{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NSSHCYDKXMHZPT2CYK6KNM6GVF","short_pith_number":"pith:NSSHCYDK","canonical_record":{"source":{"id":"1906.11188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-26T16:13:01Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"e789d25af5b2e63c27f0d0f9c503a9e30ff81df47520e522a38831367b7b8eb3","abstract_canon_sha256":"92fd871f4a015aec381cace0d94d71fa8ab4135cc0faad62d876d7ed4a2eebaf"},"schema_version":"1.0"},"canonical_sha256":"6ca471606abb0f97cf42c2bca6b3c6a9447a945af7d0f8ee6840fe58699be425","source":{"kind":"arxiv","id":"1906.11188","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11188","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11188v1","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11188","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"NSSHCYDKXMHZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NSSHCYDKXMHZPT2C","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NSSHCYDK","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NSSHCYDKXMHZPT2CYK6KNM6GVF","target":"record","payload":{"canonical_record":{"source":{"id":"1906.11188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-26T16:13:01Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"e789d25af5b2e63c27f0d0f9c503a9e30ff81df47520e522a38831367b7b8eb3","abstract_canon_sha256":"92fd871f4a015aec381cace0d94d71fa8ab4135cc0faad62d876d7ed4a2eebaf"},"schema_version":"1.0"},"canonical_sha256":"6ca471606abb0f97cf42c2bca6b3c6a9447a945af7d0f8ee6840fe58699be425","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:09.524667Z","signature_b64":"rwSBnRz3SN2Otvq59Y0Gp99TrSxMm/iniAALrO4M8JQCbA1CPaMBvgpTxipUheCpFDfJCODIZRtTmmdBOywWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ca471606abb0f97cf42c2bca6b3c6a9447a945af7d0f8ee6840fe58699be425","last_reissued_at":"2026-05-17T23:42:09.523965Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:09.523965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.11188","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2xgG5d4LjmLtMghjGs+kpc753Gz9yFdUFCHvnnCji2f63rfoEhvlD1PkDfq8cfzcFYexdZ7hFYxgncxkvKvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:28:03.048033Z"},"content_sha256":"1cdb13b7db833b0dd8b855784dead2e9ed169838b4fd8d6d0ee7501afb448133","schema_version":"1.0","event_id":"sha256:1cdb13b7db833b0dd8b855784dead2e9ed169838b4fd8d6d0ee7501afb448133"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NSSHCYDKXMHZPT2CYK6KNM6GVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher arithmetic degrees of dominant rational self-maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Fei Hu, John Lesieutre, Matthew Satriano, Nguyen-Bac Dang","submitted_at":"2019-06-26T16:13:01Z","abstract_excerpt":"Suppose that $f \\colon X \\dashrightarrow X$ is a dominant rational self-map of a smooth projective variety defined over ${\\overline{\\mathbf Q}}$. Kawaguchi and Silverman conjectured that if $P \\in X({\\overline{\\mathbf Q}})$ is a point with well-defined forward orbit, then the growth rate of the height along the orbit exists, and coincides with the first dynamical degree $\\lambda_1(f)$ of $f$ if the orbit of $P$ is Zariski dense in $X$.\n  In this note, we extend the Kawaguchi-Silverman conjecture to the setting of orbits of higher-dimensional subvarieties of $X$. We begin by defining a set of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11188","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lwEOCrGK2838COI43S7CeTv+hiKXPBtZ+XOuVx2r4AG3hPazBSVUYQDHTw5umr4eOF8ha5X2xy50lrAmwEUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:28:03.048407Z"},"content_sha256":"e7ad628185c90f02f272e4dde9ecb63134838cab8c12a4c6df811d3fea1da67b","schema_version":"1.0","event_id":"sha256:e7ad628185c90f02f272e4dde9ecb63134838cab8c12a4c6df811d3fea1da67b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF/bundle.json","state_url":"https://pith.science/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF/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":"2026-05-30T00:28:03Z","links":{"resolver":"https://pith.science/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF","bundle":"https://pith.science/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF/bundle.json","state":"https://pith.science/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSSHCYDKXMHZPT2CYK6KNM6GVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NSSHCYDKXMHZPT2CYK6KNM6GVF","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":"92fd871f4a015aec381cace0d94d71fa8ab4135cc0faad62d876d7ed4a2eebaf","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-26T16:13:01Z","title_canon_sha256":"e789d25af5b2e63c27f0d0f9c503a9e30ff81df47520e522a38831367b7b8eb3"},"schema_version":"1.0","source":{"id":"1906.11188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11188","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11188v1","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11188","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"NSSHCYDKXMHZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NSSHCYDKXMHZPT2C","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NSSHCYDK","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:e7ad628185c90f02f272e4dde9ecb63134838cab8c12a4c6df811d3fea1da67b","target":"graph","created_at":"2026-05-17T23:42:09Z","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":"Suppose that $f \\colon X \\dashrightarrow X$ is a dominant rational self-map of a smooth projective variety defined over ${\\overline{\\mathbf Q}}$. Kawaguchi and Silverman conjectured that if $P \\in X({\\overline{\\mathbf Q}})$ is a point with well-defined forward orbit, then the growth rate of the height along the orbit exists, and coincides with the first dynamical degree $\\lambda_1(f)$ of $f$ if the orbit of $P$ is Zariski dense in $X$.\n  In this note, we extend the Kawaguchi-Silverman conjecture to the setting of orbits of higher-dimensional subvarieties of $X$. We begin by defining a set of a","authors_text":"Dragos Ghioca, Fei Hu, John Lesieutre, Matthew Satriano, Nguyen-Bac Dang","cross_cats":["math.AG","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-26T16:13:01Z","title":"Higher arithmetic degrees of dominant rational self-maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11188","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":"sha256:1cdb13b7db833b0dd8b855784dead2e9ed169838b4fd8d6d0ee7501afb448133","target":"record","created_at":"2026-05-17T23:42:09Z","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":"92fd871f4a015aec381cace0d94d71fa8ab4135cc0faad62d876d7ed4a2eebaf","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-26T16:13:01Z","title_canon_sha256":"e789d25af5b2e63c27f0d0f9c503a9e30ff81df47520e522a38831367b7b8eb3"},"schema_version":"1.0","source":{"id":"1906.11188","kind":"arxiv","version":1}},"canonical_sha256":"6ca471606abb0f97cf42c2bca6b3c6a9447a945af7d0f8ee6840fe58699be425","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ca471606abb0f97cf42c2bca6b3c6a9447a945af7d0f8ee6840fe58699be425","first_computed_at":"2026-05-17T23:42:09.523965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:09.523965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rwSBnRz3SN2Otvq59Y0Gp99TrSxMm/iniAALrO4M8JQCbA1CPaMBvgpTxipUheCpFDfJCODIZRtTmmdBOywWBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:09.524667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cdb13b7db833b0dd8b855784dead2e9ed169838b4fd8d6d0ee7501afb448133","sha256:e7ad628185c90f02f272e4dde9ecb63134838cab8c12a4c6df811d3fea1da67b"],"state_sha256":"ad6d03403b827329473230e3ce0b21b71fa8796123ad09ffe3edc09d2d2f55d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QU4v9Hq1TDZrixxVi1IfQmUAIGlQTAAmZqortaAjqZzAoRBfrtU9UhMPg7akvbIf44NXbhkHWyKJH6icnYHeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:28:03.050788Z","bundle_sha256":"715c32b32ad5c8146906181c0964f94f80501af12f2a2b16e29e161683e27fa7"}}