{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PFH35HFSZZCPL4KSF7BRNAB5ZP","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":"6414d792be8761b237b694e2a81ee2a5e2da765e5adf20743db1845ab29d3393","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-12T17:33:05Z","title_canon_sha256":"7404428da68506ba04ea1ee709124715a9e356a83ad895332753b4e910bd8c29"},"schema_version":"1.0","source":{"id":"1101.2413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2413","created_at":"2026-05-18T04:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2413v1","created_at":"2026-05-18T04:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2413","created_at":"2026-05-18T04:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"PFH35HFSZZCP","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFH35HFSZZCPL4KS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFH35HFS","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:be029f45ea2056c7263b56ba1e7060380a9fa2aa5c074d4487bd63c45d10a6d9","target":"graph","created_at":"2026-05-18T04:31:43Z","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":"Cremona maps defined by monomials of degree 2 are thoroughly analyzed and classified via integer arithmetic and graph combinatorics. In particular, the structure of the inverse map to such a monomial Cremona map is made very explicit as is the degree of its monomial defining coordinates. As a special case, one proves that any monomial Cremona map of degree 2 has inverse of degree 2 if and only if it is an involution up to permutation in the source and in the target. This statement is subsumed in a recent result of L. Pirio and F. Russo, but the proof is entirely different and holds in all char","authors_text":"Aron Simis, Barbara Costa","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-12T17:33:05Z","title":"Cremona maps defined by monomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2413","kind":"arxiv","version":1},"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":"sha256:854d2bb6e95bb04a278e38fdebee1ded7c271ec996ca3c6554e3f2acd33c68ec","target":"record","created_at":"2026-05-18T04:31:43Z","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":"6414d792be8761b237b694e2a81ee2a5e2da765e5adf20743db1845ab29d3393","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-12T17:33:05Z","title_canon_sha256":"7404428da68506ba04ea1ee709124715a9e356a83ad895332753b4e910bd8c29"},"schema_version":"1.0","source":{"id":"1101.2413","kind":"arxiv","version":1}},"canonical_sha256":"794fbe9cb2ce44f5f1522fc316803dcbc57cdcde6b0848abd6054e16454c746e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"794fbe9cb2ce44f5f1522fc316803dcbc57cdcde6b0848abd6054e16454c746e","first_computed_at":"2026-05-18T04:31:43.068738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:43.068738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vCi/ZGEIGcuMkyV0d48LakOXfcIz5icgjPN2XzegLg3a9vL68Q8X3//Gq/BJ5TAo7002frxaac6RgYpzM1pIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:43.069294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:854d2bb6e95bb04a278e38fdebee1ded7c271ec996ca3c6554e3f2acd33c68ec","sha256:be029f45ea2056c7263b56ba1e7060380a9fa2aa5c074d4487bd63c45d10a6d9"],"state_sha256":"76b8a449db9fbffb6d40cf4765fb5602660bb14fa8c731ddd71ad087b563e3a5"}