{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UBMUKK376DBN2E6UIINBWKIDL5","short_pith_number":"pith:UBMUKK37","canonical_record":{"source":{"id":"1601.04222","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-16T22:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"61f6fa7f2edec55d29d268741d780ca1eea53f9cdb7a3931be7e2454d6ce79df","abstract_canon_sha256":"4097a5b81e75b40b4c39d78b74dd152241a702f9cd46e90575e1c3f4f48ece5f"},"schema_version":"1.0"},"canonical_sha256":"a059452b7ff0c2dd13d4421a1b29035f572175c5c1d62353bd568d116ae3bc47","source":{"kind":"arxiv","id":"1601.04222","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04222","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04222v3","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04222","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"UBMUKK376DBN","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UBMUKK376DBN2E6U","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UBMUKK37","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UBMUKK376DBN2E6UIINBWKIDL5","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04222","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-16T22:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"61f6fa7f2edec55d29d268741d780ca1eea53f9cdb7a3931be7e2454d6ce79df","abstract_canon_sha256":"4097a5b81e75b40b4c39d78b74dd152241a702f9cd46e90575e1c3f4f48ece5f"},"schema_version":"1.0"},"canonical_sha256":"a059452b7ff0c2dd13d4421a1b29035f572175c5c1d62353bd568d116ae3bc47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:15.800113Z","signature_b64":"YTincek/2WzKhl6lx5BDHIQasEIgzgrvimIaUJ4CzLyfdCu/dT9sIUoIbCzeaZ7FaSmE9CqXmA+1h5oTLPwFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a059452b7ff0c2dd13d4421a1b29035f572175c5c1d62353bd568d116ae3bc47","last_reissued_at":"2026-05-18T00:53:15.799612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:15.799612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04222","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":"2026-05-18T00:53:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IrC6Y1dQ3BUYUPS0kA8z2NN3NqhccPKFvnYJzn7TzKp/duc5PgfibrHdKdGQpFlNNp4KiUrlIUo6+GZcOrtNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:08:18.590419Z"},"content_sha256":"0bfa651f837091077ca34f836a58f81f5f0e9c06761d9f6a6afb15183f7b184c","schema_version":"1.0","event_id":"sha256:0bfa651f837091077ca34f836a58f81f5f0e9c06761d9f6a6afb15183f7b184c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UBMUKK376DBN2E6UIINBWKIDL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Salem numbers and Enriques surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Igor Dolgachev","submitted_at":"2016-01-16T22:35:51Z","abstract_excerpt":"It is known that the dynamical degree, or equivalently, the topological entropy of an automorphism g of an algebraic surface S is lower semi-continuous when (S,g) varies in a algebraic family. In this paper we make a series of experiments confirming this behavior with the aim to realize small Salem numbers as the dynamical degrees of automorphisms of Enriques surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04222","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":"2026-05-18T00:53:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YnIK6ULb9q2WnunpEiP19ajWEQfJx8GbyQPZmiLY+fIbNtVW1eMWXj4dDGph1nd79rSwgmXFN/sPiCM3+sjcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:08:18.590765Z"},"content_sha256":"837818f6c8bba437cd1a48a8a4fac7fa133e332014998d09ef1f4df145738eb4","schema_version":"1.0","event_id":"sha256:837818f6c8bba437cd1a48a8a4fac7fa133e332014998d09ef1f4df145738eb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBMUKK376DBN2E6UIINBWKIDL5/bundle.json","state_url":"https://pith.science/pith/UBMUKK376DBN2E6UIINBWKIDL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBMUKK376DBN2E6UIINBWKIDL5/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":"2026-07-03T02:08:18Z","links":{"resolver":"https://pith.science/pith/UBMUKK376DBN2E6UIINBWKIDL5","bundle":"https://pith.science/pith/UBMUKK376DBN2E6UIINBWKIDL5/bundle.json","state":"https://pith.science/pith/UBMUKK376DBN2E6UIINBWKIDL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBMUKK376DBN2E6UIINBWKIDL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UBMUKK376DBN2E6UIINBWKIDL5","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":"4097a5b81e75b40b4c39d78b74dd152241a702f9cd46e90575e1c3f4f48ece5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-16T22:35:51Z","title_canon_sha256":"61f6fa7f2edec55d29d268741d780ca1eea53f9cdb7a3931be7e2454d6ce79df"},"schema_version":"1.0","source":{"id":"1601.04222","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04222","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04222v3","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04222","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"UBMUKK376DBN","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UBMUKK376DBN2E6U","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UBMUKK37","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:837818f6c8bba437cd1a48a8a4fac7fa133e332014998d09ef1f4df145738eb4","target":"graph","created_at":"2026-05-18T00:53:15Z","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":"It is known that the dynamical degree, or equivalently, the topological entropy of an automorphism g of an algebraic surface S is lower semi-continuous when (S,g) varies in a algebraic family. In this paper we make a series of experiments confirming this behavior with the aim to realize small Salem numbers as the dynamical degrees of automorphisms of Enriques surfaces.","authors_text":"Igor Dolgachev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-16T22:35:51Z","title":"Salem numbers and Enriques surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04222","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":"sha256:0bfa651f837091077ca34f836a58f81f5f0e9c06761d9f6a6afb15183f7b184c","target":"record","created_at":"2026-05-18T00:53:15Z","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":"4097a5b81e75b40b4c39d78b74dd152241a702f9cd46e90575e1c3f4f48ece5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-16T22:35:51Z","title_canon_sha256":"61f6fa7f2edec55d29d268741d780ca1eea53f9cdb7a3931be7e2454d6ce79df"},"schema_version":"1.0","source":{"id":"1601.04222","kind":"arxiv","version":3}},"canonical_sha256":"a059452b7ff0c2dd13d4421a1b29035f572175c5c1d62353bd568d116ae3bc47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a059452b7ff0c2dd13d4421a1b29035f572175c5c1d62353bd568d116ae3bc47","first_computed_at":"2026-05-18T00:53:15.799612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:15.799612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTincek/2WzKhl6lx5BDHIQasEIgzgrvimIaUJ4CzLyfdCu/dT9sIUoIbCzeaZ7FaSmE9CqXmA+1h5oTLPwFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:15.800113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04222","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bfa651f837091077ca34f836a58f81f5f0e9c06761d9f6a6afb15183f7b184c","sha256:837818f6c8bba437cd1a48a8a4fac7fa133e332014998d09ef1f4df145738eb4"],"state_sha256":"62595e483d007ac35a9e682e27c605493acf9aa5b8019c2d189fe2ead5b681c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92IdpU6dzfe4l/Q8xx7lYjgYBBRNxx6S+kTp7wsQaS6R08f6yiwEAjbmQgCbFlBtU9LvvzCHPC/ANb2RETaMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T02:08:18.592840Z","bundle_sha256":"bfc0b4d075bac68bb606fb58294f3b027c1beda0d9bb30b5a845d208407dd046"}}