{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:IULLO7Z2DQOUUS6ZIJ3MGDJUPW","short_pith_number":"pith:IULLO7Z2","canonical_record":{"source":{"id":"0710.1470","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-10-08T06:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"6ca81c665e739fe1e2779d676592c7074701b31fce08e7e7526b38eeeb9d8be5","abstract_canon_sha256":"b13738ccacb329706f4f1cbe045197fdf5c315e2b3ed07b1dea58b292390adc9"},"schema_version":"1.0"},"canonical_sha256":"4516b77f3a1c1d4a4bd94276c30d347d853f1511dd34812fbf4dd4f38db2ff79","source":{"kind":"arxiv","id":"0710.1470","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.1470","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"0710.1470v1","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.1470","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"IULLO7Z2DQOU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IULLO7Z2DQOUUS6Z","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IULLO7Z2","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:IULLO7Z2DQOUUS6ZIJ3MGDJUPW","target":"record","payload":{"canonical_record":{"source":{"id":"0710.1470","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-10-08T06:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"6ca81c665e739fe1e2779d676592c7074701b31fce08e7e7526b38eeeb9d8be5","abstract_canon_sha256":"b13738ccacb329706f4f1cbe045197fdf5c315e2b3ed07b1dea58b292390adc9"},"schema_version":"1.0"},"canonical_sha256":"4516b77f3a1c1d4a4bd94276c30d347d853f1511dd34812fbf4dd4f38db2ff79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:08.909691Z","signature_b64":"eOtorMrIFR4ksgAiwuErrx1eSz+xekfaKhOwiGscn++BX1O0idaVOA8nJN1sqoZtd4303GTwt1JnYKPiDH6AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4516b77f3a1c1d4a4bd94276c30d347d853f1511dd34812fbf4dd4f38db2ff79","last_reissued_at":"2026-05-18T00:40:08.909050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:08.909050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.1470","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":"2026-05-18T00:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRwQ7gZppN1DtjslfCatdzTgeaW8GyPPKdbwYj/iJky26ry8aiTTfLA8oQe6LW5U0iRsk1OMH77WiTyKtVHKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:29:22.814824Z"},"content_sha256":"6c9f937487a55c4d1c51af5a4b12d71781c04fa38439fb22ed98d657039951f2","schema_version":"1.0","event_id":"sha256:6c9f937487a55c4d1c51af5a4b12d71781c04fa38439fb22ed98d657039951f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:IULLO7Z2DQOUUS6ZIJ3MGDJUPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymmetry of near-critical percolation interfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"LM-Orsay), Pierre Nolin (DMA, Wendelin Werner (DMA","submitted_at":"2007-10-08T06:23:02Z","abstract_excerpt":"We study the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice. When one lets the percolation parameter p(N) vary with the size N of the box that one is considering, three possibilities arise in the large-scale limit. It is known that when p(N) does not converge to 1/2 fast enough, then the scaling limits are degenerate, whereas if p(N) - 1 / 2 goes to zero quickly, the scaling limits are SLE(6) as when p=1/2. We study some properties of the (non-void) intermediate regime where the large scale behavior is neither SLE(6) nor degenerate. We prove that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.1470","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":"2026-05-18T00:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdEpUhLorwHPqLaBUxbbhoREoF9yAPaUEdyOVLt7HRPLp2S4eioJGn6yQ0Waad+MC3A12va2idDDvlznPNJnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:29:22.815561Z"},"content_sha256":"ab8048c6f308557432bd4ea96326b04a357a28218441e8ef0f4bc6b0f2887297","schema_version":"1.0","event_id":"sha256:ab8048c6f308557432bd4ea96326b04a357a28218441e8ef0f4bc6b0f2887297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW/bundle.json","state_url":"https://pith.science/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW/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":"2026-06-10T07:29:22Z","links":{"resolver":"https://pith.science/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW","bundle":"https://pith.science/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW/bundle.json","state":"https://pith.science/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IULLO7Z2DQOUUS6ZIJ3MGDJUPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:IULLO7Z2DQOUUS6ZIJ3MGDJUPW","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":"b13738ccacb329706f4f1cbe045197fdf5c315e2b3ed07b1dea58b292390adc9","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-10-08T06:23:02Z","title_canon_sha256":"6ca81c665e739fe1e2779d676592c7074701b31fce08e7e7526b38eeeb9d8be5"},"schema_version":"1.0","source":{"id":"0710.1470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.1470","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"0710.1470v1","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.1470","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"IULLO7Z2DQOU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IULLO7Z2DQOUUS6Z","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IULLO7Z2","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:ab8048c6f308557432bd4ea96326b04a357a28218441e8ef0f4bc6b0f2887297","target":"graph","created_at":"2026-05-18T00:40:08Z","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 the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice. When one lets the percolation parameter p(N) vary with the size N of the box that one is considering, three possibilities arise in the large-scale limit. It is known that when p(N) does not converge to 1/2 fast enough, then the scaling limits are degenerate, whereas if p(N) - 1 / 2 goes to zero quickly, the scaling limits are SLE(6) as when p=1/2. We study some properties of the (non-void) intermediate regime where the large scale behavior is neither SLE(6) nor degenerate. We prove that ","authors_text":"LM-Orsay), Pierre Nolin (DMA, Wendelin Werner (DMA","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-10-08T06:23:02Z","title":"Asymmetry of near-critical percolation interfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.1470","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":"sha256:6c9f937487a55c4d1c51af5a4b12d71781c04fa38439fb22ed98d657039951f2","target":"record","created_at":"2026-05-18T00:40:08Z","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":"b13738ccacb329706f4f1cbe045197fdf5c315e2b3ed07b1dea58b292390adc9","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-10-08T06:23:02Z","title_canon_sha256":"6ca81c665e739fe1e2779d676592c7074701b31fce08e7e7526b38eeeb9d8be5"},"schema_version":"1.0","source":{"id":"0710.1470","kind":"arxiv","version":1}},"canonical_sha256":"4516b77f3a1c1d4a4bd94276c30d347d853f1511dd34812fbf4dd4f38db2ff79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4516b77f3a1c1d4a4bd94276c30d347d853f1511dd34812fbf4dd4f38db2ff79","first_computed_at":"2026-05-18T00:40:08.909050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:08.909050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eOtorMrIFR4ksgAiwuErrx1eSz+xekfaKhOwiGscn++BX1O0idaVOA8nJN1sqoZtd4303GTwt1JnYKPiDH6AAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:08.909691Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.1470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c9f937487a55c4d1c51af5a4b12d71781c04fa38439fb22ed98d657039951f2","sha256:ab8048c6f308557432bd4ea96326b04a357a28218441e8ef0f4bc6b0f2887297"],"state_sha256":"e5ae56ef8afba65fb4ad5f2c5b87d61fec5b01af27e7e62495f0213448cc22a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HI6jGgiTkZFsZLvubiwb6d4jbLAAoxueFM+MF5pMQE6chddx9BY3Vn1eS6uBOGiNgXJlgGb00qwrNGYDMwaBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:29:22.819612Z","bundle_sha256":"3e77421d99e0535baa6196f1b3bf73afa4fedef1e28a635b274fbad10dae49d8"}}