{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R763YSY45DQN3IIUTVDRFBYXFI","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":"df5380cb64a7eebd7d72a82a7f5b0323124fe0125a788492ea7d850f288dc07d","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-16T05:29:41Z","title_canon_sha256":"b52274b87261479b2a533fbff8d7ba6c01ce1edea41f1baf0cc7f30442e6f51c"},"schema_version":"1.0","source":{"id":"1704.04726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.04726","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1704.04726v2","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04726","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"R763YSY45DQN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R763YSY45DQN3IIU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R763YSY4","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:3e34aa4479926824c98dd467893eb760ee44024a0927d5f86306c48cf6e5f450","target":"graph","created_at":"2026-05-18T00:06:12Z","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 the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs $f\\colon (X,x_0)\\to (X,x_0)$, where $X$ is a complex surface having $x_0$ as a normal singularity. We prove that as long as $x_0$ is not a cusp singularity of $X$, then it is possible to find arbitrarily high modifications $\\pi\\colon X_\\pi\\to (X,x_0)$ such that the dynamics of $f$ (or more precisely of $f^N$ for $N$ big enough) on $X_\\pi$ is algebraically stable. This result is proved by understanding the dynamics induced by $f$ on a space of valuations associated to $X$; in fact, we ar","authors_text":"Matteo Ruggiero, William Gignac","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-16T05:29:41Z","title":"Local dynamics of non-invertible maps near normal surface singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04726","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:ba2818bdcf909819e89d20dfe5a339ffb0da07a5a7fafe0fb2d9ade97eff81cc","target":"record","created_at":"2026-05-18T00:06:12Z","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":"df5380cb64a7eebd7d72a82a7f5b0323124fe0125a788492ea7d850f288dc07d","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-16T05:29:41Z","title_canon_sha256":"b52274b87261479b2a533fbff8d7ba6c01ce1edea41f1baf0cc7f30442e6f51c"},"schema_version":"1.0","source":{"id":"1704.04726","kind":"arxiv","version":2}},"canonical_sha256":"8ffdbc4b1ce8e0dda1149d471287172a1aef0996c4a4e31c8f2993fac959a1c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ffdbc4b1ce8e0dda1149d471287172a1aef0996c4a4e31c8f2993fac959a1c1","first_computed_at":"2026-05-18T00:06:12.442594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:12.442594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/MBPlg7WUzk5UtyJwx/UPNE/zaEG9b1ZsrQxBmHwPkXPaTeJhl5NFqLSi8NMnmjm+PeIB2E/VXGxy0dcLDf/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:12.443118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.04726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba2818bdcf909819e89d20dfe5a339ffb0da07a5a7fafe0fb2d9ade97eff81cc","sha256:3e34aa4479926824c98dd467893eb760ee44024a0927d5f86306c48cf6e5f450"],"state_sha256":"24b72f6add48ea027dc7d52531f9dec1b867a071e7d5bc0272c53c96dcf12d55"}