{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:6LLZOZMUM6KIX73DSRDNTPW3KV","short_pith_number":"pith:6LLZOZMU","canonical_record":{"source":{"id":"0711.0094","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-11-01T10:10:20Z","cross_cats_sorted":[],"title_canon_sha256":"acebf59006bddd5ded06aa3c250777b4195951df455d5583c8bf5db1ae55e06a","abstract_canon_sha256":"cfab818c9a6b7d59a8ae31af9a1aec8220aff8bcfb943639ca9bd9786ff6cea5"},"schema_version":"1.0"},"canonical_sha256":"f2d797659467948bff639446d9bedb55678b14d3be67264a68ef819df2dffcfc","source":{"kind":"arxiv","id":"0711.0094","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0094","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0094v4","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0094","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"6LLZOZMUM6KI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6LLZOZMUM6KIX73D","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6LLZOZMU","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:6LLZOZMUM6KIX73DSRDNTPW3KV","target":"record","payload":{"canonical_record":{"source":{"id":"0711.0094","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-11-01T10:10:20Z","cross_cats_sorted":[],"title_canon_sha256":"acebf59006bddd5ded06aa3c250777b4195951df455d5583c8bf5db1ae55e06a","abstract_canon_sha256":"cfab818c9a6b7d59a8ae31af9a1aec8220aff8bcfb943639ca9bd9786ff6cea5"},"schema_version":"1.0"},"canonical_sha256":"f2d797659467948bff639446d9bedb55678b14d3be67264a68ef819df2dffcfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:35.220069Z","signature_b64":"T4iZwk3cbYXXtkHGSr2hbanoeOPui3UtJRz5YQRj5Iak4vQuXBjNQMgkk9R4y8vO5ffdjR/o6m+nC/eXWgANCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2d797659467948bff639446d9bedb55678b14d3be67264a68ef819df2dffcfc","last_reissued_at":"2026-05-18T04:41:35.219620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:35.219620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0711.0094","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qc2MiTMc2Smc+5lfDcL6T2psRBBwU7y7cVGuFH1kNBwfnoYkP+Y7VJYmgthmTwesVGTkTbl1usKRx6OyE7kaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:07:22.975874Z"},"content_sha256":"f1092f08fd7406d73523bbf55cdf943f4928ed1b703b8f49cc18ea3204c4f82a","schema_version":"1.0","event_id":"sha256:f1092f08fd7406d73523bbf55cdf943f4928ed1b703b8f49cc18ea3204c4f82a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:6LLZOZMUM6KIX73DSRDNTPW3KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry of A_g and Its Compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Samuel Grushevsky","submitted_at":"2007-11-01T10:10:20Z","abstract_excerpt":"In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed include: compactifications; birational geometry: nef and effective cones, canonical models; homology, Chow rings and intersection theory; and subvarieties of moduli spaces. We also discuss some open problems and possible further directions. This is an expanded and updated version of the talk given at the 2005 Summer Institute for Algebraic Geometry"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0094","kind":"arxiv","version":4},"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":"2026-05-18T04:41:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UOpXhovrwUCNrJ0VW1xrKhm7ksjO2w6X+LpGPs2yysMMxtSapnOZ1eQUyEDsSzhNJ6risD+1jqYxtEACNNXeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:07:22.976545Z"},"content_sha256":"57c9c7a1a128c14a8e89ebfc38f7e7ead18696191b21a5d32181b37f70cd7453","schema_version":"1.0","event_id":"sha256:57c9c7a1a128c14a8e89ebfc38f7e7ead18696191b21a5d32181b37f70cd7453"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LLZOZMUM6KIX73DSRDNTPW3KV/bundle.json","state_url":"https://pith.science/pith/6LLZOZMUM6KIX73DSRDNTPW3KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LLZOZMUM6KIX73DSRDNTPW3KV/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":"2026-05-31T23:07:22Z","links":{"resolver":"https://pith.science/pith/6LLZOZMUM6KIX73DSRDNTPW3KV","bundle":"https://pith.science/pith/6LLZOZMUM6KIX73DSRDNTPW3KV/bundle.json","state":"https://pith.science/pith/6LLZOZMUM6KIX73DSRDNTPW3KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LLZOZMUM6KIX73DSRDNTPW3KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6LLZOZMUM6KIX73DSRDNTPW3KV","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":"cfab818c9a6b7d59a8ae31af9a1aec8220aff8bcfb943639ca9bd9786ff6cea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-11-01T10:10:20Z","title_canon_sha256":"acebf59006bddd5ded06aa3c250777b4195951df455d5583c8bf5db1ae55e06a"},"schema_version":"1.0","source":{"id":"0711.0094","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0094","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0094v4","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0094","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"6LLZOZMUM6KI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6LLZOZMUM6KIX73D","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6LLZOZMU","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:57c9c7a1a128c14a8e89ebfc38f7e7ead18696191b21a5d32181b37f70cd7453","target":"graph","created_at":"2026-05-18T04:41:35Z","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":"In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed include: compactifications; birational geometry: nef and effective cones, canonical models; homology, Chow rings and intersection theory; and subvarieties of moduli spaces. We also discuss some open problems and possible further directions. This is an expanded and updated version of the talk given at the 2005 Summer Institute for Algebraic Geometry","authors_text":"Samuel Grushevsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-11-01T10:10:20Z","title":"Geometry of A_g and Its Compactifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0094","kind":"arxiv","version":4},"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:f1092f08fd7406d73523bbf55cdf943f4928ed1b703b8f49cc18ea3204c4f82a","target":"record","created_at":"2026-05-18T04:41:35Z","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":"cfab818c9a6b7d59a8ae31af9a1aec8220aff8bcfb943639ca9bd9786ff6cea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-11-01T10:10:20Z","title_canon_sha256":"acebf59006bddd5ded06aa3c250777b4195951df455d5583c8bf5db1ae55e06a"},"schema_version":"1.0","source":{"id":"0711.0094","kind":"arxiv","version":4}},"canonical_sha256":"f2d797659467948bff639446d9bedb55678b14d3be67264a68ef819df2dffcfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2d797659467948bff639446d9bedb55678b14d3be67264a68ef819df2dffcfc","first_computed_at":"2026-05-18T04:41:35.219620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:35.219620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T4iZwk3cbYXXtkHGSr2hbanoeOPui3UtJRz5YQRj5Iak4vQuXBjNQMgkk9R4y8vO5ffdjR/o6m+nC/eXWgANCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:35.220069Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.0094","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1092f08fd7406d73523bbf55cdf943f4928ed1b703b8f49cc18ea3204c4f82a","sha256:57c9c7a1a128c14a8e89ebfc38f7e7ead18696191b21a5d32181b37f70cd7453"],"state_sha256":"60808409cbe11f127b6bca2244a22d59f6e3dd027c383be321a8a1a7ec359a6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hVv6YPIUMT8RIU5msco9XkZnO58hTjop2mFhzyNFxIEt+hzM0cE/tYQTqT/X65djVlgoQhkKrmB2c/DkjuMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:07:22.979793Z","bundle_sha256":"ac79773b2e9a474b7d5a55da62e35cb8ef2187e962f554927ee4a36c7fd63f17"}}