{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZEXU574EOGQ67ZUXL2NE426SO5","short_pith_number":"pith:ZEXU574E","canonical_record":{"source":{"id":"1805.00030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T18:00:05Z","cross_cats_sorted":["math.AG","math.DS","math.RT"],"title_canon_sha256":"a04d3f81b8b606d08f28f1c4e257f59eb04939db94fbf2b563bb01b5b205d113","abstract_canon_sha256":"41d848c5072b5941a07ccf628bec2668579c11a8a08eaabfed74ed5c40e92fcb"},"schema_version":"1.0"},"canonical_sha256":"c92f4eff8471a1efe6975e9a4e6bd27775bfa08c0909378b47a6bb160cec4144","source":{"kind":"arxiv","id":"1805.00030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00030","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00030v2","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00030","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZEXU574EOGQ6","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZEXU574EOGQ67ZUX","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZEXU574E","created_at":"2026-07-05T00:19:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZEXU574EOGQ67ZUXL2NE426SO5","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T18:00:05Z","cross_cats_sorted":["math.AG","math.DS","math.RT"],"title_canon_sha256":"a04d3f81b8b606d08f28f1c4e257f59eb04939db94fbf2b563bb01b5b205d113","abstract_canon_sha256":"41d848c5072b5941a07ccf628bec2668579c11a8a08eaabfed74ed5c40e92fcb"},"schema_version":"1.0"},"canonical_sha256":"c92f4eff8471a1efe6975e9a4e6bd27775bfa08c0909378b47a6bb160cec4144","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:19:17.884419Z","signature_b64":"L6O5zRJ9io9m/lVt8ohxMO3YR2sqX/g7Ey51Y3YOVI/03YW5Wagp3gIkO/EQ0AvO/7b59QoNYMHexNl/Kf7TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c92f4eff8471a1efe6975e9a4e6bd27775bfa08c0909378b47a6bb160cec4144","last_reissued_at":"2026-07-05T00:19:17.883934Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:19:17.883934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00030","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":"2026-07-05T00:19:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5yz+uZM/Vfk8O4J2VecBxXolXLUXDMhQhgtdqLrOjAuOS1UG1xfDBe2s9itG6PvbFQCZwpsmJieUIWnaMXxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:23:45.810456Z"},"content_sha256":"b08762476f693500a37602141c5f4d43b674c401dd534c69d6f96b124c95ee50","schema_version":"1.0","event_id":"sha256:b08762476f693500a37602141c5f4d43b674c401dd534c69d6f96b124c95ee50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZEXU574EOGQ67ZUXL2NE426SO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster exchange groupoids and framed quadratic differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS","math.RT"],"primary_cat":"math.GT","authors_text":"Alastair King, Yu Qiu","submitted_at":"2018-04-30T18:00:05Z","abstract_excerpt":"We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is modelled on the graph of triangulations of the marked surface, we show that the universal cover of this groupoid can be constructed using the covering graph of triangulations of the surface with extra decorations.\n  This covering graph is a skeleton for a space of suitably framed quadratic differentials on the surface, which in turn models the space of Bridgelan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00030","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1805.00030/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:19:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/u/5UOLYJmCQw5Y+KXoBNJkP49dRRDLFcCR8wNLrnh4GH9cw5rQxDbENbosMPbmYa+nfKya7VQpJ8rA178h6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:23:45.811301Z"},"content_sha256":"d9aece3cb2bf110f5de47389a30d1431aec902a0f077da3047c5b57922af5cd9","schema_version":"1.0","event_id":"sha256:d9aece3cb2bf110f5de47389a30d1431aec902a0f077da3047c5b57922af5cd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEXU574EOGQ67ZUXL2NE426SO5/bundle.json","state_url":"https://pith.science/pith/ZEXU574EOGQ67ZUXL2NE426SO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEXU574EOGQ67ZUXL2NE426SO5/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":"2026-08-12T05:23:45Z","links":{"resolver":"https://pith.science/pith/ZEXU574EOGQ67ZUXL2NE426SO5","bundle":"https://pith.science/pith/ZEXU574EOGQ67ZUXL2NE426SO5/bundle.json","state":"https://pith.science/pith/ZEXU574EOGQ67ZUXL2NE426SO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEXU574EOGQ67ZUXL2NE426SO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZEXU574EOGQ67ZUXL2NE426SO5","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":"41d848c5072b5941a07ccf628bec2668579c11a8a08eaabfed74ed5c40e92fcb","cross_cats_sorted":["math.AG","math.DS","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T18:00:05Z","title_canon_sha256":"a04d3f81b8b606d08f28f1c4e257f59eb04939db94fbf2b563bb01b5b205d113"},"schema_version":"1.0","source":{"id":"1805.00030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00030","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00030v2","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00030","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZEXU574EOGQ6","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZEXU574EOGQ67ZUX","created_at":"2026-07-05T00:19:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZEXU574E","created_at":"2026-07-05T00:19:17Z"}],"graph_snapshots":[{"event_id":"sha256:d9aece3cb2bf110f5de47389a30d1431aec902a0f077da3047c5b57922af5cd9","target":"graph","created_at":"2026-07-05T00:19:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1805.00030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is modelled on the graph of triangulations of the marked surface, we show that the universal cover of this groupoid can be constructed using the covering graph of triangulations of the surface with extra decorations.\n  This covering graph is a skeleton for a space of suitably framed quadratic differentials on the surface, which in turn models the space of Bridgelan","authors_text":"Alastair King, Yu Qiu","cross_cats":["math.AG","math.DS","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T18:00:05Z","title":"Cluster exchange groupoids and framed quadratic differentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00030","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:b08762476f693500a37602141c5f4d43b674c401dd534c69d6f96b124c95ee50","target":"record","created_at":"2026-07-05T00:19:17Z","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":"41d848c5072b5941a07ccf628bec2668579c11a8a08eaabfed74ed5c40e92fcb","cross_cats_sorted":["math.AG","math.DS","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-30T18:00:05Z","title_canon_sha256":"a04d3f81b8b606d08f28f1c4e257f59eb04939db94fbf2b563bb01b5b205d113"},"schema_version":"1.0","source":{"id":"1805.00030","kind":"arxiv","version":2}},"canonical_sha256":"c92f4eff8471a1efe6975e9a4e6bd27775bfa08c0909378b47a6bb160cec4144","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c92f4eff8471a1efe6975e9a4e6bd27775bfa08c0909378b47a6bb160cec4144","first_computed_at":"2026-07-05T00:19:17.883934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:19:17.883934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L6O5zRJ9io9m/lVt8ohxMO3YR2sqX/g7Ey51Y3YOVI/03YW5Wagp3gIkO/EQ0AvO/7b59QoNYMHexNl/Kf7TAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:19:17.884419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b08762476f693500a37602141c5f4d43b674c401dd534c69d6f96b124c95ee50","sha256:d9aece3cb2bf110f5de47389a30d1431aec902a0f077da3047c5b57922af5cd9"],"state_sha256":"0a0b3eb695a37302507bc0985e6ea6a7d9abe6cc774bcd10bcaa01fc70842cef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odeXgJeYEkg/NeRCp2yaKEIFncv+aHXQX5E0KBIBK1PsZ1X1+r4ShJKWx5ZQ8hdZy3rhWD8Zt+BK0i+C4cy2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T05:23:45.816617Z","bundle_sha256":"a57a0beab031d5b1693332227d62eddda8d8e5a9af822f62c527506bf60c7793"}}