{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AY4NFCSDR2DZY2YHMKDYHRPOQ6","short_pith_number":"pith:AY4NFCSD","canonical_record":{"source":{"id":"1109.2362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-11T23:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"e0393bc7aa9cfd9ce4ad0ea439b1c137f6f6a67b2069d76182c87eaf39bad4fb","abstract_canon_sha256":"46949604292be30956d4f5664f64a2cbcc00270ee81c578fa187fde310750c16"},"schema_version":"1.0"},"canonical_sha256":"0638d28a438e879c6b07628783c5ee879774630070f80055761467848123d603","source":{"kind":"arxiv","id":"1109.2362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2362","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2362v1","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2362","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"AY4NFCSDR2DZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AY4NFCSDR2DZY2YH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AY4NFCSD","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AY4NFCSDR2DZY2YHMKDYHRPOQ6","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-11T23:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"e0393bc7aa9cfd9ce4ad0ea439b1c137f6f6a67b2069d76182c87eaf39bad4fb","abstract_canon_sha256":"46949604292be30956d4f5664f64a2cbcc00270ee81c578fa187fde310750c16"},"schema_version":"1.0"},"canonical_sha256":"0638d28a438e879c6b07628783c5ee879774630070f80055761467848123d603","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:39.730065Z","signature_b64":"MrSL3eJRL+4KIseGVq5wJ9mq1JCEVPIcofp7uEDroZidJkWH4tJQqMA3X8XGykwuqADQP+hoga0CD84XtvptBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0638d28a438e879c6b07628783c5ee879774630070f80055761467848123d603","last_reissued_at":"2026-05-18T00:55:39.729566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:39.729566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2362","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":"2026-05-18T00:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cftckWkrfKoN2GW7cuedDw+8Zuf5enl6frIlxvwcpYBoriimxBtgpi1i0ah1CkGiARb+MmVypuPRPbh6eEQnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:54:23.529193Z"},"content_sha256":"f54405ea7de2aafa71349083dca13ab3088ef1ced28fd5d37f3f8ca750392c3c","schema_version":"1.0","event_id":"sha256:f54405ea7de2aafa71349083dca13ab3088ef1ced28fd5d37f3f8ca750392c3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AY4NFCSDR2DZY2YHMKDYHRPOQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a ring of modular forms related to the Theta gradients map in genus 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessio Fiorentino","submitted_at":"2011-09-11T23:25:16Z","abstract_excerpt":"The level moduli space $A_g^{4,8}$ is mapped to the projective space by means of gradients of odd Theta functions, such a map turning out no to be injective in the genus 2 case. In this work a congruence subgroup $\\Gamma$ is located between $\\Gamma_2(4,8)$ and $\\Gamma_2(2,4)$ in such a way the map factors on the related level moduli space $A_{\\Gamma}$, the new map being injective on $A_{\\Gamma}$. Satake's compactification $\\text{Proj}A(\\Gamma)$ and the desingularization $\\text{Proj}S(\\Gamma)$ are also due to be investigated, since the map does not extend to the boundary of the compactification"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2362","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":"2026-05-18T00:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxwhtqYGrxvA5Aa9kxdPouNHnWKJfwTH3j5sbT+sfZz8tSCULBH4I00pQTOc0TAmyrUswz2r8CLTx5SsTtOHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:54:23.529843Z"},"content_sha256":"4a3bb18ced57226310240e54d2558e4cd2a9c3a46d986da52ac47d393721c852","schema_version":"1.0","event_id":"sha256:4a3bb18ced57226310240e54d2558e4cd2a9c3a46d986da52ac47d393721c852"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6/bundle.json","state_url":"https://pith.science/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6/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":"2026-05-30T08:54:23Z","links":{"resolver":"https://pith.science/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6","bundle":"https://pith.science/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6/bundle.json","state":"https://pith.science/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AY4NFCSDR2DZY2YHMKDYHRPOQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AY4NFCSDR2DZY2YHMKDYHRPOQ6","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":"46949604292be30956d4f5664f64a2cbcc00270ee81c578fa187fde310750c16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-11T23:25:16Z","title_canon_sha256":"e0393bc7aa9cfd9ce4ad0ea439b1c137f6f6a67b2069d76182c87eaf39bad4fb"},"schema_version":"1.0","source":{"id":"1109.2362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2362","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2362v1","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2362","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"AY4NFCSDR2DZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AY4NFCSDR2DZY2YH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AY4NFCSD","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:4a3bb18ced57226310240e54d2558e4cd2a9c3a46d986da52ac47d393721c852","target":"graph","created_at":"2026-05-18T00:55:39Z","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 level moduli space $A_g^{4,8}$ is mapped to the projective space by means of gradients of odd Theta functions, such a map turning out no to be injective in the genus 2 case. In this work a congruence subgroup $\\Gamma$ is located between $\\Gamma_2(4,8)$ and $\\Gamma_2(2,4)$ in such a way the map factors on the related level moduli space $A_{\\Gamma}$, the new map being injective on $A_{\\Gamma}$. Satake's compactification $\\text{Proj}A(\\Gamma)$ and the desingularization $\\text{Proj}S(\\Gamma)$ are also due to be investigated, since the map does not extend to the boundary of the compactification","authors_text":"Alessio Fiorentino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-11T23:25:16Z","title":"On a ring of modular forms related to the Theta gradients map in genus 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2362","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:f54405ea7de2aafa71349083dca13ab3088ef1ced28fd5d37f3f8ca750392c3c","target":"record","created_at":"2026-05-18T00:55:39Z","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":"46949604292be30956d4f5664f64a2cbcc00270ee81c578fa187fde310750c16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-11T23:25:16Z","title_canon_sha256":"e0393bc7aa9cfd9ce4ad0ea439b1c137f6f6a67b2069d76182c87eaf39bad4fb"},"schema_version":"1.0","source":{"id":"1109.2362","kind":"arxiv","version":1}},"canonical_sha256":"0638d28a438e879c6b07628783c5ee879774630070f80055761467848123d603","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0638d28a438e879c6b07628783c5ee879774630070f80055761467848123d603","first_computed_at":"2026-05-18T00:55:39.729566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:39.729566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MrSL3eJRL+4KIseGVq5wJ9mq1JCEVPIcofp7uEDroZidJkWH4tJQqMA3X8XGykwuqADQP+hoga0CD84XtvptBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:39.730065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f54405ea7de2aafa71349083dca13ab3088ef1ced28fd5d37f3f8ca750392c3c","sha256:4a3bb18ced57226310240e54d2558e4cd2a9c3a46d986da52ac47d393721c852"],"state_sha256":"10282b0e811cab1ab9a57ca6ca102841058bdb82ba1bc66d71a594b3e122f8dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVnL/x3tTUKWtPZ/EE0Nufoq/BSSOURG0wHTQUSlaBGffjeWdEd9Xlx+h1fdplc6LkRmsxdRn9/txN/8bHdTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:54:23.533446Z","bundle_sha256":"b596860bc8a073f726439b98d092ea9ead5f2d92999d69ede1a677597fbca5f8"}}