{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VZT3V2EMTBU74BG72BPJ3ZZD24","short_pith_number":"pith:VZT3V2EM","canonical_record":{"source":{"id":"1008.1378","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-08T03:58:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"17f00fdb17424cac0f9545b324e6a18a4d84cb834fb235a785680c451640b64d","abstract_canon_sha256":"bffebd04c363b60cb223d8974d2c6f393bd2887e869f22eb95341b40fdb95994"},"schema_version":"1.0"},"canonical_sha256":"ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36","source":{"kind":"arxiv","id":"1008.1378","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1378","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1378v5","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1378","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"pith_short_12","alias_value":"VZT3V2EMTBU7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VZT3V2EMTBU74BG7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VZT3V2EM","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VZT3V2EMTBU74BG72BPJ3ZZD24","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1378","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-08T03:58:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"17f00fdb17424cac0f9545b324e6a18a4d84cb834fb235a785680c451640b64d","abstract_canon_sha256":"bffebd04c363b60cb223d8974d2c6f393bd2887e869f22eb95341b40fdb95994"},"schema_version":"1.0"},"canonical_sha256":"ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:06.882685Z","signature_b64":"0kKNmv7Dl9VSoHErmoVEgiNlHPtIatTzjJ2gPjU9aaOVUVYsLjKIauBZgim9XjBxnlRuHCBHDJMtwdf1KD5zCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36","last_reissued_at":"2026-05-18T02:59:06.881813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:06.881813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1378","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:59:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KVk39GoknU+83PbVcb9Aqr/GVjMHc1da787qghJwlIOvLHcU5ivJw9l221pU1xn0vInHFVozpziYGjFm8rwcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:46:33.397174Z"},"content_sha256":"e919458533d134e93088d564738f17bbdc350db0a85288c8415c805ed617d207","schema_version":"1.0","event_id":"sha256:e919458533d134e93088d564738f17bbdc350db0a85288c8415c805ed617d207"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VZT3V2EMTBU74BG72BPJ3ZZD24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pivotal, cluster and interface measures for critical planar percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christophe Garban, G\\'abor Pete, Oded Schramm","submitted_at":"2010-08-08T03:58:42Z","abstract_excerpt":"This work is the first in a series of papers devoted to the construction and study of scaling limits of dynamical and near-critical planar percolation and related objects like invasion percolation and the Minimal Spanning Tree. We show here that the counting measure on the set of pivotal points of critical site percolation on the triangular grid, normalized appropriately, has a scaling limit, which is a function of the scaling limit of the percolation configuration. We also show that this limit measure is conformally covariant, with exponent 3/4. Similar results hold for the counting measure o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1378","kind":"arxiv","version":5},"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":"2026-05-18T02:59:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnSzwEA+V56jAHk20r1ForIJsIKviFOaS+ShQU8ep0ABf96vpvPiT8sLJ9ogTHDi/v6JizcIKwYS4e0BAdwnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:46:33.397539Z"},"content_sha256":"8cd3bd9b022dbe17718091a3b4fbc571ea69c85c65f32fb8bdb6a00df9cfdc75","schema_version":"1.0","event_id":"sha256:8cd3bd9b022dbe17718091a3b4fbc571ea69c85c65f32fb8bdb6a00df9cfdc75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZT3V2EMTBU74BG72BPJ3ZZD24/bundle.json","state_url":"https://pith.science/pith/VZT3V2EMTBU74BG72BPJ3ZZD24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZT3V2EMTBU74BG72BPJ3ZZD24/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":"2026-05-26T20:46:33Z","links":{"resolver":"https://pith.science/pith/VZT3V2EMTBU74BG72BPJ3ZZD24","bundle":"https://pith.science/pith/VZT3V2EMTBU74BG72BPJ3ZZD24/bundle.json","state":"https://pith.science/pith/VZT3V2EMTBU74BG72BPJ3ZZD24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZT3V2EMTBU74BG72BPJ3ZZD24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VZT3V2EMTBU74BG72BPJ3ZZD24","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":"bffebd04c363b60cb223d8974d2c6f393bd2887e869f22eb95341b40fdb95994","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-08T03:58:42Z","title_canon_sha256":"17f00fdb17424cac0f9545b324e6a18a4d84cb834fb235a785680c451640b64d"},"schema_version":"1.0","source":{"id":"1008.1378","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1378","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1378v5","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1378","created_at":"2026-05-18T02:59:06Z"},{"alias_kind":"pith_short_12","alias_value":"VZT3V2EMTBU7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VZT3V2EMTBU74BG7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VZT3V2EM","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:8cd3bd9b022dbe17718091a3b4fbc571ea69c85c65f32fb8bdb6a00df9cfdc75","target":"graph","created_at":"2026-05-18T02:59:06Z","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"},"paper":{"abstract_excerpt":"This work is the first in a series of papers devoted to the construction and study of scaling limits of dynamical and near-critical planar percolation and related objects like invasion percolation and the Minimal Spanning Tree. We show here that the counting measure on the set of pivotal points of critical site percolation on the triangular grid, normalized appropriately, has a scaling limit, which is a function of the scaling limit of the percolation configuration. We also show that this limit measure is conformally covariant, with exponent 3/4. Similar results hold for the counting measure o","authors_text":"Christophe Garban, G\\'abor Pete, Oded Schramm","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-08T03:58:42Z","title":"Pivotal, cluster and interface measures for critical planar percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1378","kind":"arxiv","version":5},"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:e919458533d134e93088d564738f17bbdc350db0a85288c8415c805ed617d207","target":"record","created_at":"2026-05-18T02:59:06Z","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":"bffebd04c363b60cb223d8974d2c6f393bd2887e869f22eb95341b40fdb95994","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-08T03:58:42Z","title_canon_sha256":"17f00fdb17424cac0f9545b324e6a18a4d84cb834fb235a785680c451640b64d"},"schema_version":"1.0","source":{"id":"1008.1378","kind":"arxiv","version":5}},"canonical_sha256":"ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36","first_computed_at":"2026-05-18T02:59:06.881813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:06.881813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kKNmv7Dl9VSoHErmoVEgiNlHPtIatTzjJ2gPjU9aaOVUVYsLjKIauBZgim9XjBxnlRuHCBHDJMtwdf1KD5zCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:06.882685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1378","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e919458533d134e93088d564738f17bbdc350db0a85288c8415c805ed617d207","sha256:8cd3bd9b022dbe17718091a3b4fbc571ea69c85c65f32fb8bdb6a00df9cfdc75"],"state_sha256":"1db9a5958d4b1143a06451f717b5602cce773fb7fb2035d7744c79cb3901e769"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DvxNu9FfqYBc6LcmqAd5a8YZWw+k4OaPpnQ3qHDisunj+fDEavIpkV7anWTWspLYLkr18dMhAjLRx3tbdDx+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:46:33.400089Z","bundle_sha256":"e8e3d3cc79311ba366c89abbc38f5a427152ac8ed4d592d2e37b48b0a67f4d2d"}}