{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:T2CET42F2V2G6O3IVSTN53SQKL","short_pith_number":"pith:T2CET42F","schema_version":"1.0","canonical_sha256":"9e8449f345d5746f3b68aca6deee5052d3336e07f5e9216e87adcb0e948af512","source":{"kind":"arxiv","id":"nlin/0505024","version":1},"attestation_state":"computed","paper":{"title":"Post-critical set and non existence of preserved meromorphic two-forms","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.CD","authors_text":"J.-M. Maillard, M. Bouamra, S. Boukraa, S. Hassani","submitted_at":"2005-05-09T12:57:40Z","abstract_excerpt":"We present a family of birational transformations in $ CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some \"non-analytic\" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \\emph{degrees of the parameters}, while one has an exponential growth out o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"nlin/0505024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2005-05-09T12:57:40Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"41168f75da8fdcfa91887443adc1fe676e84c4dc2705f2a0bc250793d8b3eeeb","abstract_canon_sha256":"6f0d32409e98802a663220a209442f30170eefc9c5835c777ad2bd264866fded"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:21.749941Z","signature_b64":"hi3J4Fq7ijOKxkwheLxTSuIVoWvFXgmT8b395Tti08yPin98uMQz9Vo2Fb+o3ef/w0K2bq3G/sKluuYseKCWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e8449f345d5746f3b68aca6deee5052d3336e07f5e9216e87adcb0e948af512","last_reissued_at":"2026-05-18T01:05:21.749251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:21.749251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Post-critical set and non existence of preserved meromorphic two-forms","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.CD","authors_text":"J.-M. Maillard, M. Bouamra, S. Boukraa, S. Hassani","submitted_at":"2005-05-09T12:57:40Z","abstract_excerpt":"We present a family of birational transformations in $ CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some \"non-analytic\" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \\emph{degrees of the parameters}, while one has an exponential growth out o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0505024","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0505024","created_at":"2026-05-18T01:05:21.749369+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0505024v1","created_at":"2026-05-18T01:05:21.749369+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0505024","created_at":"2026-05-18T01:05:21.749369+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2CET42F2V2G","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2CET42F2V2G6O3I","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2CET42F","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL","json":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL.json","graph_json":"https://pith.science/api/pith-number/T2CET42F2V2G6O3IVSTN53SQKL/graph.json","events_json":"https://pith.science/api/pith-number/T2CET42F2V2G6O3IVSTN53SQKL/events.json","paper":"https://pith.science/paper/T2CET42F"},"agent_actions":{"view_html":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL","download_json":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL.json","view_paper":"https://pith.science/paper/T2CET42F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0505024&json=true","fetch_graph":"https://pith.science/api/pith-number/T2CET42F2V2G6O3IVSTN53SQKL/graph.json","fetch_events":"https://pith.science/api/pith-number/T2CET42F2V2G6O3IVSTN53SQKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL/action/storage_attestation","attest_author":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL/action/author_attestation","sign_citation":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL/action/citation_signature","submit_replication":"https://pith.science/pith/T2CET42F2V2G6O3IVSTN53SQKL/action/replication_record"}},"created_at":"2026-05-18T01:05:21.749369+00:00","updated_at":"2026-05-18T01:05:21.749369+00:00"}