{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ATZ22GMURKF7BB6SF6SHY7QQPS","short_pith_number":"pith:ATZ22GMU","canonical_record":{"source":{"id":"1206.5123","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-22T12:08:05Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"d17584163d9484bdc97fedfd9a90c3d46d7f329dd537caaa674ddc885fe6c1a0","abstract_canon_sha256":"2e7e33a49ebc79ab0ebb6a1ad3026b06ceba079e210bf11836cef05f77efe6aa"},"schema_version":"1.0"},"canonical_sha256":"04f3ad19948a8bf087d22fa47c7e107c8ef23cd6cc7633a568374646e0277f65","source":{"kind":"arxiv","id":"1206.5123","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5123","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5123v3","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5123","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"ATZ22GMURKF7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ATZ22GMURKF7BB6S","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ATZ22GMU","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ATZ22GMURKF7BB6SF6SHY7QQPS","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5123","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-22T12:08:05Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"d17584163d9484bdc97fedfd9a90c3d46d7f329dd537caaa674ddc885fe6c1a0","abstract_canon_sha256":"2e7e33a49ebc79ab0ebb6a1ad3026b06ceba079e210bf11836cef05f77efe6aa"},"schema_version":"1.0"},"canonical_sha256":"04f3ad19948a8bf087d22fa47c7e107c8ef23cd6cc7633a568374646e0277f65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:53.393935Z","signature_b64":"6teAkPWm3tSruz0vMo/DRfofa/CERy3x/G1gVHWP7hlP/ltTEjpIz858IcFgHe7kjW7LfVVnRWQRamyqDoC9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04f3ad19948a8bf087d22fa47c7e107c8ef23cd6cc7633a568374646e0277f65","last_reissued_at":"2026-05-18T02:29:53.393351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:53.393351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5123","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":"2026-05-18T02:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vTFf2vOH8wqcKeVKfnSgBWOZPVw/82dxVup8xSGLIa4KSPYT456OfGYXQyAA/xPIgctd/WKTqurCI2trBS0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:09:27.003946Z"},"content_sha256":"621fb6264c292d6a182a553d8085804ea5e18bd8d3683f9a372124b74cbe1e85","schema_version":"1.0","event_id":"sha256:621fb6264c292d6a182a553d8085804ea5e18bd8d3683f9a372124b74cbe1e85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ATZ22GMURKF7BB6SF6SHY7QQPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Leonid Petrov","submitted_at":"2012-06-22T12:08:05Z","abstract_excerpt":"We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows arbitrarily large number of sides), we show that these fluctuations are asymptotically governed by a Gaussian free (massless) field. This complements the similar result obtained in Kenyon [Comm. Math. Phys. 281 (2008) 675-709] about tilings of regions without frozen facets of the limit shape. In our asymptotic analysis we use the explicit double contour integral formula for the determinantal correlatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5123","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":""},"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":"2026-05-18T02:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wjGHT18fzaMBTmhvyDqW2u/GcyL3jNj21qXXTwTWTKVZxs62TtkliKbtFms4lMF9h0onFeZJX7Q85K1+yyyRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:09:27.004416Z"},"content_sha256":"4bc12e7c70817d6803576ee95e10261908fd5c86f3f0c52b4fbe944566381e86","schema_version":"1.0","event_id":"sha256:4bc12e7c70817d6803576ee95e10261908fd5c86f3f0c52b4fbe944566381e86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ATZ22GMURKF7BB6SF6SHY7QQPS/bundle.json","state_url":"https://pith.science/pith/ATZ22GMURKF7BB6SF6SHY7QQPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ATZ22GMURKF7BB6SF6SHY7QQPS/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":"2026-08-09T12:09:27Z","links":{"resolver":"https://pith.science/pith/ATZ22GMURKF7BB6SF6SHY7QQPS","bundle":"https://pith.science/pith/ATZ22GMURKF7BB6SF6SHY7QQPS/bundle.json","state":"https://pith.science/pith/ATZ22GMURKF7BB6SF6SHY7QQPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ATZ22GMURKF7BB6SF6SHY7QQPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ATZ22GMURKF7BB6SF6SHY7QQPS","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":"2e7e33a49ebc79ab0ebb6a1ad3026b06ceba079e210bf11836cef05f77efe6aa","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-22T12:08:05Z","title_canon_sha256":"d17584163d9484bdc97fedfd9a90c3d46d7f329dd537caaa674ddc885fe6c1a0"},"schema_version":"1.0","source":{"id":"1206.5123","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5123","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5123v3","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5123","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"ATZ22GMURKF7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ATZ22GMURKF7BB6S","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ATZ22GMU","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:4bc12e7c70817d6803576ee95e10261908fd5c86f3f0c52b4fbe944566381e86","target":"graph","created_at":"2026-05-18T02:29:53Z","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":"We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows arbitrarily large number of sides), we show that these fluctuations are asymptotically governed by a Gaussian free (massless) field. This complements the similar result obtained in Kenyon [Comm. Math. Phys. 281 (2008) 675-709] about tilings of regions without frozen facets of the limit shape. In our asymptotic analysis we use the explicit double contour integral formula for the determinantal correlatio","authors_text":"Leonid Petrov","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-22T12:08:05Z","title":"Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5123","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":"sha256:621fb6264c292d6a182a553d8085804ea5e18bd8d3683f9a372124b74cbe1e85","target":"record","created_at":"2026-05-18T02:29:53Z","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":"2e7e33a49ebc79ab0ebb6a1ad3026b06ceba079e210bf11836cef05f77efe6aa","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-22T12:08:05Z","title_canon_sha256":"d17584163d9484bdc97fedfd9a90c3d46d7f329dd537caaa674ddc885fe6c1a0"},"schema_version":"1.0","source":{"id":"1206.5123","kind":"arxiv","version":3}},"canonical_sha256":"04f3ad19948a8bf087d22fa47c7e107c8ef23cd6cc7633a568374646e0277f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04f3ad19948a8bf087d22fa47c7e107c8ef23cd6cc7633a568374646e0277f65","first_computed_at":"2026-05-18T02:29:53.393351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.393351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6teAkPWm3tSruz0vMo/DRfofa/CERy3x/G1gVHWP7hlP/ltTEjpIz858IcFgHe7kjW7LfVVnRWQRamyqDoC9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.393935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5123","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:621fb6264c292d6a182a553d8085804ea5e18bd8d3683f9a372124b74cbe1e85","sha256:4bc12e7c70817d6803576ee95e10261908fd5c86f3f0c52b4fbe944566381e86"],"state_sha256":"39489ef16e516d0296f2055fc78b5567ddc0849896d1d7b3ce7ddc26d9266bf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aWuCE5XHJT3PzSyLBA9EVVsqyGTZ4qjQTLWVlWQ+jm4fk5y232ckNavey9xUdj0Hc8Px4SH11jq7sEwXHdV0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:09:27.009659Z","bundle_sha256":"491540248c9c7f903c518fc887775490d8ffc7abdd149d753c77730d83faf38a"}}