{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:65CKGMKOD2MUVPWPBUQEG2Y3L4","short_pith_number":"pith:65CKGMKO","canonical_record":{"source":{"id":"1307.2494","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-09T15:27:48Z","cross_cats_sorted":["math.GT","math.MP"],"title_canon_sha256":"880c507d24c8b1770484b67d1405a811d0b444dac9c770be1f79309640f8b606","abstract_canon_sha256":"f262aedc9c3d8adc02da214d06900498f291f85c052068668d9eadd8886c5e35"},"schema_version":"1.0"},"canonical_sha256":"f744a3314e1e994abecf0d20436b1b5f0f139486dc61d064b18aeea814b64c9f","source":{"kind":"arxiv","id":"1307.2494","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2494","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2494v4","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2494","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"65CKGMKOD2MU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"65CKGMKOD2MUVPWP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"65CKGMKO","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:65CKGMKOD2MUVPWPBUQEG2Y3L4","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2494","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-09T15:27:48Z","cross_cats_sorted":["math.GT","math.MP"],"title_canon_sha256":"880c507d24c8b1770484b67d1405a811d0b444dac9c770be1f79309640f8b606","abstract_canon_sha256":"f262aedc9c3d8adc02da214d06900498f291f85c052068668d9eadd8886c5e35"},"schema_version":"1.0"},"canonical_sha256":"f744a3314e1e994abecf0d20436b1b5f0f139486dc61d064b18aeea814b64c9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:16.363462Z","signature_b64":"IGbJZSFBeHY+gw7tQHff3Y8qDq6kL0zTDSul1+CMsvDhSCTiZSc85GDScxtu0ncGE/+tZy1+KXtLPMscpCNkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f744a3314e1e994abecf0d20436b1b5f0f139486dc61d064b18aeea814b64c9f","last_reissued_at":"2026-05-18T01:01:16.362803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:16.362803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2494","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":"2026-05-18T01:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0NpMjVwcqtnP1YS3PlYIkt0lxe7TqiSI2JIdFX4wOTW6QAvZREVNf+uAHdJcfzP64OB1qIFxwhpiXwUzdswAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:39:33.837299Z"},"content_sha256":"143549ca98acb4ad88d93172890a88b75215e9690be5cc6d18eab42878f19ed7","schema_version":"1.0","event_id":"sha256:143549ca98acb4ad88d93172890a88b75215e9690be5cc6d18eab42878f19ed7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:65CKGMKOD2MUVPWPBUQEG2Y3L4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kac-Ward operators, Kasteleyn operators, and s-holomorphicity on arbitrary surface graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"David Cimasoni","submitted_at":"2013-07-09T15:27:48Z","abstract_excerpt":"The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we define a generalized notion of s-holomorphicity for functions on arbitrary weighted surface graphs. We then give three criteria for s-holomorphicity involving the Kac-Ward, Kasteleyn, and discrete Dirac operators, respectively. Also, we show that some crucial results known to hold in the planar isoradial case extend to this general setting: in particular,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2494","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":""},"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":"2026-05-18T01:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJlhmQkih2jLtGWDfqKAvMhJiViYOxYMOtVWf/GhlqVF+7tqyZ9+MBc6xHzwgdNAUGeK5icg/GpvfUZqjEQrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:39:33.837664Z"},"content_sha256":"4eaed3817b3bcca8c691caa28a86db8a10aff90474cc8c2500d4b236e80559b1","schema_version":"1.0","event_id":"sha256:4eaed3817b3bcca8c691caa28a86db8a10aff90474cc8c2500d4b236e80559b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4/bundle.json","state_url":"https://pith.science/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4/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":"2026-06-28T10:39:33Z","links":{"resolver":"https://pith.science/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4","bundle":"https://pith.science/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4/bundle.json","state":"https://pith.science/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/65CKGMKOD2MUVPWPBUQEG2Y3L4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:65CKGMKOD2MUVPWPBUQEG2Y3L4","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":"f262aedc9c3d8adc02da214d06900498f291f85c052068668d9eadd8886c5e35","cross_cats_sorted":["math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-09T15:27:48Z","title_canon_sha256":"880c507d24c8b1770484b67d1405a811d0b444dac9c770be1f79309640f8b606"},"schema_version":"1.0","source":{"id":"1307.2494","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2494","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2494v4","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2494","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"65CKGMKOD2MU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"65CKGMKOD2MUVPWP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"65CKGMKO","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:4eaed3817b3bcca8c691caa28a86db8a10aff90474cc8c2500d4b236e80559b1","target":"graph","created_at":"2026-05-18T01:01:16Z","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":"The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we define a generalized notion of s-holomorphicity for functions on arbitrary weighted surface graphs. We then give three criteria for s-holomorphicity involving the Kac-Ward, Kasteleyn, and discrete Dirac operators, respectively. Also, we show that some crucial results known to hold in the planar isoradial case extend to this general setting: in particular,","authors_text":"David Cimasoni","cross_cats":["math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-09T15:27:48Z","title":"Kac-Ward operators, Kasteleyn operators, and s-holomorphicity on arbitrary surface graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2494","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":"sha256:143549ca98acb4ad88d93172890a88b75215e9690be5cc6d18eab42878f19ed7","target":"record","created_at":"2026-05-18T01:01:16Z","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":"f262aedc9c3d8adc02da214d06900498f291f85c052068668d9eadd8886c5e35","cross_cats_sorted":["math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-09T15:27:48Z","title_canon_sha256":"880c507d24c8b1770484b67d1405a811d0b444dac9c770be1f79309640f8b606"},"schema_version":"1.0","source":{"id":"1307.2494","kind":"arxiv","version":4}},"canonical_sha256":"f744a3314e1e994abecf0d20436b1b5f0f139486dc61d064b18aeea814b64c9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f744a3314e1e994abecf0d20436b1b5f0f139486dc61d064b18aeea814b64c9f","first_computed_at":"2026-05-18T01:01:16.362803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:16.362803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGbJZSFBeHY+gw7tQHff3Y8qDq6kL0zTDSul1+CMsvDhSCTiZSc85GDScxtu0ncGE/+tZy1+KXtLPMscpCNkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:16.363462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2494","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:143549ca98acb4ad88d93172890a88b75215e9690be5cc6d18eab42878f19ed7","sha256:4eaed3817b3bcca8c691caa28a86db8a10aff90474cc8c2500d4b236e80559b1"],"state_sha256":"b4f33118c4a478441403f2c459b067b9a6db3c2d75afd638a791b9edc6601039"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pdPXnT0XtTzqTXMWHmUtfheJpju5rXT+o20GH7405hlhg076xMycUSB/4hJrxwKIAKOnwuyBHFfzGwIv7VZdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:39:33.839538Z","bundle_sha256":"27078847148d11fb3bd362149e5fc00217a6c93cdba1d30ad60c160f82b1fc07"}}