{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2YHYGYUV6EFP2FQEOVQCDAYL4R","short_pith_number":"pith:2YHYGYUV","canonical_record":{"source":{"id":"1203.1222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-06T15:11:59Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9357a6833350d44327c09e7ef19b93d9ee269697b44a7e971e7d2d5be1eeafd3","abstract_canon_sha256":"41486372d62d87c2d68b84349dfec90aadec8004e8998c4db6c448df2b1572f2"},"schema_version":"1.0"},"canonical_sha256":"d60f836295f10afd1604756021830be454d1a8a43133e1faaf9ccccd5705940c","source":{"kind":"arxiv","id":"1203.1222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1222","created_at":"2026-05-18T04:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1222v1","created_at":"2026-05-18T04:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1222","created_at":"2026-05-18T04:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"2YHYGYUV6EFP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2YHYGYUV6EFP2FQE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2YHYGYUV","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2YHYGYUV6EFP2FQEOVQCDAYL4R","target":"record","payload":{"canonical_record":{"source":{"id":"1203.1222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-06T15:11:59Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9357a6833350d44327c09e7ef19b93d9ee269697b44a7e971e7d2d5be1eeafd3","abstract_canon_sha256":"41486372d62d87c2d68b84349dfec90aadec8004e8998c4db6c448df2b1572f2"},"schema_version":"1.0"},"canonical_sha256":"d60f836295f10afd1604756021830be454d1a8a43133e1faaf9ccccd5705940c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:40.045968Z","signature_b64":"ydcIMArVkcXX4ZRaNZsx53N90/fIV81lYUv8rUxTiRYAMHQD9bnVkowX0TMHJJBaf/jhjNN0RPExjQl+8cLdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d60f836295f10afd1604756021830be454d1a8a43133e1faaf9ccccd5705940c","last_reissued_at":"2026-05-18T04:00:40.045425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:40.045425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.1222","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":"2026-05-18T04:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jCG1gun87M/RSI7BKWo8C/R6tCXIL9QExJ3SzAjPyrsXQEl2rhoKAnZEri4zCsLPSwwePLYpaTrvaKXQlcOwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:02:59.687131Z"},"content_sha256":"e26ba602a431c5eb7c9ab785971fd7869bed10a3f74910890fb13cabdf9a0a38","schema_version":"1.0","event_id":"sha256:e26ba602a431c5eb7c9ab785971fd7869bed10a3f74910890fb13cabdf9a0a38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2YHYGYUV6EFP2FQEOVQCDAYL4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finiteness of commutable maps of bounded degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Chong Gyu Lee, Hexi Ye","submitted_at":"2012-03-06T15:11:59Z","abstract_excerpt":"In this paper, we study the relation between two dynamical systems (V,f) and (V,g) with f. g = g . f. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Pre(f) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1222","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":"2026-05-18T04:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JhmAt0Co+mkn/Wg3gacey30hbZdJpP39/G5eHJ186XNuas6K1rzXNgZ6LDwgYyHxEMrPW4F4HYnZUDW1PtGKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:02:59.687527Z"},"content_sha256":"bd3aae7955c6b5c1456209dbf6fef1567cc419298465a5cbc9acc01f6810b844","schema_version":"1.0","event_id":"sha256:bd3aae7955c6b5c1456209dbf6fef1567cc419298465a5cbc9acc01f6810b844"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R/bundle.json","state_url":"https://pith.science/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R/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":"2026-06-20T10:02:59Z","links":{"resolver":"https://pith.science/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R","bundle":"https://pith.science/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R/bundle.json","state":"https://pith.science/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YHYGYUV6EFP2FQEOVQCDAYL4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2YHYGYUV6EFP2FQEOVQCDAYL4R","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":"41486372d62d87c2d68b84349dfec90aadec8004e8998c4db6c448df2b1572f2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-06T15:11:59Z","title_canon_sha256":"9357a6833350d44327c09e7ef19b93d9ee269697b44a7e971e7d2d5be1eeafd3"},"schema_version":"1.0","source":{"id":"1203.1222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1222","created_at":"2026-05-18T04:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1222v1","created_at":"2026-05-18T04:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1222","created_at":"2026-05-18T04:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"2YHYGYUV6EFP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2YHYGYUV6EFP2FQE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2YHYGYUV","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:bd3aae7955c6b5c1456209dbf6fef1567cc419298465a5cbc9acc01f6810b844","target":"graph","created_at":"2026-05-18T04:00:40Z","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":"In this paper, we study the relation between two dynamical systems (V,f) and (V,g) with f. g = g . f. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Pre(f) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f.","authors_text":"Chong Gyu Lee, Hexi Ye","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-06T15:11:59Z","title":"Finiteness of commutable maps of bounded degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1222","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:e26ba602a431c5eb7c9ab785971fd7869bed10a3f74910890fb13cabdf9a0a38","target":"record","created_at":"2026-05-18T04:00:40Z","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":"41486372d62d87c2d68b84349dfec90aadec8004e8998c4db6c448df2b1572f2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-06T15:11:59Z","title_canon_sha256":"9357a6833350d44327c09e7ef19b93d9ee269697b44a7e971e7d2d5be1eeafd3"},"schema_version":"1.0","source":{"id":"1203.1222","kind":"arxiv","version":1}},"canonical_sha256":"d60f836295f10afd1604756021830be454d1a8a43133e1faaf9ccccd5705940c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d60f836295f10afd1604756021830be454d1a8a43133e1faaf9ccccd5705940c","first_computed_at":"2026-05-18T04:00:40.045425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:40.045425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ydcIMArVkcXX4ZRaNZsx53N90/fIV81lYUv8rUxTiRYAMHQD9bnVkowX0TMHJJBaf/jhjNN0RPExjQl+8cLdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:40.045968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e26ba602a431c5eb7c9ab785971fd7869bed10a3f74910890fb13cabdf9a0a38","sha256:bd3aae7955c6b5c1456209dbf6fef1567cc419298465a5cbc9acc01f6810b844"],"state_sha256":"402bed8bf1ee706868ef131db6bee2a58a4a6417e81d0538f49bb2adcb89885a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bUMHKXBdxs/blOga0nw2ushcU1DOLXbn7JLo/CDdT7PlcdRVXjcwO44YJLrJukw2qGfJyZTVrKBtQvwtSc6aBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:02:59.689433Z","bundle_sha256":"f89414910347b4f29773b1c62c07eb3a4d6e6a2ec9354a1b5d3a802b036f1495"}}