{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WAISE3OETOXD6K4RLQZKWICUVY","short_pith_number":"pith:WAISE3OE","canonical_record":{"source":{"id":"1903.01636","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-05T02:52:23Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"cd9dfa8b9aa6db1db8ea9c91c2e51841e09635af4bfb025c2a9866ab1bc403c0","abstract_canon_sha256":"5e456172bd9a11d72ffe952b157f22246f9bd784b746d4750972cbe7e4574512"},"schema_version":"1.0"},"canonical_sha256":"b011226dc49bae3f2b915c32ab2054ae173ff34e505f57a200a88f700e00b743","source":{"kind":"arxiv","id":"1903.01636","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01636","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01636v3","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01636","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"WAISE3OETOXD","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_16","alias_value":"WAISE3OETOXD6K4R","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_8","alias_value":"WAISE3OE","created_at":"2026-07-05T04:15:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WAISE3OETOXD6K4RLQZKWICUVY","target":"record","payload":{"canonical_record":{"source":{"id":"1903.01636","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-05T02:52:23Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"cd9dfa8b9aa6db1db8ea9c91c2e51841e09635af4bfb025c2a9866ab1bc403c0","abstract_canon_sha256":"5e456172bd9a11d72ffe952b157f22246f9bd784b746d4750972cbe7e4574512"},"schema_version":"1.0"},"canonical_sha256":"b011226dc49bae3f2b915c32ab2054ae173ff34e505f57a200a88f700e00b743","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:15:06.150598Z","signature_b64":"qVOIopcHrRjOspMoOfwu4LJhBVln+Ing0coI1XxaDcaoN9AFu4A9qB40WlAMMVFECHJqzz6j4P1S4U8CWjfTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b011226dc49bae3f2b915c32ab2054ae173ff34e505f57a200a88f700e00b743","last_reissued_at":"2026-07-05T04:15:06.150108Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:15:06.150108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.01636","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:15:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W/avgpdT7SeEOXdagsCesdZpJHOz27FDkgEmp1kIV9F4mofiWgkN44AATAFIhO44tv8jwohlx7VUE/TkRqMbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:53:16.749119Z"},"content_sha256":"fbb7ea9fa05f5453be25d5c71feab5e6c5ae6747674c4ab37a8abdd71f4be0e2","schema_version":"1.0","event_id":"sha256:fbb7ea9fa05f5453be25d5c71feab5e6c5ae6747674c4ab37a8abdd71f4be0e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WAISE3OETOXD6K4RLQZKWICUVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations of Dimer Models","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Yusuke Nakajima","submitted_at":"2019-03-05T02:52:23Z","abstract_excerpt":"The combinatorial mutation of polygons, which transforms a given lattice polygon into another one, is an important operation to understand mirror partners for two-dimensional Fano manifolds, and the mutation-equivalent polygons give ${\\mathbb Q}$-Gorenstein deformation-equivalent toric varieties. On the other hand, for a dimer model, which is a bipartite graph described on the real two-torus, one can assign a lattice polygon called the perfect matching polygon. It is known that for each lattice polygon $P$ there exists a dimer model having $P$ as the perfect matching polygon and satisfying cer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01636","kind":"arxiv","version":3},"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/1903.01636/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":"2026-07-05T04:15:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zbAtlNvzv6yLuWLm3SFJjm07LMeFdTGCA9o+lO+FfmtB1nZrEpDmTsSabuBaW/bU4eDls7veyA/nippksm8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:53:16.749611Z"},"content_sha256":"a8fe2df1a2eaf323d4a7fb57a7e852ffb1bbe5d007634261ff90dbb9bcb2afde","schema_version":"1.0","event_id":"sha256:a8fe2df1a2eaf323d4a7fb57a7e852ffb1bbe5d007634261ff90dbb9bcb2afde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAISE3OETOXD6K4RLQZKWICUVY/bundle.json","state_url":"https://pith.science/pith/WAISE3OETOXD6K4RLQZKWICUVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAISE3OETOXD6K4RLQZKWICUVY/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":"2026-08-22T14:53:16Z","links":{"resolver":"https://pith.science/pith/WAISE3OETOXD6K4RLQZKWICUVY","bundle":"https://pith.science/pith/WAISE3OETOXD6K4RLQZKWICUVY/bundle.json","state":"https://pith.science/pith/WAISE3OETOXD6K4RLQZKWICUVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAISE3OETOXD6K4RLQZKWICUVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WAISE3OETOXD6K4RLQZKWICUVY","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":"5e456172bd9a11d72ffe952b157f22246f9bd784b746d4750972cbe7e4574512","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-05T02:52:23Z","title_canon_sha256":"cd9dfa8b9aa6db1db8ea9c91c2e51841e09635af4bfb025c2a9866ab1bc403c0"},"schema_version":"1.0","source":{"id":"1903.01636","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01636","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01636v3","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01636","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"WAISE3OETOXD","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_16","alias_value":"WAISE3OETOXD6K4R","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_8","alias_value":"WAISE3OE","created_at":"2026-07-05T04:15:06Z"}],"graph_snapshots":[{"event_id":"sha256:a8fe2df1a2eaf323d4a7fb57a7e852ffb1bbe5d007634261ff90dbb9bcb2afde","target":"graph","created_at":"2026-07-05T04:15:06Z","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/1903.01636/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The combinatorial mutation of polygons, which transforms a given lattice polygon into another one, is an important operation to understand mirror partners for two-dimensional Fano manifolds, and the mutation-equivalent polygons give ${\\mathbb Q}$-Gorenstein deformation-equivalent toric varieties. On the other hand, for a dimer model, which is a bipartite graph described on the real two-torus, one can assign a lattice polygon called the perfect matching polygon. It is known that for each lattice polygon $P$ there exists a dimer model having $P$ as the perfect matching polygon and satisfying cer","authors_text":"Akihiro Higashitani, Yusuke Nakajima","cross_cats":["math-ph","math.AG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-05T02:52:23Z","title":"Deformations of Dimer Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01636","kind":"arxiv","version":3},"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:fbb7ea9fa05f5453be25d5c71feab5e6c5ae6747674c4ab37a8abdd71f4be0e2","target":"record","created_at":"2026-07-05T04:15:06Z","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":"5e456172bd9a11d72ffe952b157f22246f9bd784b746d4750972cbe7e4574512","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-05T02:52:23Z","title_canon_sha256":"cd9dfa8b9aa6db1db8ea9c91c2e51841e09635af4bfb025c2a9866ab1bc403c0"},"schema_version":"1.0","source":{"id":"1903.01636","kind":"arxiv","version":3}},"canonical_sha256":"b011226dc49bae3f2b915c32ab2054ae173ff34e505f57a200a88f700e00b743","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b011226dc49bae3f2b915c32ab2054ae173ff34e505f57a200a88f700e00b743","first_computed_at":"2026-07-05T04:15:06.150108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:15:06.150108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qVOIopcHrRjOspMoOfwu4LJhBVln+Ing0coI1XxaDcaoN9AFu4A9qB40WlAMMVFECHJqzz6j4P1S4U8CWjfTDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:15:06.150598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01636","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbb7ea9fa05f5453be25d5c71feab5e6c5ae6747674c4ab37a8abdd71f4be0e2","sha256:a8fe2df1a2eaf323d4a7fb57a7e852ffb1bbe5d007634261ff90dbb9bcb2afde"],"state_sha256":"88af77310bc39d3c1f2c6f235253f9e226876acec22dfc5a7139b41eb9d0ada3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/o7NH/i7EZAZPNxrII1CI0TQBOE1FVxBP7pHEm+ulbR0WUoPS7V75XbcG0HQ1EHF58DpUT9N6nyI70LwhRNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T14:53:16.753081Z","bundle_sha256":"9af0cb5fddf2d13c51706699bba257bbc254f7a46288c60d21e8955473337994"}}