{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:64YTHRCWESC3HRX5UXGZ3TTMQN","short_pith_number":"pith:64YTHRCW","canonical_record":{"source":{"id":"1308.2567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T13:59:11Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e87d1b6b52b1078ecb365459afe506f51587f74de05380f552c84204309d1f6c","abstract_canon_sha256":"9c18dd36149d93364dc699a8d8404b1275b0a6ce3b4a354222d051d6f381368d"},"schema_version":"1.0"},"canonical_sha256":"f73133c4562485b3c6fda5cd9dce6c8370873790f54bc511c70b6b3951fdeaa7","source":{"kind":"arxiv","id":"1308.2567","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2567","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2567v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2567","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"64YTHRCWESC3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"64YTHRCWESC3HRX5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"64YTHRCW","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:64YTHRCWESC3HRX5UXGZ3TTMQN","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T13:59:11Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e87d1b6b52b1078ecb365459afe506f51587f74de05380f552c84204309d1f6c","abstract_canon_sha256":"9c18dd36149d93364dc699a8d8404b1275b0a6ce3b4a354222d051d6f381368d"},"schema_version":"1.0"},"canonical_sha256":"f73133c4562485b3c6fda5cd9dce6c8370873790f54bc511c70b6b3951fdeaa7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:22.772227Z","signature_b64":"P84JtsyU0y8iCfecUtnwiUooGdzxj36TBGgaPCbeuDegR9hbFS9j3D5QdwasDqV0mz3kicLg8uXDfxnrrNsnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f73133c4562485b3c6fda5cd9dce6c8370873790f54bc511c70b6b3951fdeaa7","last_reissued_at":"2026-05-18T02:46:22.771725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:22.771725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2567","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":"2026-05-18T02:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MS6tu61UjbCTQJLhuYkbu5GSgJNSZiOlVaV08CWv436nAzlPrxJLqbaIsE+2RgqxRDFJZ2kxW0U0083DndAgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:23:47.172723Z"},"content_sha256":"716b6c93c4ea0ff9ecebd4db8f1dfaed8ac5e02077457b0b7c774b48762a082e","schema_version":"1.0","event_id":"sha256:716b6c93c4ea0ff9ecebd4db8f1dfaed8ac5e02077457b0b7c774b48762a082e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:64YTHRCWESC3HRX5UXGZ3TTMQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational surface maps with invariant meromorphic two forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Jan-Li Lin, Jeffrey Diller","submitted_at":"2013-08-12T13:59:11Z","abstract_excerpt":"We consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational change of coordinate. In this context, when the form has no zeroes, we investigate the notion of algebraic stability for f. We show in particular that algebraic stability is equivalent to a more tractable condition involving the behavior of f on the poles of the form. Finally, we illustrate our results in the particular case where S is the projective plane "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2567","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":"2026-05-18T02:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"liG25rl50voyJj3GvTBmcsj6Ryhpl+vbx4DMPZMIuCw6GOmOoSU9SCNcJapc6nrIijLavamY/RRp7/VeUs/2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:23:47.173297Z"},"content_sha256":"b02c74c1e8665df878f6cc3ceecf028014615735eff0691a1e380cc9baf34640","schema_version":"1.0","event_id":"sha256:b02c74c1e8665df878f6cc3ceecf028014615735eff0691a1e380cc9baf34640"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64YTHRCWESC3HRX5UXGZ3TTMQN/bundle.json","state_url":"https://pith.science/pith/64YTHRCWESC3HRX5UXGZ3TTMQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64YTHRCWESC3HRX5UXGZ3TTMQN/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":"2026-06-21T14:23:47Z","links":{"resolver":"https://pith.science/pith/64YTHRCWESC3HRX5UXGZ3TTMQN","bundle":"https://pith.science/pith/64YTHRCWESC3HRX5UXGZ3TTMQN/bundle.json","state":"https://pith.science/pith/64YTHRCWESC3HRX5UXGZ3TTMQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64YTHRCWESC3HRX5UXGZ3TTMQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:64YTHRCWESC3HRX5UXGZ3TTMQN","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":"9c18dd36149d93364dc699a8d8404b1275b0a6ce3b4a354222d051d6f381368d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T13:59:11Z","title_canon_sha256":"e87d1b6b52b1078ecb365459afe506f51587f74de05380f552c84204309d1f6c"},"schema_version":"1.0","source":{"id":"1308.2567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2567","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2567v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2567","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"64YTHRCWESC3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"64YTHRCWESC3HRX5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"64YTHRCW","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:b02c74c1e8665df878f6cc3ceecf028014615735eff0691a1e380cc9baf34640","target":"graph","created_at":"2026-05-18T02:46:22Z","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 consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational change of coordinate. In this context, when the form has no zeroes, we investigate the notion of algebraic stability for f. We show in particular that algebraic stability is equivalent to a more tractable condition involving the behavior of f on the poles of the form. Finally, we illustrate our results in the particular case where S is the projective plane ","authors_text":"Jan-Li Lin, Jeffrey Diller","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T13:59:11Z","title":"Rational surface maps with invariant meromorphic two forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2567","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":"sha256:716b6c93c4ea0ff9ecebd4db8f1dfaed8ac5e02077457b0b7c774b48762a082e","target":"record","created_at":"2026-05-18T02:46:22Z","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":"9c18dd36149d93364dc699a8d8404b1275b0a6ce3b4a354222d051d6f381368d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T13:59:11Z","title_canon_sha256":"e87d1b6b52b1078ecb365459afe506f51587f74de05380f552c84204309d1f6c"},"schema_version":"1.0","source":{"id":"1308.2567","kind":"arxiv","version":2}},"canonical_sha256":"f73133c4562485b3c6fda5cd9dce6c8370873790f54bc511c70b6b3951fdeaa7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f73133c4562485b3c6fda5cd9dce6c8370873790f54bc511c70b6b3951fdeaa7","first_computed_at":"2026-05-18T02:46:22.771725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:22.771725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P84JtsyU0y8iCfecUtnwiUooGdzxj36TBGgaPCbeuDegR9hbFS9j3D5QdwasDqV0mz3kicLg8uXDfxnrrNsnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:22.772227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:716b6c93c4ea0ff9ecebd4db8f1dfaed8ac5e02077457b0b7c774b48762a082e","sha256:b02c74c1e8665df878f6cc3ceecf028014615735eff0691a1e380cc9baf34640"],"state_sha256":"bf3f967798ed1ee8d750bd7699bf091f172c252706a2e15a52250075241e96e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7X74lZlXvKCznXHewMuTWDbPPDq6nD17xP//ZAgftoV7XQ2CIWXNMavcYs78k2cwKg5fxeBRoYC6+ipODen/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:23:47.175261Z","bundle_sha256":"9a1341133b533456f5e17049554538c51ed8b7a1bdbde5732f2b13d3596b16ba"}}