{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:Y3XX7MPFL2DBCEPT3642RDCK3J","short_pith_number":"pith:Y3XX7MPF","canonical_record":{"source":{"id":"1010.3751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-18T22:11:32Z","cross_cats_sorted":[],"title_canon_sha256":"2d074115b8b85022a7a2826c324885009a804e2d4c33b6394470734fbbb72509","abstract_canon_sha256":"e0786eb96dfc811fdaed46dd8c2604bbe81f366a9fda8160a51a4299abbeb744"},"schema_version":"1.0"},"canonical_sha256":"c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc","source":{"kind":"arxiv","id":"1010.3751","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3751","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3751v2","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3751","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"Y3XX7MPFL2DB","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y3XX7MPFL2DBCEPT","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y3XX7MPF","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:Y3XX7MPFL2DBCEPT3642RDCK3J","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-18T22:11:32Z","cross_cats_sorted":[],"title_canon_sha256":"2d074115b8b85022a7a2826c324885009a804e2d4c33b6394470734fbbb72509","abstract_canon_sha256":"e0786eb96dfc811fdaed46dd8c2604bbe81f366a9fda8160a51a4299abbeb744"},"schema_version":"1.0"},"canonical_sha256":"c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:38.408289Z","signature_b64":"A8elnCGjVvqO2eRVeeQ1OxOhnYIUtWqEfMsr7sN6cOCCtevWnVtuMOb8huRdszgbq99uUd1nVNthjge3W2djBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc","last_reissued_at":"2026-05-18T04:20:38.407597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:38.407597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3751","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":"2026-05-18T04:20:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nm7bjYH1oGHuRCarpSy+Alcnqk2JuJVP0RIeDx3WjCwqM7YpDIjprShEypxSblyJ2dq7Xx+EETzn4gL4j9/ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:01:21.561507Z"},"content_sha256":"60b5592694eb428312cac1ceb8346c2fb4131b72da5925ecabce4550ff790ae7","schema_version":"1.0","event_id":"sha256:60b5592694eb428312cac1ceb8346c2fb4131b72da5925ecabce4550ff790ae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:Y3XX7MPFL2DBCEPT3642RDCK3J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularities with G_m-action and the log minimal model program for $\\bar{M}_g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Ishii Smyth, Jarod Alper, Maksym Fedorchuk","submitted_at":"2010-10-18T22:11:32Z","abstract_excerpt":"We give a precise formulation of the modularity principle for the log canonical models of $\\bar{M}_g$. Assuming the modularity principle holds, we develop and compare two methods for determining the critical alpha-values at which a singularity or complete curve with G_m-action arises in the modular interpretations of log canonical models of $\\bar{M}_g$. The first method involves a new invariant of curve singularities with G_m-action, constructed via the characters of the induced G_m-action on spaces of pluricanonical forms. The second method involves intersection theory on the variety of stabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3751","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":"2026-05-18T04:20:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rCSRw30r5eYI2awMCiVq7AUCU2YocHY+ni4p+QBBFSb0LXIfZEgFSL0oF7NHLUZqK60MuphHhY7P90N7WNCMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:01:21.561857Z"},"content_sha256":"603fbd0666c3dbc5cc5ecdc85e5e3b0b227a48e0e5bccc7261fb695507aa4044","schema_version":"1.0","event_id":"sha256:603fbd0666c3dbc5cc5ecdc85e5e3b0b227a48e0e5bccc7261fb695507aa4044"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3XX7MPFL2DBCEPT3642RDCK3J/bundle.json","state_url":"https://pith.science/pith/Y3XX7MPFL2DBCEPT3642RDCK3J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3XX7MPFL2DBCEPT3642RDCK3J/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":"2026-06-04T18:01:21Z","links":{"resolver":"https://pith.science/pith/Y3XX7MPFL2DBCEPT3642RDCK3J","bundle":"https://pith.science/pith/Y3XX7MPFL2DBCEPT3642RDCK3J/bundle.json","state":"https://pith.science/pith/Y3XX7MPFL2DBCEPT3642RDCK3J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3XX7MPFL2DBCEPT3642RDCK3J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Y3XX7MPFL2DBCEPT3642RDCK3J","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":"e0786eb96dfc811fdaed46dd8c2604bbe81f366a9fda8160a51a4299abbeb744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-18T22:11:32Z","title_canon_sha256":"2d074115b8b85022a7a2826c324885009a804e2d4c33b6394470734fbbb72509"},"schema_version":"1.0","source":{"id":"1010.3751","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3751","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3751v2","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3751","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"Y3XX7MPFL2DB","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y3XX7MPFL2DBCEPT","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y3XX7MPF","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:603fbd0666c3dbc5cc5ecdc85e5e3b0b227a48e0e5bccc7261fb695507aa4044","target":"graph","created_at":"2026-05-18T04:20:38Z","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 give a precise formulation of the modularity principle for the log canonical models of $\\bar{M}_g$. Assuming the modularity principle holds, we develop and compare two methods for determining the critical alpha-values at which a singularity or complete curve with G_m-action arises in the modular interpretations of log canonical models of $\\bar{M}_g$. The first method involves a new invariant of curve singularities with G_m-action, constructed via the characters of the induced G_m-action on spaces of pluricanonical forms. The second method involves intersection theory on the variety of stabl","authors_text":"David Ishii Smyth, Jarod Alper, Maksym Fedorchuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-18T22:11:32Z","title":"Singularities with G_m-action and the log minimal model program for $\\bar{M}_g$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3751","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":"sha256:60b5592694eb428312cac1ceb8346c2fb4131b72da5925ecabce4550ff790ae7","target":"record","created_at":"2026-05-18T04:20:38Z","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":"e0786eb96dfc811fdaed46dd8c2604bbe81f366a9fda8160a51a4299abbeb744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-18T22:11:32Z","title_canon_sha256":"2d074115b8b85022a7a2826c324885009a804e2d4c33b6394470734fbbb72509"},"schema_version":"1.0","source":{"id":"1010.3751","kind":"arxiv","version":2}},"canonical_sha256":"c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc","first_computed_at":"2026-05-18T04:20:38.407597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:38.407597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A8elnCGjVvqO2eRVeeQ1OxOhnYIUtWqEfMsr7sN6cOCCtevWnVtuMOb8huRdszgbq99uUd1nVNthjge3W2djBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:38.408289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3751","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60b5592694eb428312cac1ceb8346c2fb4131b72da5925ecabce4550ff790ae7","sha256:603fbd0666c3dbc5cc5ecdc85e5e3b0b227a48e0e5bccc7261fb695507aa4044"],"state_sha256":"7bd6113f49000f24d9c318e9457f6a162e51d1e009eb2d94e11288f329e3d2b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXElPKX9WXq0d9yFvh5uGSdMO4H1EjBZQCSTRBwldjCSgVoB94y4nkl+zrfaswyVCgsY0qHT+0FiMy2G0NEwDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:01:21.563878Z","bundle_sha256":"038846377e88ae0f3afdd8d0400d2e06e28246a02795e1f54005efdfa0e86038"}}