":"https://pith.science/pith/P7BQAYRPB5C3UP3GIKCI43CV5O/bundle.json","state":"https://pith.science/pith/P7BQAYRPB5C3UP3GIKCI43CV5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7BQAYRPB5C3UP3GIKCI43CV5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P7BQAYRPB5C3UP3GIKCI43CV5O","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":"5a0481d6bb94cfa55ce4472acc28bfe6753bb0eae239c0aafd0ec115cc1d0311","cross_cats_sorted":["math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-27T17:52:14Z","title_canon_sha256":"9ec0a4c08f3d5b825fa4e6ae3c935d16470506af22b235ba10f100406fc9d05d"},"schema_version":"1.0","source":{"id":"1205.5990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5990","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5990v2","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5990","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"P7BQAYRPB5C3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P7BQAYRPB5C3UP3G","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P7BQAYRP","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:00b0ad5550180c8096d6821ca8277d26fd4a002a3603394bcb280f15233b53b8","target":"graph","created_at":"2026-05-18T01:57:16Z","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 represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called \"genus two G-function\". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.","authors_text":"Boris Dubrovin, Si-Qi Liu, Youjin Zhang","cross_cats":["math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-27T17:52:14Z","title":"On the Genus Two Free Energies for Semisimple Frobenius Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5990","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":"sha256:97ea1dd73efdcdeafc648782b7298df2f0ef395b9e11dfc2f1360c6acf958df4","target":"record","created_at":"2026-05-18T01:57:16Z","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":"5a0481d6bb94cfa55ce4472acc28bfe6753bb0eae239c0aafd0ec115cc1d0311","cross_cats_sorted":["math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-27T17:52:14Z","title_canon_sha256":"9ec0a4c08f3d5b825fa4e6ae3c935d16470506af22b235ba10f100406fc9d05d"},"schema_version":"1.0","source":{"id":"1205.5990","kind":"arxiv","version":2}},"canonical_sha256":"7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117","first_computed_at":"2026-05-18T01:57:16.761161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:16.761161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bNF4tq0rqOfguwJzoWbsAc+6C4j8vIOzL7QIl0KSz6nEZ6pkKV1cbpSZc4DuhMl5T3D9WXkRNERRk3ggpM1zCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:16.761752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97ea1dd73efdcdeafc648782b7298df2f0ef395b9e11dfc2f1360c6acf958df4","sha256:00b0ad5550180c8096d6821ca8277d26fd4a002a3603394bcb280f15233b53b8"],"state_sha256":"4e8abba7a97982e7aa56e2a655103f20e3496beb059361a71964f5e470b2a802"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ayzL2kRNWrDkGLYpDb5iLWnyOD1eNsQXh6AncWebyVXnJt05w6C7uW4wPmTV1mEgK7f42e/A9lJ2RkxP1so9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:35:59.618792Z","bundle_sha256":"fb1454751ac9b697a50b4bc8bf80d5ee50d0e6e7140d9a7cc852dfcd59a8ab00"}}