{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZKMSQXJSI27P2E3LZNDU6SLE22","short_pith_number":"pith:ZKMSQXJS","canonical_record":{"source":{"id":"1110.6905","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T18:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"4cb90179b27c65d8d824022392163deb9c9afb631608c5173e38e752b232ef59","abstract_canon_sha256":"1173713cb2577b54d467b142e87efef127ca503a52f637f90cde6e382c1e0ad7"},"schema_version":"1.0"},"canonical_sha256":"ca99285d3246befd136bcb474f4964d6a7acd078b410ceb89d5eea7a61423a6a","source":{"kind":"arxiv","id":"1110.6905","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6905","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6905v3","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6905","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZKMSQXJSI27P","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZKMSQXJSI27P2E3L","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZKMSQXJS","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZKMSQXJSI27P2E3LZNDU6SLE22","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6905","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T18:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"4cb90179b27c65d8d824022392163deb9c9afb631608c5173e38e752b232ef59","abstract_canon_sha256":"1173713cb2577b54d467b142e87efef127ca503a52f637f90cde6e382c1e0ad7"},"schema_version":"1.0"},"canonical_sha256":"ca99285d3246befd136bcb474f4964d6a7acd078b410ceb89d5eea7a61423a6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:58.474232Z","signature_b64":"JiUJERTDMnUOJMUyP2jUF0nt98i9Zm6VZBoh9FPIxsAgaWFIax3X1a2C7r8NQGusqTXOdTXHsBaBYheIK6IEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca99285d3246befd136bcb474f4964d6a7acd078b410ceb89d5eea7a61423a6a","last_reissued_at":"2026-05-18T01:36:58.473602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:58.473602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6905","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":"2026-05-18T01:36:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7UCz8J4qcaNv3haNlx5hf2+yFn9XnlP4QRZLG0mU9mLL/8R8ep6vIsAS09fGSjSwqvKIHmFBMNpZ+RsqOnDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:08:26.541096Z"},"content_sha256":"de412520cc171504b46808ecfad79d972f2c75f5487b8af349f290c880ef88ee","schema_version":"1.0","event_id":"sha256:de412520cc171504b46808ecfad79d972f2c75f5487b8af349f290c880ef88ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZKMSQXJSI27P2E3LZNDU6SLE22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic Compactifications of C^2 part I - curvettes at infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pinaki Mondal","submitted_at":"2011-10-31T18:58:52Z","abstract_excerpt":"We study normal analytic compactifications of C^2 and describe their singularities and configuration of curves at infinity, in particular improving and generalizing results of (Brenton, Math. Ann. 206:303--310, 1973). As a by product we give new proofs of Jung's theorem on polynomial automorphisms of C^2 and Remmert and Van de Ven's result that CP^2 is the only smooth analytic compactification of C^2 for which the curve at infinity is irreducible. We also give a complete answer to the question of existence of compactifications of C^2 with prescribed divisorial valuations at infinity. In partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6905","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":"2026-05-18T01:36:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swDl5qG+RU5Rb6BFkm9pgDoQovv2Q6VE2xa+ouJ+SiaNu6cE7XzO+uxkdYPl0AyRkL227CYa9GlqhyDW1LmeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:08:26.541456Z"},"content_sha256":"7c47fae80a8d320b69467462a444df4ffdb4b4321600904a7fbcf7497baf6b2a","schema_version":"1.0","event_id":"sha256:7c47fae80a8d320b69467462a444df4ffdb4b4321600904a7fbcf7497baf6b2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKMSQXJSI27P2E3LZNDU6SLE22/bundle.json","state_url":"https://pith.science/pith/ZKMSQXJSI27P2E3LZNDU6SLE22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKMSQXJSI27P2E3LZNDU6SLE22/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":"2026-06-25T11:08:26Z","links":{"resolver":"https://pith.science/pith/ZKMSQXJSI27P2E3LZNDU6SLE22","bundle":"https://pith.science/pith/ZKMSQXJSI27P2E3LZNDU6SLE22/bundle.json","state":"https://pith.science/pith/ZKMSQXJSI27P2E3LZNDU6SLE22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKMSQXJSI27P2E3LZNDU6SLE22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZKMSQXJSI27P2E3LZNDU6SLE22","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":"1173713cb2577b54d467b142e87efef127ca503a52f637f90cde6e382c1e0ad7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T18:58:52Z","title_canon_sha256":"4cb90179b27c65d8d824022392163deb9c9afb631608c5173e38e752b232ef59"},"schema_version":"1.0","source":{"id":"1110.6905","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6905","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6905v3","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6905","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZKMSQXJSI27P","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZKMSQXJSI27P2E3L","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZKMSQXJS","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:7c47fae80a8d320b69467462a444df4ffdb4b4321600904a7fbcf7497baf6b2a","target":"graph","created_at":"2026-05-18T01:36:58Z","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 study normal analytic compactifications of C^2 and describe their singularities and configuration of curves at infinity, in particular improving and generalizing results of (Brenton, Math. Ann. 206:303--310, 1973). As a by product we give new proofs of Jung's theorem on polynomial automorphisms of C^2 and Remmert and Van de Ven's result that CP^2 is the only smooth analytic compactification of C^2 for which the curve at infinity is irreducible. We also give a complete answer to the question of existence of compactifications of C^2 with prescribed divisorial valuations at infinity. In partic","authors_text":"Pinaki Mondal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T18:58:52Z","title":"Analytic Compactifications of C^2 part I - curvettes at infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6905","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:de412520cc171504b46808ecfad79d972f2c75f5487b8af349f290c880ef88ee","target":"record","created_at":"2026-05-18T01:36:58Z","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":"1173713cb2577b54d467b142e87efef127ca503a52f637f90cde6e382c1e0ad7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T18:58:52Z","title_canon_sha256":"4cb90179b27c65d8d824022392163deb9c9afb631608c5173e38e752b232ef59"},"schema_version":"1.0","source":{"id":"1110.6905","kind":"arxiv","version":3}},"canonical_sha256":"ca99285d3246befd136bcb474f4964d6a7acd078b410ceb89d5eea7a61423a6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca99285d3246befd136bcb474f4964d6a7acd078b410ceb89d5eea7a61423a6a","first_computed_at":"2026-05-18T01:36:58.473602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:58.473602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JiUJERTDMnUOJMUyP2jUF0nt98i9Zm6VZBoh9FPIxsAgaWFIax3X1a2C7r8NQGusqTXOdTXHsBaBYheIK6IEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:58.474232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6905","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de412520cc171504b46808ecfad79d972f2c75f5487b8af349f290c880ef88ee","sha256:7c47fae80a8d320b69467462a444df4ffdb4b4321600904a7fbcf7497baf6b2a"],"state_sha256":"26d3f22b0c100ba0b03f0a3a2717fc7aeab67f2e5d8f90c59869d56af93147a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmEEHx28Lrs23cvmgfw1hx6fQI3ehRcqTsbC0FIfADkLNCPrfI0x+VtAG0giVePC1CqmTnCfNy0QaVdGr/79Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:08:26.543421Z","bundle_sha256":"fa377edf9e28be73893497206e51dff5f72707a357e50b95cc910028c705c5d3"}}