{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:FEAFRJFURI6FA3MGGZFTRCJGOE","short_pith_number":"pith:FEAFRJFU","canonical_record":{"source":{"id":"math-ph/9910002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1999-10-01T11:26:01Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"ce10ccb579703f1e16e36d3618ecd83157ec20ea5094056fc4ca94d0bc76ade3","abstract_canon_sha256":"0516c568d71a44224e6cdb1aa7e192f953c3e28cad3e79c2c889f9a767d82510"},"schema_version":"1.0"},"canonical_sha256":"290058a4b48a3c506d86364b3889267105a33cc32cb1f9736e76d96a7a8b7a98","source":{"kind":"arxiv","id":"math-ph/9910002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9910002","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9910002v1","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9910002","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"FEAFRJFURI6F","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"FEAFRJFURI6FA3MG","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"FEAFRJFU","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:FEAFRJFURI6FA3MGGZFTRCJGOE","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/9910002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1999-10-01T11:26:01Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"ce10ccb579703f1e16e36d3618ecd83157ec20ea5094056fc4ca94d0bc76ade3","abstract_canon_sha256":"0516c568d71a44224e6cdb1aa7e192f953c3e28cad3e79c2c889f9a767d82510"},"schema_version":"1.0"},"canonical_sha256":"290058a4b48a3c506d86364b3889267105a33cc32cb1f9736e76d96a7a8b7a98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.881477Z","signature_b64":"xdslP1++1+6cIy0jXb9cyM6yTfBp+ixZCWI+5no8Bc73oaOxvo+nWgoFnSHAcl8DCJuTRhz5eo7LmWv197fGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"290058a4b48a3c506d86364b3889267105a33cc32cb1f9736e76d96a7a8b7a98","last_reissued_at":"2026-05-18T01:05:29.880990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.880990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/9910002","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53qIwxdJxmZ5ZfL+uenVJml8hH1XYCYnxqIv41uA7VGuNMPSDRYpt87pKrR92eym9NMetpc5/oOElRYb6OyaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:49:29.820625Z"},"content_sha256":"1472b79f58f8e3d73495ba14f23de0ee7551dade6400096ed37897a86f9d18ae","schema_version":"1.0","event_id":"sha256:1472b79f58f8e3d73495ba14f23de0ee7551dade6400096ed37897a86f9d18ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:FEAFRJFURI6FA3MGGZFTRCJGOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal invariance of domino tiling","license":"","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Richard Kenyon","submitted_at":"1999-10-01T11:26:01Z","abstract_excerpt":"Let U be a multiply-connected region in R^2 with smooth boundary. Let P_epsilon be a polyomino in epsilon Z^2 approximating U as epsilon tends to 0. We show that, for certain boundary conditions on P_epsilon, the height distribution on a random domino tiling (dimer covering) of P_epsilon is conformally invariant in the limit as epsilon tends to\n 0, in the sense that the distribution of heights of boundary components only depends on the conformal type of U. The mean height and all the moments are explicitly evaluated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9910002","kind":"arxiv","version":1},"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":"2026-05-18T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hv9+TSqFr+KQpTXXNs5H5VZAymZNQDZZ5EttAspLIAbtMPUUnNY5bT/S6Le0Q5IDLXsJ5eNmT6T7BnFT7AScAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:49:29.821346Z"},"content_sha256":"d1f73a87bc434c0f6bf6c2bfa5a1dcee0bb85bce5d20c814233b2f70362779a3","schema_version":"1.0","event_id":"sha256:d1f73a87bc434c0f6bf6c2bfa5a1dcee0bb85bce5d20c814233b2f70362779a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FEAFRJFURI6FA3MGGZFTRCJGOE/bundle.json","state_url":"https://pith.science/pith/FEAFRJFURI6FA3MGGZFTRCJGOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FEAFRJFURI6FA3MGGZFTRCJGOE/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":"2026-06-11T23:49:29Z","links":{"resolver":"https://pith.science/pith/FEAFRJFURI6FA3MGGZFTRCJGOE","bundle":"https://pith.science/pith/FEAFRJFURI6FA3MGGZFTRCJGOE/bundle.json","state":"https://pith.science/pith/FEAFRJFURI6FA3MGGZFTRCJGOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FEAFRJFURI6FA3MGGZFTRCJGOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:FEAFRJFURI6FA3MGGZFTRCJGOE","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":"0516c568d71a44224e6cdb1aa7e192f953c3e28cad3e79c2c889f9a767d82510","cross_cats_sorted":["math.CO","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1999-10-01T11:26:01Z","title_canon_sha256":"ce10ccb579703f1e16e36d3618ecd83157ec20ea5094056fc4ca94d0bc76ade3"},"schema_version":"1.0","source":{"id":"math-ph/9910002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9910002","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9910002v1","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9910002","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"FEAFRJFURI6F","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"FEAFRJFURI6FA3MG","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"FEAFRJFU","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:d1f73a87bc434c0f6bf6c2bfa5a1dcee0bb85bce5d20c814233b2f70362779a3","target":"graph","created_at":"2026-05-18T01:05:29Z","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":"Let U be a multiply-connected region in R^2 with smooth boundary. Let P_epsilon be a polyomino in epsilon Z^2 approximating U as epsilon tends to 0. We show that, for certain boundary conditions on P_epsilon, the height distribution on a random domino tiling (dimer covering) of P_epsilon is conformally invariant in the limit as epsilon tends to\n 0, in the sense that the distribution of heights of boundary components only depends on the conformal type of U. The mean height and all the moments are explicitly evaluated.","authors_text":"Richard Kenyon","cross_cats":["math.CO","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1999-10-01T11:26:01Z","title":"Conformal invariance of domino tiling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9910002","kind":"arxiv","version":1},"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":"sha256:1472b79f58f8e3d73495ba14f23de0ee7551dade6400096ed37897a86f9d18ae","target":"record","created_at":"2026-05-18T01:05:29Z","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":"0516c568d71a44224e6cdb1aa7e192f953c3e28cad3e79c2c889f9a767d82510","cross_cats_sorted":["math.CO","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1999-10-01T11:26:01Z","title_canon_sha256":"ce10ccb579703f1e16e36d3618ecd83157ec20ea5094056fc4ca94d0bc76ade3"},"schema_version":"1.0","source":{"id":"math-ph/9910002","kind":"arxiv","version":1}},"canonical_sha256":"290058a4b48a3c506d86364b3889267105a33cc32cb1f9736e76d96a7a8b7a98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"290058a4b48a3c506d86364b3889267105a33cc32cb1f9736e76d96a7a8b7a98","first_computed_at":"2026-05-18T01:05:29.880990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:29.880990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xdslP1++1+6cIy0jXb9cyM6yTfBp+ixZCWI+5no8Bc73oaOxvo+nWgoFnSHAcl8DCJuTRhz5eo7LmWv197fGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:29.881477Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9910002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1472b79f58f8e3d73495ba14f23de0ee7551dade6400096ed37897a86f9d18ae","sha256:d1f73a87bc434c0f6bf6c2bfa5a1dcee0bb85bce5d20c814233b2f70362779a3"],"state_sha256":"6d8a3da5dd69ee985ff3d2791e1f9339b9ede3e57b6beb95f3e18d7f29090268"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MAikbqNO8W8o3dlVMb/8OjJIx6+cGSHWTJIkdKaCoGQBiFo+CAj1i4OZ07rCSlIQ2eyl+n0kv+fmcAwzQTJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:49:29.825580Z","bundle_sha256":"2df8672c14647fc39a9e0d1e92de24124b25dd4f54eb04c2309ae5e7183ec758"}}