{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LCDI4COOKYICDMXZRVOPWT6HNN","short_pith_number":"pith:LCDI4COO","canonical_record":{"source":{"id":"1509.02359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-08T13:19:13Z","cross_cats_sorted":[],"title_canon_sha256":"16dce92cc9f62a7a29e71fb7974334eb61ce5c2a78b66f7e25668f2ded4f066c","abstract_canon_sha256":"ff32056f23eb0a81ea5b40be9f5e7fa1d087827b6a005cf37af525b18e597dd7"},"schema_version":"1.0"},"canonical_sha256":"58868e09ce561021b2f98d5cfb4fc76b40ae456f734d6b77f1f6cf2c2711cb58","source":{"kind":"arxiv","id":"1509.02359","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02359","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02359v3","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02359","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"LCDI4COOKYIC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LCDI4COOKYICDMXZ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LCDI4COO","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LCDI4COOKYICDMXZRVOPWT6HNN","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-08T13:19:13Z","cross_cats_sorted":[],"title_canon_sha256":"16dce92cc9f62a7a29e71fb7974334eb61ce5c2a78b66f7e25668f2ded4f066c","abstract_canon_sha256":"ff32056f23eb0a81ea5b40be9f5e7fa1d087827b6a005cf37af525b18e597dd7"},"schema_version":"1.0"},"canonical_sha256":"58868e09ce561021b2f98d5cfb4fc76b40ae456f734d6b77f1f6cf2c2711cb58","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:00.923627Z","signature_b64":"eZ9Jf7owzhYlmkpeOt4LjgtYY1OzfSS4D/DQiOEkyUJ9gM9nrGwNz6+hg489Vqi4nvrlw+jXSd96TWUXV4VwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58868e09ce561021b2f98d5cfb4fc76b40ae456f734d6b77f1f6cf2c2711cb58","last_reissued_at":"2026-05-17T23:56:00.922999Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:00.922999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02359","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWa4bFCUNoASExbwwewWId9tukPBcriSVEOaTuVOti9BdCj/hqX/BHv2Rm7HXWehCqIvE8UY0Hon6UViHIaHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:07:34.640361Z"},"content_sha256":"47e335fa955f645c3d933b14370558d8b7a45f52df5dca3ebe4d61eb56d67a89","schema_version":"1.0","event_id":"sha256:47e335fa955f645c3d933b14370558d8b7a45f52df5dca3ebe4d61eb56d67a89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LCDI4COOKYICDMXZRVOPWT6HNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the class of caustic on the moduli space of odd spin curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mikhail Basok","submitted_at":"2015-09-08T13:19:13Z","abstract_excerpt":"Let $C$ be a smooth projective curve of genus $g\\geq 3$ and let $\\eta$ be an odd theta characteristic on it such that $h^0(C,\\eta) = 1$. Pick a point $p$ from the support of $\\eta$ and consider the one-dimensional linear system $|\\eta + p|$. In general this linear system is base-point free and all its ramification points (i.e. ramification points of the corresponding branched cover $C\\to\\mathbb P^1\\simeq \\mathbb PH^0(C,\\eta+p)$) are simple. We study the locus in the moduli space of odd spin curves where the linear system $|\\eta + p|$ fails to have this general behavior. This locus splits into "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02359","kind":"arxiv","version":3},"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":"2026-05-17T23:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ucDnSLMRjtbdMfbujJCYRhEtRWO5pZW2XRYVlF5z2pwxEQLsRq4fvbHnnED4CEY/SfUQPhGI9aaNTj/QWdqsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:07:34.640716Z"},"content_sha256":"497a1ea94ad18a627b97cb874f30ce35715d9c22c07f917a3a9fe1a507ffdf66","schema_version":"1.0","event_id":"sha256:497a1ea94ad18a627b97cb874f30ce35715d9c22c07f917a3a9fe1a507ffdf66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCDI4COOKYICDMXZRVOPWT6HNN/bundle.json","state_url":"https://pith.science/pith/LCDI4COOKYICDMXZRVOPWT6HNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCDI4COOKYICDMXZRVOPWT6HNN/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":"2026-06-01T21:07:34Z","links":{"resolver":"https://pith.science/pith/LCDI4COOKYICDMXZRVOPWT6HNN","bundle":"https://pith.science/pith/LCDI4COOKYICDMXZRVOPWT6HNN/bundle.json","state":"https://pith.science/pith/LCDI4COOKYICDMXZRVOPWT6HNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCDI4COOKYICDMXZRVOPWT6HNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LCDI4COOKYICDMXZRVOPWT6HNN","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":"ff32056f23eb0a81ea5b40be9f5e7fa1d087827b6a005cf37af525b18e597dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-08T13:19:13Z","title_canon_sha256":"16dce92cc9f62a7a29e71fb7974334eb61ce5c2a78b66f7e25668f2ded4f066c"},"schema_version":"1.0","source":{"id":"1509.02359","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02359","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02359v3","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02359","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"LCDI4COOKYIC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LCDI4COOKYICDMXZ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LCDI4COO","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:497a1ea94ad18a627b97cb874f30ce35715d9c22c07f917a3a9fe1a507ffdf66","target":"graph","created_at":"2026-05-17T23:56:00Z","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":"Let $C$ be a smooth projective curve of genus $g\\geq 3$ and let $\\eta$ be an odd theta characteristic on it such that $h^0(C,\\eta) = 1$. Pick a point $p$ from the support of $\\eta$ and consider the one-dimensional linear system $|\\eta + p|$. In general this linear system is base-point free and all its ramification points (i.e. ramification points of the corresponding branched cover $C\\to\\mathbb P^1\\simeq \\mathbb PH^0(C,\\eta+p)$) are simple. We study the locus in the moduli space of odd spin curves where the linear system $|\\eta + p|$ fails to have this general behavior. This locus splits into ","authors_text":"Mikhail Basok","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-08T13:19:13Z","title":"On the class of caustic on the moduli space of odd spin curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02359","kind":"arxiv","version":3},"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":"sha256:47e335fa955f645c3d933b14370558d8b7a45f52df5dca3ebe4d61eb56d67a89","target":"record","created_at":"2026-05-17T23:56:00Z","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":"ff32056f23eb0a81ea5b40be9f5e7fa1d087827b6a005cf37af525b18e597dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-08T13:19:13Z","title_canon_sha256":"16dce92cc9f62a7a29e71fb7974334eb61ce5c2a78b66f7e25668f2ded4f066c"},"schema_version":"1.0","source":{"id":"1509.02359","kind":"arxiv","version":3}},"canonical_sha256":"58868e09ce561021b2f98d5cfb4fc76b40ae456f734d6b77f1f6cf2c2711cb58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58868e09ce561021b2f98d5cfb4fc76b40ae456f734d6b77f1f6cf2c2711cb58","first_computed_at":"2026-05-17T23:56:00.922999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:00.922999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eZ9Jf7owzhYlmkpeOt4LjgtYY1OzfSS4D/DQiOEkyUJ9gM9nrGwNz6+hg489Vqi4nvrlw+jXSd96TWUXV4VwCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:00.923627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02359","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e335fa955f645c3d933b14370558d8b7a45f52df5dca3ebe4d61eb56d67a89","sha256:497a1ea94ad18a627b97cb874f30ce35715d9c22c07f917a3a9fe1a507ffdf66"],"state_sha256":"26e6842605b9cf0106abea0d6af01ea8dbcbfe8fe9094479314310b87d94629f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CezDjGGktAeWpnddixD0iaIddsUQ7MSnxfBl6qg9Vs23pVkfj/xnXDfrykkCeHh5gHvKdSgz9KOD5jn/TRbtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:07:34.642714Z","bundle_sha256":"8be057270bed61ab1defb008c6b711da7a72681fbc2776da7b1abd562d70cee4"}}