{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:URS5O7GOONBH4YZ3MJRPWZMXPJ","short_pith_number":"pith:URS5O7GO","canonical_record":{"source":{"id":"cond-mat/0610550","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-10-19T17:50:02Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"8939603f9c713f1f99de45fce591720a3300672723444ac7a390350ed743ac90","abstract_canon_sha256":"347f865229bfd006256b50973e1c6d82620becdcd71612f549733dce45cb2de5"},"schema_version":"1.0"},"canonical_sha256":"a465d77cce73427e633b6262fb65977a5ed98151715f45a3787e089deb98f54b","source":{"kind":"arxiv","id":"cond-mat/0610550","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0610550","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0610550v2","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0610550","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"pith_short_12","alias_value":"URS5O7GOONBH","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"pith_short_16","alias_value":"URS5O7GOONBH4YZ3","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"pith_short_8","alias_value":"URS5O7GO","created_at":"2026-07-04T14:59:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:URS5O7GOONBH4YZ3MJRPWZMXPJ","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0610550","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-10-19T17:50:02Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"8939603f9c713f1f99de45fce591720a3300672723444ac7a390350ed743ac90","abstract_canon_sha256":"347f865229bfd006256b50973e1c6d82620becdcd71612f549733dce45cb2de5"},"schema_version":"1.0"},"canonical_sha256":"a465d77cce73427e633b6262fb65977a5ed98151715f45a3787e089deb98f54b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:59:30.144744Z","signature_b64":"4dMQTcEeGNUD6sOy2q8JH+SROQQeo6bKnyTbKVjv9amI2WlCuJeMTFNaEpOUteFv5/ik/0Y19mfPnuK0EpzHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a465d77cce73427e633b6262fb65977a5ed98151715f45a3787e089deb98f54b","last_reissued_at":"2026-07-04T14:59:30.144356Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:59:30.144356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0610550","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:59:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7bTUiN6mSIXLpBhJNoyH/1wtLw0MFI7xcEpVNHlSW09KEktnpwfCbtX6cgRSqKNXw+lcsk59QpRr06d2hnqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:32:59.034012Z"},"content_sha256":"e466ea01f7697659db69851fcdb279d727a9738b1f200c84adb37c65403dcee5","schema_version":"1.0","event_id":"sha256:e466ea01f7697659db69851fcdb279d727a9738b1f200c84adb37c65403dcee5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:URS5O7GOONBH4YZ3MJRPWZMXPJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical curves in conformally invariant statistical systems","license":"","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"E. Bettelheim, I. A. Gruzberg, I. Rushkin, P. Wiegmann","submitted_at":"2006-10-19T17:50:02Z","abstract_excerpt":"We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0610550","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0610550/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:59:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQ9x4OvAJhrY/62EAgrMEN4VWShk84OR8UwZaKLb4CQxlQfnmxFoR7whj71VsmYwuJFkgd3TQfoUCHQAogAzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:32:59.034530Z"},"content_sha256":"25e62709a5a2037a644966502983716539e6d18e38824f476cac856ded3e0348","schema_version":"1.0","event_id":"sha256:25e62709a5a2037a644966502983716539e6d18e38824f476cac856ded3e0348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ/bundle.json","state_url":"https://pith.science/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ/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":"2026-08-16T23:32:59Z","links":{"resolver":"https://pith.science/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ","bundle":"https://pith.science/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ/bundle.json","state":"https://pith.science/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URS5O7GOONBH4YZ3MJRPWZMXPJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:URS5O7GOONBH4YZ3MJRPWZMXPJ","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":"347f865229bfd006256b50973e1c6d82620becdcd71612f549733dce45cb2de5","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-10-19T17:50:02Z","title_canon_sha256":"8939603f9c713f1f99de45fce591720a3300672723444ac7a390350ed743ac90"},"schema_version":"1.0","source":{"id":"cond-mat/0610550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0610550","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0610550v2","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0610550","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"pith_short_12","alias_value":"URS5O7GOONBH","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"pith_short_16","alias_value":"URS5O7GOONBH4YZ3","created_at":"2026-07-04T14:59:30Z"},{"alias_kind":"pith_short_8","alias_value":"URS5O7GO","created_at":"2026-07-04T14:59:30Z"}],"graph_snapshots":[{"event_id":"sha256:25e62709a5a2037a644966502983716539e6d18e38824f476cac856ded3e0348","target":"graph","created_at":"2026-07-04T14:59:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0610550/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be ob","authors_text":"E. Bettelheim, I. A. Gruzberg, I. Rushkin, P. Wiegmann","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-10-19T17:50:02Z","title":"Critical curves in conformally invariant statistical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0610550","kind":"arxiv","version":2},"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:e466ea01f7697659db69851fcdb279d727a9738b1f200c84adb37c65403dcee5","target":"record","created_at":"2026-07-04T14:59:30Z","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":"347f865229bfd006256b50973e1c6d82620becdcd71612f549733dce45cb2de5","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-10-19T17:50:02Z","title_canon_sha256":"8939603f9c713f1f99de45fce591720a3300672723444ac7a390350ed743ac90"},"schema_version":"1.0","source":{"id":"cond-mat/0610550","kind":"arxiv","version":2}},"canonical_sha256":"a465d77cce73427e633b6262fb65977a5ed98151715f45a3787e089deb98f54b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a465d77cce73427e633b6262fb65977a5ed98151715f45a3787e089deb98f54b","first_computed_at":"2026-07-04T14:59:30.144356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:59:30.144356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dMQTcEeGNUD6sOy2q8JH+SROQQeo6bKnyTbKVjv9amI2WlCuJeMTFNaEpOUteFv5/ik/0Y19mfPnuK0EpzHDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:59:30.144744Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0610550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e466ea01f7697659db69851fcdb279d727a9738b1f200c84adb37c65403dcee5","sha256:25e62709a5a2037a644966502983716539e6d18e38824f476cac856ded3e0348"],"state_sha256":"284a8cfec94c33d5edb3046b319ab32d62f4d14724dd3903a03fdcb39d6db161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mRRa8zWQLXR6NlTEiWExygng7ooHiuVNcXeAm7iDtHD/bAgOafzOY9CKfNph/Wax5DRG3758LFO9R33T1WxuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T23:32:59.093496Z","bundle_sha256":"3cd624ae7c9784d74556562c07e961d56d9bdf03a162f6e712e2ec2a9f0c1f9a"}}