{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HYM2XN736BOTSGVCR5X3VZ6DYO","short_pith_number":"pith:HYM2XN73","canonical_record":{"source":{"id":"1410.5702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"135f750ae0e28ede0247522fa165aebb488713abb3a9be5f3a03e44273e63a12","abstract_canon_sha256":"994a2b32bea0564ba882df466bf43f5dd392092f2ec4396f58b47c39ba6d009f"},"schema_version":"1.0"},"canonical_sha256":"3e19abb7fbf05d391aa28f6fbae7c3c388369b85715f79fb72f1a9fe533a6882","source":{"kind":"arxiv","id":"1410.5702","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5702","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5702v2","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5702","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"pith_short_12","alias_value":"HYM2XN736BOT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYM2XN736BOTSGVC","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYM2XN73","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HYM2XN736BOTSGVCR5X3VZ6DYO","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"135f750ae0e28ede0247522fa165aebb488713abb3a9be5f3a03e44273e63a12","abstract_canon_sha256":"994a2b32bea0564ba882df466bf43f5dd392092f2ec4396f58b47c39ba6d009f"},"schema_version":"1.0"},"canonical_sha256":"3e19abb7fbf05d391aa28f6fbae7c3c388369b85715f79fb72f1a9fe533a6882","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:26.662335Z","signature_b64":"ApNk9dSozOwa47YBXGdHDRPoMTkwu2+77nkygiKHJQP8ZCpY1c4gPDbhB3RLdUvyDEMLiXiO27P7sKux2OZYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e19abb7fbf05d391aa28f6fbae7c3c388369b85715f79fb72f1a9fe533a6882","last_reissued_at":"2026-05-18T01:16:26.661730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:26.661730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5702","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gr5R4KnR2Ejawex9+kW9z1Ndorhj5UJYrgenELwcNuQyl1DxwkaMjoh2b74xG3xuQGyOuDFQAmeiBtTMjasgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:59:13.449472Z"},"content_sha256":"7251bde1263db558dd42de30cd66cdd105226afdd553d2447339c3b3316c4939","schema_version":"1.0","event_id":"sha256:7251bde1263db558dd42de30cd66cdd105226afdd553d2447339c3b3316c4939"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HYM2XN736BOTSGVCR5X3VZ6DYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On rooted cluster morphisms and cluster structures in $2$-Calabi-Yau triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Zhu, Wen Chang","submitted_at":"2014-10-21T15:24:02Z","abstract_excerpt":"We study rooted cluster algebras and rooted cluster morphisms which were introduced in \\cite{ADS13} recently and cluster structures in $2$-Calabi-Yau triangulated categories. An example of rooted cluster morphism which is not ideal is given, this clarifies a doubt in \\cite{ADS13}. We introduce the notion of frozenization of a seed and show that an injective rooted cluster morphism always arises from a frozenization and a subseed. Moreover, it is a section if and only if it arises from a subseed. This answers the Problem 7.7 in \\cite{ADS13}. We prove that an inducible rooted cluster morphism is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5702","kind":"arxiv","version":2},"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":"2026-05-18T01:16:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yiofRgMkRNIAP12o2JxZR3UH9To6oRP0joJVpadm/sp+DGqBxhN+Q8QhapYYhpSH4F+mdKsa7qO+VjLdJjr9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:59:13.449813Z"},"content_sha256":"6e98bbd6489b220b9f26dbf6b5ef99f635c6c869d6a77672be4e7ae6ad07bc46","schema_version":"1.0","event_id":"sha256:6e98bbd6489b220b9f26dbf6b5ef99f635c6c869d6a77672be4e7ae6ad07bc46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYM2XN736BOTSGVCR5X3VZ6DYO/bundle.json","state_url":"https://pith.science/pith/HYM2XN736BOTSGVCR5X3VZ6DYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYM2XN736BOTSGVCR5X3VZ6DYO/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":"2026-06-25T11:59:13Z","links":{"resolver":"https://pith.science/pith/HYM2XN736BOTSGVCR5X3VZ6DYO","bundle":"https://pith.science/pith/HYM2XN736BOTSGVCR5X3VZ6DYO/bundle.json","state":"https://pith.science/pith/HYM2XN736BOTSGVCR5X3VZ6DYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYM2XN736BOTSGVCR5X3VZ6DYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HYM2XN736BOTSGVCR5X3VZ6DYO","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":"994a2b32bea0564ba882df466bf43f5dd392092f2ec4396f58b47c39ba6d009f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:24:02Z","title_canon_sha256":"135f750ae0e28ede0247522fa165aebb488713abb3a9be5f3a03e44273e63a12"},"schema_version":"1.0","source":{"id":"1410.5702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5702","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5702v2","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5702","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"pith_short_12","alias_value":"HYM2XN736BOT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYM2XN736BOTSGVC","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYM2XN73","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:6e98bbd6489b220b9f26dbf6b5ef99f635c6c869d6a77672be4e7ae6ad07bc46","target":"graph","created_at":"2026-05-18T01:16:26Z","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 rooted cluster algebras and rooted cluster morphisms which were introduced in \\cite{ADS13} recently and cluster structures in $2$-Calabi-Yau triangulated categories. An example of rooted cluster morphism which is not ideal is given, this clarifies a doubt in \\cite{ADS13}. We introduce the notion of frozenization of a seed and show that an injective rooted cluster morphism always arises from a frozenization and a subseed. Moreover, it is a section if and only if it arises from a subseed. This answers the Problem 7.7 in \\cite{ADS13}. We prove that an inducible rooted cluster morphism is","authors_text":"Bin Zhu, Wen Chang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:24:02Z","title":"On rooted cluster morphisms and cluster structures in $2$-Calabi-Yau triangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5702","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":"sha256:7251bde1263db558dd42de30cd66cdd105226afdd553d2447339c3b3316c4939","target":"record","created_at":"2026-05-18T01:16:26Z","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":"994a2b32bea0564ba882df466bf43f5dd392092f2ec4396f58b47c39ba6d009f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-21T15:24:02Z","title_canon_sha256":"135f750ae0e28ede0247522fa165aebb488713abb3a9be5f3a03e44273e63a12"},"schema_version":"1.0","source":{"id":"1410.5702","kind":"arxiv","version":2}},"canonical_sha256":"3e19abb7fbf05d391aa28f6fbae7c3c388369b85715f79fb72f1a9fe533a6882","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e19abb7fbf05d391aa28f6fbae7c3c388369b85715f79fb72f1a9fe533a6882","first_computed_at":"2026-05-18T01:16:26.661730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:26.661730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ApNk9dSozOwa47YBXGdHDRPoMTkwu2+77nkygiKHJQP8ZCpY1c4gPDbhB3RLdUvyDEMLiXiO27P7sKux2OZYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:26.662335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7251bde1263db558dd42de30cd66cdd105226afdd553d2447339c3b3316c4939","sha256:6e98bbd6489b220b9f26dbf6b5ef99f635c6c869d6a77672be4e7ae6ad07bc46"],"state_sha256":"1a86f42ea880f9868821016b67b43ed0dd067c13a01a49f9e4ac0129812d67d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbB19RvH9ZIEN8XEUu1m7UQ4MI+YPzQb6Sw2Y/w7M52AsWpqiTrr6rjHoxi86g/YEPtccFRrukuUUQ574XgoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:59:13.451881Z","bundle_sha256":"dfcdeb77e6322cb94807dd5dfac609e563fb7f91731df7d906ed088793b7d112"}}