{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:7YCGG2JAKNO3EZQOWEZB5JDFXK","short_pith_number":"pith:7YCGG2JA","canonical_record":{"source":{"id":"2311.06033","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-10T12:40:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4b3399789c501e997d6fecf463df428a60c425d56c9e57f33f84c640bc5b41cb","abstract_canon_sha256":"95902c740a765b3f0f2415ace261e1f2b457a4dfa7bb0bc254973a2c638330a0"},"schema_version":"1.0"},"canonical_sha256":"fe04636920535db2660eb1321ea465ba8e6fc0c9b010ece1638cd68853090ab8","source":{"kind":"arxiv","id":"2311.06033","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06033","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06033v4","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06033","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"7YCGG2JAKNO3","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"pith_short_16","alias_value":"7YCGG2JAKNO3EZQO","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"pith_short_8","alias_value":"7YCGG2JA","created_at":"2026-07-05T08:09:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:7YCGG2JAKNO3EZQOWEZB5JDFXK","target":"record","payload":{"canonical_record":{"source":{"id":"2311.06033","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-10T12:40:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4b3399789c501e997d6fecf463df428a60c425d56c9e57f33f84c640bc5b41cb","abstract_canon_sha256":"95902c740a765b3f0f2415ace261e1f2b457a4dfa7bb0bc254973a2c638330a0"},"schema_version":"1.0"},"canonical_sha256":"fe04636920535db2660eb1321ea465ba8e6fc0c9b010ece1638cd68853090ab8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:09:25.951695Z","signature_b64":"n52872OuPALrAC7BQicWTvlP9Hm29URthyCFYzQzLnu+MgPtnlQVmhfodW5Pl142IWuYAEBNcnY/lHoG8mh9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe04636920535db2660eb1321ea465ba8e6fc0c9b010ece1638cd68853090ab8","last_reissued_at":"2026-07-05T08:09:25.951187Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:09:25.951187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.06033","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/8QVgYIqfJuA2uUTyHkA/zQyaqPtZ95Py2/4R93JBPQxcYPIcIpOiPWO6VFh2DdywMA4NFSnH9pd9qJPtaAyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:57:11.628945Z"},"content_sha256":"71a2bffd249d0f309c737a35d4ab61c884aed563ad752471e4788b5c9bc4089e","schema_version":"1.0","event_id":"sha256:71a2bffd249d0f309c737a35d4ab61c884aed563ad752471e4788b5c9bc4089e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:7YCGG2JAKNO3EZQOWEZB5JDFXK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Posets for $F$-polynomials in cluster algebras from surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Nathan Reading, Sibylle Schroll, Vincent Pilaud","submitted_at":"2023-11-10T12:40:09Z","abstract_excerpt":"We prove a simple formula for arbitrary cluster variables in the marked surfaces model. As part of the formula, we associate a labeled poset to each tagged arc, such that the associated $F$-polynomial is a weighted sum of order ideals. Each element of the poset has a weight, and the weight of an ideal is the product of the weights of the elements of the ideal. In the unpunctured case, the weight on each element is a single $\\hat{y}_i$, in the usual sense of principal coefficients. In the presence of punctures, some elements may have weights of the form $\\hat{y}_i/\\hat{y}_j$. Our search for suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06033","kind":"arxiv","version":4},"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/2311.06033/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":"2026-07-05T08:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ioim2oP7LodiyqHCd/ZKxDyaeqB7cYHo0KdKbB5TJ/WlZ9WC5bMcC4N5W+ylFiHZ1kNH1VrMziTVHtSUe7K2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:57:11.629846Z"},"content_sha256":"394b96717b49cc7ba888c743130510c8aeb9ffce4a75b86479f8b104e7a12568","schema_version":"1.0","event_id":"sha256:394b96717b49cc7ba888c743130510c8aeb9ffce4a75b86479f8b104e7a12568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK/bundle.json","state_url":"https://pith.science/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK/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":"2026-08-14T23:57:11Z","links":{"resolver":"https://pith.science/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK","bundle":"https://pith.science/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK/bundle.json","state":"https://pith.science/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7YCGG2JAKNO3EZQOWEZB5JDFXK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7YCGG2JAKNO3EZQOWEZB5JDFXK","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":"95902c740a765b3f0f2415ace261e1f2b457a4dfa7bb0bc254973a2c638330a0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-10T12:40:09Z","title_canon_sha256":"4b3399789c501e997d6fecf463df428a60c425d56c9e57f33f84c640bc5b41cb"},"schema_version":"1.0","source":{"id":"2311.06033","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06033","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06033v4","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06033","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"7YCGG2JAKNO3","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"pith_short_16","alias_value":"7YCGG2JAKNO3EZQO","created_at":"2026-07-05T08:09:25Z"},{"alias_kind":"pith_short_8","alias_value":"7YCGG2JA","created_at":"2026-07-05T08:09:25Z"}],"graph_snapshots":[{"event_id":"sha256:394b96717b49cc7ba888c743130510c8aeb9ffce4a75b86479f8b104e7a12568","target":"graph","created_at":"2026-07-05T08:09:25Z","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/2311.06033/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a simple formula for arbitrary cluster variables in the marked surfaces model. As part of the formula, we associate a labeled poset to each tagged arc, such that the associated $F$-polynomial is a weighted sum of order ideals. Each element of the poset has a weight, and the weight of an ideal is the product of the weights of the elements of the ideal. In the unpunctured case, the weight on each element is a single $\\hat{y}_i$, in the usual sense of principal coefficients. In the presence of punctures, some elements may have weights of the form $\\hat{y}_i/\\hat{y}_j$. Our search for suc","authors_text":"Nathan Reading, Sibylle Schroll, Vincent Pilaud","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-10T12:40:09Z","title":"Posets for $F$-polynomials in cluster algebras from surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06033","kind":"arxiv","version":4},"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":"sha256:71a2bffd249d0f309c737a35d4ab61c884aed563ad752471e4788b5c9bc4089e","target":"record","created_at":"2026-07-05T08:09:25Z","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":"95902c740a765b3f0f2415ace261e1f2b457a4dfa7bb0bc254973a2c638330a0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-10T12:40:09Z","title_canon_sha256":"4b3399789c501e997d6fecf463df428a60c425d56c9e57f33f84c640bc5b41cb"},"schema_version":"1.0","source":{"id":"2311.06033","kind":"arxiv","version":4}},"canonical_sha256":"fe04636920535db2660eb1321ea465ba8e6fc0c9b010ece1638cd68853090ab8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe04636920535db2660eb1321ea465ba8e6fc0c9b010ece1638cd68853090ab8","first_computed_at":"2026-07-05T08:09:25.951187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:09:25.951187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n52872OuPALrAC7BQicWTvlP9Hm29URthyCFYzQzLnu+MgPtnlQVmhfodW5Pl142IWuYAEBNcnY/lHoG8mh9DA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:09:25.951695Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.06033","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71a2bffd249d0f309c737a35d4ab61c884aed563ad752471e4788b5c9bc4089e","sha256:394b96717b49cc7ba888c743130510c8aeb9ffce4a75b86479f8b104e7a12568"],"state_sha256":"73b488a246b36298f18d58becf367881c2a17e8b9c4f3a56d568c14a9122701c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7szfbav4i9oxMrdXWIZ3AVMFSOIrhap7BtwMqCI8RUoI5D+G0OxbcMW7b1BZqK6DGkloyJiEpPN0SzDVtSRdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T23:57:11.635576Z","bundle_sha256":"a560f9d739c0497d275bb05644fa93c665caa0b399991e075e62d7c96f3cf312"}}