{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IURCYEMUHONXOW6P2JAW3X36CQ","short_pith_number":"pith:IURCYEMU","canonical_record":{"source":{"id":"1301.0316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-02T21:00:00Z","cross_cats_sorted":["math-ph","math.AG","math.CO","math.MP"],"title_canon_sha256":"78916436960c02d9f050e4a89b811e44e82df2dea9558ab9b93ffecad95dd94a","abstract_canon_sha256":"8e8af7fbf1521871c75641d036d006e6067aa4f2b2f6e61cc251ad73d6bc6bc7"},"schema_version":"1.0"},"canonical_sha256":"45222c11943b9b775bcfd2416ddf7e14162c61db1b1886fb63ea0327fa4f3b5c","source":{"kind":"arxiv","id":"1301.0316","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0316","created_at":"2026-05-18T01:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0316v2","created_at":"2026-05-18T01:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0316","created_at":"2026-05-18T01:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"IURCYEMUHONX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IURCYEMUHONXOW6P","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IURCYEMU","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IURCYEMUHONXOW6P2JAW3X36CQ","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-02T21:00:00Z","cross_cats_sorted":["math-ph","math.AG","math.CO","math.MP"],"title_canon_sha256":"78916436960c02d9f050e4a89b811e44e82df2dea9558ab9b93ffecad95dd94a","abstract_canon_sha256":"8e8af7fbf1521871c75641d036d006e6067aa4f2b2f6e61cc251ad73d6bc6bc7"},"schema_version":"1.0"},"canonical_sha256":"45222c11943b9b775bcfd2416ddf7e14162c61db1b1886fb63ea0327fa4f3b5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:22.137025Z","signature_b64":"/NesN2jeCcndtbFxWjXsWum5r46uxaIJP2VkcnSgzClN2MvdZk+FtMq5svERFPEvRgA7uH+oSzRoqdFLAXeiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45222c11943b9b775bcfd2416ddf7e14162c61db1b1886fb63ea0327fa4f3b5c","last_reissued_at":"2026-05-18T01:52:22.136608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:22.136608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0316","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":"2026-05-18T01:52:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MdfJRqBcPLJ4IU3RLI6L/Ikt0IMoAKNLd6k6BD+YTmezPziIs+waM+7amA3VTad8Is7nFTA0gRt7VU/3rI/PCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:52:24.842418Z"},"content_sha256":"0c4162cf52eb94dbf284c67b3ec09617d277010c2a786d0aa34db75965c2258d","schema_version":"1.0","event_id":"sha256:0c4162cf52eb94dbf284c67b3ec09617d277010c2a786d0aa34db75965c2258d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IURCYEMUHONXOW6P2JAW3X36CQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster Transformations from Bipartite Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.CO","math.MP"],"primary_cat":"hep-th","authors_text":"Sebastian Franco","submitted_at":"2013-01-02T21:00:00Z","abstract_excerpt":"Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph. In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs. For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian. This represents a new addition to the list of combinatorial objects for the Grassmannian, such as matc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0316","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":"2026-05-18T01:52:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PD3LNeNElRAsatfEqjY4HWabOqDEe+ov/48ng4RfA+UbHrOOR7bM6QBZHehWxGD4iRaZiOl+RwcJmimGxSFTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:52:24.842878Z"},"content_sha256":"56c1b7b2c1d8eb5be49a219cbff95517892cb76c2c6f5c8d0600bd65bb9de294","schema_version":"1.0","event_id":"sha256:56c1b7b2c1d8eb5be49a219cbff95517892cb76c2c6f5c8d0600bd65bb9de294"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IURCYEMUHONXOW6P2JAW3X36CQ/bundle.json","state_url":"https://pith.science/pith/IURCYEMUHONXOW6P2JAW3X36CQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IURCYEMUHONXOW6P2JAW3X36CQ/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":"2026-08-04T06:52:24Z","links":{"resolver":"https://pith.science/pith/IURCYEMUHONXOW6P2JAW3X36CQ","bundle":"https://pith.science/pith/IURCYEMUHONXOW6P2JAW3X36CQ/bundle.json","state":"https://pith.science/pith/IURCYEMUHONXOW6P2JAW3X36CQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IURCYEMUHONXOW6P2JAW3X36CQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IURCYEMUHONXOW6P2JAW3X36CQ","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":"8e8af7fbf1521871c75641d036d006e6067aa4f2b2f6e61cc251ad73d6bc6bc7","cross_cats_sorted":["math-ph","math.AG","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-02T21:00:00Z","title_canon_sha256":"78916436960c02d9f050e4a89b811e44e82df2dea9558ab9b93ffecad95dd94a"},"schema_version":"1.0","source":{"id":"1301.0316","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0316","created_at":"2026-05-18T01:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0316v2","created_at":"2026-05-18T01:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0316","created_at":"2026-05-18T01:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"IURCYEMUHONX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IURCYEMUHONXOW6P","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IURCYEMU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:56c1b7b2c1d8eb5be49a219cbff95517892cb76c2c6f5c8d0600bd65bb9de294","target":"graph","created_at":"2026-05-18T01:52:22Z","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":"Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph. In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs. For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian. This represents a new addition to the list of combinatorial objects for the Grassmannian, such as matc","authors_text":"Sebastian Franco","cross_cats":["math-ph","math.AG","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-02T21:00:00Z","title":"Cluster Transformations from Bipartite Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0316","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":"sha256:0c4162cf52eb94dbf284c67b3ec09617d277010c2a786d0aa34db75965c2258d","target":"record","created_at":"2026-05-18T01:52:22Z","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":"8e8af7fbf1521871c75641d036d006e6067aa4f2b2f6e61cc251ad73d6bc6bc7","cross_cats_sorted":["math-ph","math.AG","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-02T21:00:00Z","title_canon_sha256":"78916436960c02d9f050e4a89b811e44e82df2dea9558ab9b93ffecad95dd94a"},"schema_version":"1.0","source":{"id":"1301.0316","kind":"arxiv","version":2}},"canonical_sha256":"45222c11943b9b775bcfd2416ddf7e14162c61db1b1886fb63ea0327fa4f3b5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45222c11943b9b775bcfd2416ddf7e14162c61db1b1886fb63ea0327fa4f3b5c","first_computed_at":"2026-05-18T01:52:22.136608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:22.136608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/NesN2jeCcndtbFxWjXsWum5r46uxaIJP2VkcnSgzClN2MvdZk+FtMq5svERFPEvRgA7uH+oSzRoqdFLAXeiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:22.137025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0316","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c4162cf52eb94dbf284c67b3ec09617d277010c2a786d0aa34db75965c2258d","sha256:56c1b7b2c1d8eb5be49a219cbff95517892cb76c2c6f5c8d0600bd65bb9de294"],"state_sha256":"a242ebb6a6e73103c662693955f8ee44ce3f0eae84663b1fcf9b7a415022f87f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8xDVJU0SycX5771vtDFXZBV8pgYkuHmR9Q89wG+CkuQDW0NBIGu7IyWZSh7a2TogJFHUqSukcGOuIQodBQ4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:52:24.846317Z","bundle_sha256":"aed59f5080e4896f8dcfa80cab48458b916b9fa7a8de2b9c331309136acebf97"}}