{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FR6MSZSMDN7RAL6IZRV7VQEPS2","short_pith_number":"pith:FR6MSZSM","canonical_record":{"source":{"id":"1502.02384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T07:18:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"198be1b12c7d65f270653d45eb2b27a28963cddc50b9e12166aa22eea8a487e7","abstract_canon_sha256":"2d72536bb2a7d944d53c0cd3b3296a84893530304848d85907a2b10ece936b99"},"schema_version":"1.0"},"canonical_sha256":"2c7cc9664c1b7f102fc8cc6bfac08f9695f88a0b0ae5d76720d813e6ff735d90","source":{"kind":"arxiv","id":"1502.02384","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02384","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02384v1","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02384","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"FR6MSZSMDN7R","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FR6MSZSMDN7RAL6I","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FR6MSZSM","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FR6MSZSMDN7RAL6IZRV7VQEPS2","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T07:18:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"198be1b12c7d65f270653d45eb2b27a28963cddc50b9e12166aa22eea8a487e7","abstract_canon_sha256":"2d72536bb2a7d944d53c0cd3b3296a84893530304848d85907a2b10ece936b99"},"schema_version":"1.0"},"canonical_sha256":"2c7cc9664c1b7f102fc8cc6bfac08f9695f88a0b0ae5d76720d813e6ff735d90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:42.575618Z","signature_b64":"eleubpmIUWDOZLXjjhelFk9JDJM1XkgscqNkYQ77+Mdb9LlGizjFPBFX7MUGG5OWgpHBQ12CcSdg0b5UxWh9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c7cc9664c1b7f102fc8cc6bfac08f9695f88a0b0ae5d76720d813e6ff735d90","last_reissued_at":"2026-05-18T02:27:42.574922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:42.574922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02384","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":"2026-05-18T02:27:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bUiJOq/6J8ny0p3TIheFxhQ1DeqlQcb/IKTIe9IUprpMQ7WaABYWr9OweI0IBmzs0Mz1TlK2GasoRlv3jRVgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:17:08.383905Z"},"content_sha256":"3c3cc3cd73c052bb6ab931145bef678eefbc48f3e29ce981f762384b84441eb0","schema_version":"1.0","event_id":"sha256:3c3cc3cd73c052bb6ab931145bef678eefbc48f3e29ce981f762384b84441eb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FR6MSZSMDN7RAL6IZRV7VQEPS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K\\\"ahler structure on Hurwitz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Georg Schumacher, Indranil Biswas, Reynir Axelsson","submitted_at":"2015-02-09T07:18:55Z","abstract_excerpt":"The classical Hurwitz spaces, that parameterize compact Riemann surfaces equipped with covering maps to ${\\mathbb P}_1$ of fixed numerical type with simple branch points, are extensively studied in the literature. We apply deformation theory, and present a study of the K\\\"ahler structure of the Hurwitz spaces, which reflects the variation of the complex structure of the Riemann surface as well as the variation of the meromorphic map. We introduce a generalized Weil-Petersson K\\\"ahler form on the Hurwitz space. This form turns out to be the curvature of a Quillen metric on a determinant line bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02384","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":""},"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":"2026-05-18T02:27:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAJcuSQ5sL1IsVsGmwgAfBUNOg0bFKkm2a2PjvNZb2KjZmoTYB9l+n79y7gT3vwiVlxhcCAhQ8yto2/1IFZICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:17:08.384248Z"},"content_sha256":"53f9ca176576dde1b23ed6b4a375dcb209bf08953b119841e52491c739ef6cc0","schema_version":"1.0","event_id":"sha256:53f9ca176576dde1b23ed6b4a375dcb209bf08953b119841e52491c739ef6cc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2/bundle.json","state_url":"https://pith.science/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2/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":"2026-05-30T18:17:08Z","links":{"resolver":"https://pith.science/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2","bundle":"https://pith.science/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2/bundle.json","state":"https://pith.science/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FR6MSZSMDN7RAL6IZRV7VQEPS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FR6MSZSMDN7RAL6IZRV7VQEPS2","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":"2d72536bb2a7d944d53c0cd3b3296a84893530304848d85907a2b10ece936b99","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T07:18:55Z","title_canon_sha256":"198be1b12c7d65f270653d45eb2b27a28963cddc50b9e12166aa22eea8a487e7"},"schema_version":"1.0","source":{"id":"1502.02384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02384","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02384v1","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02384","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"FR6MSZSMDN7R","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FR6MSZSMDN7RAL6I","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FR6MSZSM","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:53f9ca176576dde1b23ed6b4a375dcb209bf08953b119841e52491c739ef6cc0","target":"graph","created_at":"2026-05-18T02:27:42Z","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":"The classical Hurwitz spaces, that parameterize compact Riemann surfaces equipped with covering maps to ${\\mathbb P}_1$ of fixed numerical type with simple branch points, are extensively studied in the literature. We apply deformation theory, and present a study of the K\\\"ahler structure of the Hurwitz spaces, which reflects the variation of the complex structure of the Riemann surface as well as the variation of the meromorphic map. We introduce a generalized Weil-Petersson K\\\"ahler form on the Hurwitz space. This form turns out to be the curvature of a Quillen metric on a determinant line bu","authors_text":"Georg Schumacher, Indranil Biswas, Reynir Axelsson","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T07:18:55Z","title":"K\\\"ahler structure on Hurwitz spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02384","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":"sha256:3c3cc3cd73c052bb6ab931145bef678eefbc48f3e29ce981f762384b84441eb0","target":"record","created_at":"2026-05-18T02:27:42Z","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":"2d72536bb2a7d944d53c0cd3b3296a84893530304848d85907a2b10ece936b99","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T07:18:55Z","title_canon_sha256":"198be1b12c7d65f270653d45eb2b27a28963cddc50b9e12166aa22eea8a487e7"},"schema_version":"1.0","source":{"id":"1502.02384","kind":"arxiv","version":1}},"canonical_sha256":"2c7cc9664c1b7f102fc8cc6bfac08f9695f88a0b0ae5d76720d813e6ff735d90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c7cc9664c1b7f102fc8cc6bfac08f9695f88a0b0ae5d76720d813e6ff735d90","first_computed_at":"2026-05-18T02:27:42.574922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:42.574922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eleubpmIUWDOZLXjjhelFk9JDJM1XkgscqNkYQ77+Mdb9LlGizjFPBFX7MUGG5OWgpHBQ12CcSdg0b5UxWh9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:42.575618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c3cc3cd73c052bb6ab931145bef678eefbc48f3e29ce981f762384b84441eb0","sha256:53f9ca176576dde1b23ed6b4a375dcb209bf08953b119841e52491c739ef6cc0"],"state_sha256":"9f73c533e9e89c3b942b83dac6272ac80b604a130869259ababb519e882c053c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5GEnHOCIUSBdgWYit91M6c7Pw6GVv6RSGqpNwXpPLMNkz6tOApI6ty0wTEvkXXOHavqjlfceIKrsSof15UkCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:17:08.386864Z","bundle_sha256":"3fb37263f9fa2681d3a66e548ce73b36085e3cca9ea9c19fb20f68e03294a9f1"}}