{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V5TGAPD5INECMSY75DEQ4C5EOG","short_pith_number":"pith:V5TGAPD5","canonical_record":{"source":{"id":"1605.03112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T17:25:37Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"b1fde39bc6142e43dbc52e8d474a55582ac5354efbb2f2bef1e8e5215abbb340","abstract_canon_sha256":"11ca03d3e280ef0e3532aa5810295df7174c7c3ee08a1b5b5169047e4ad03fa4"},"schema_version":"1.0"},"canonical_sha256":"af66603c7d4348264b1fe8c90e0ba471943edd8435ac42e4035fc298cff6534f","source":{"kind":"arxiv","id":"1605.03112","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03112","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03112v2","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03112","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"V5TGAPD5INEC","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V5TGAPD5INECMSY7","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V5TGAPD5","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V5TGAPD5INECMSY75DEQ4C5EOG","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T17:25:37Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"b1fde39bc6142e43dbc52e8d474a55582ac5354efbb2f2bef1e8e5215abbb340","abstract_canon_sha256":"11ca03d3e280ef0e3532aa5810295df7174c7c3ee08a1b5b5169047e4ad03fa4"},"schema_version":"1.0"},"canonical_sha256":"af66603c7d4348264b1fe8c90e0ba471943edd8435ac42e4035fc298cff6534f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:02.683663Z","signature_b64":"cro52GHSzCbpdXB/2hDN47yAFV5y31zbR0vBiZJ1qIt36Fr4338gvE4mIRL5xvRGqDn03sf6krCNqw2ajFGmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af66603c7d4348264b1fe8c90e0ba471943edd8435ac42e4035fc298cff6534f","last_reissued_at":"2026-05-18T00:46:02.683234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:02.683234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03112","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":"2026-05-18T00:46:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BhiKarlpP4Vj7zy8ebMCXPilr9sABbDrxHt4V4wK3xlZkLZBsxozDebJd2MA8LMPJfvfVlVwvsR6wZ44lZADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:52:33.875091Z"},"content_sha256":"c893885e46d26f9f0c8add5f6f455d7888b623dfe205e71910916b21e84c2c72","schema_version":"1.0","event_id":"sha256:c893885e46d26f9f0c8add5f6f455d7888b623dfe205e71910916b21e84c2c72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V5TGAPD5INECMSY75DEQ4C5EOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral means spectrum of whole-plane SLE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Bertrand Duplantier, Dmitry Beliaev, Michel Zinsmeister","submitted_at":"2016-05-10T17:25:37Z","abstract_excerpt":"We complete the mathematical analysis of the fine structure of harmonic measure on SLE curves that was initiated by Beliaev and Smirnov, as described by the averaged integral means spectrum. For the unbounded version of whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and Loutsenko and Yermolayeva, a phase transition has been shown to occur for high enough moments from the bulk spectrum towards a novel spectrum related to the point at infinity. For the bounded version of whole-plane SLE studied here, a similar transition phenomenon, now associated with the SLE origin, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03112","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":""},"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":"2026-05-18T00:46:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9KCNOe362CfATrhC8Dt/vc/hhK1AMBYCGPEnGgj8T+O7Hqf9X2VU3HnJRkMAmNJagp1+K7T1QmGbs8z94FoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:52:33.875471Z"},"content_sha256":"73b18517dae4041b07d8806004f24ccd8f5b6cd14c7f1e5a3abaa48b6453caf8","schema_version":"1.0","event_id":"sha256:73b18517dae4041b07d8806004f24ccd8f5b6cd14c7f1e5a3abaa48b6453caf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5TGAPD5INECMSY75DEQ4C5EOG/bundle.json","state_url":"https://pith.science/pith/V5TGAPD5INECMSY75DEQ4C5EOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5TGAPD5INECMSY75DEQ4C5EOG/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":"2026-05-27T19:52:33Z","links":{"resolver":"https://pith.science/pith/V5TGAPD5INECMSY75DEQ4C5EOG","bundle":"https://pith.science/pith/V5TGAPD5INECMSY75DEQ4C5EOG/bundle.json","state":"https://pith.science/pith/V5TGAPD5INECMSY75DEQ4C5EOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5TGAPD5INECMSY75DEQ4C5EOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V5TGAPD5INECMSY75DEQ4C5EOG","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":"11ca03d3e280ef0e3532aa5810295df7174c7c3ee08a1b5b5169047e4ad03fa4","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T17:25:37Z","title_canon_sha256":"b1fde39bc6142e43dbc52e8d474a55582ac5354efbb2f2bef1e8e5215abbb340"},"schema_version":"1.0","source":{"id":"1605.03112","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03112","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03112v2","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03112","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"V5TGAPD5INEC","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V5TGAPD5INECMSY7","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V5TGAPD5","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:73b18517dae4041b07d8806004f24ccd8f5b6cd14c7f1e5a3abaa48b6453caf8","target":"graph","created_at":"2026-05-18T00:46:02Z","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 complete the mathematical analysis of the fine structure of harmonic measure on SLE curves that was initiated by Beliaev and Smirnov, as described by the averaged integral means spectrum. For the unbounded version of whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and Loutsenko and Yermolayeva, a phase transition has been shown to occur for high enough moments from the bulk spectrum towards a novel spectrum related to the point at infinity. For the bounded version of whole-plane SLE studied here, a similar transition phenomenon, now associated with the SLE origin, ","authors_text":"Bertrand Duplantier, Dmitry Beliaev, Michel Zinsmeister","cross_cats":["math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T17:25:37Z","title":"Integral means spectrum of whole-plane SLE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03112","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:c893885e46d26f9f0c8add5f6f455d7888b623dfe205e71910916b21e84c2c72","target":"record","created_at":"2026-05-18T00:46:02Z","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":"11ca03d3e280ef0e3532aa5810295df7174c7c3ee08a1b5b5169047e4ad03fa4","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T17:25:37Z","title_canon_sha256":"b1fde39bc6142e43dbc52e8d474a55582ac5354efbb2f2bef1e8e5215abbb340"},"schema_version":"1.0","source":{"id":"1605.03112","kind":"arxiv","version":2}},"canonical_sha256":"af66603c7d4348264b1fe8c90e0ba471943edd8435ac42e4035fc298cff6534f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af66603c7d4348264b1fe8c90e0ba471943edd8435ac42e4035fc298cff6534f","first_computed_at":"2026-05-18T00:46:02.683234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:02.683234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cro52GHSzCbpdXB/2hDN47yAFV5y31zbR0vBiZJ1qIt36Fr4338gvE4mIRL5xvRGqDn03sf6krCNqw2ajFGmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:02.683663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03112","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c893885e46d26f9f0c8add5f6f455d7888b623dfe205e71910916b21e84c2c72","sha256:73b18517dae4041b07d8806004f24ccd8f5b6cd14c7f1e5a3abaa48b6453caf8"],"state_sha256":"a611dc3c87b0434b3cb91fa4781ae608b4f3910357c970031f94da92a06fa731"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OVJsufhd+C62qu7h0/x9HM14HvdmJtBTL94KYtU5m17H6R7qYckvm58XGfCO/8TTP6jXKgP/3qnIpgkzLFM+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:52:33.877908Z","bundle_sha256":"a50a62b9b654666cf4158ff1fba5d0b5f791a0a0cced1901cd083621508399ad"}}