{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SJVIZKJBUJTCY3GBIZFLQQUBT4","short_pith_number":"pith:SJVIZKJB","canonical_record":{"source":{"id":"1407.6275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T15:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"10ae00047f173c33c3f20b619841992dd187bb5b1a45329894896920203adede","abstract_canon_sha256":"dc65785f6d8c6e9a1dcab5b382be28fdad1f6ea31c64e037838ce4fcc0d82f6d"},"schema_version":"1.0"},"canonical_sha256":"926a8ca921a2662c6cc1464ab842819f2da1d00ecdd3df51b3d275a0566dfeb3","source":{"kind":"arxiv","id":"1407.6275","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6275","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6275v2","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6275","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"SJVIZKJBUJTC","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SJVIZKJBUJTCY3GB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SJVIZKJB","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SJVIZKJBUJTCY3GBIZFLQQUBT4","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T15:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"10ae00047f173c33c3f20b619841992dd187bb5b1a45329894896920203adede","abstract_canon_sha256":"dc65785f6d8c6e9a1dcab5b382be28fdad1f6ea31c64e037838ce4fcc0d82f6d"},"schema_version":"1.0"},"canonical_sha256":"926a8ca921a2662c6cc1464ab842819f2da1d00ecdd3df51b3d275a0566dfeb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:40.103541Z","signature_b64":"ojzyrUhevHAKVbmAsQh0hUBz3ISQIkgeRC9D8xZKOz34jqKp1FOK0plLY2JNFL6dFn0bAEXOUcHJ504yf7UXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"926a8ca921a2662c6cc1464ab842819f2da1d00ecdd3df51b3d275a0566dfeb3","last_reissued_at":"2026-05-18T02:30:40.103026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:40.103026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6275","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":"2026-05-18T02:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LqcwfyGAziN3n6xJFNLvjCd0aHETjApBqH0dCZG46ukt3pcVkUb6G8ojFeIVXc4QjQ0feJIL13z5fb5X8BdLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:04:44.982049Z"},"content_sha256":"321b0a394ed01988476b0263939112aadbeaf67cc8e0a0b0dffdfa5de291a241","schema_version":"1.0","event_id":"sha256:321b0a394ed01988476b0263939112aadbeaf67cc8e0a0b0dffdfa5de291a241"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SJVIZKJBUJTCY3GBIZFLQQUBT4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mandelbrot cascades on random weighted trees and nonlinear smoothing transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacques Peyri\\`ere, Julien Barral","submitted_at":"2014-07-23T15:52:12Z","abstract_excerpt":"We consider complex Mandelbrot multiplicative cascades on a random weigh\\-ted tree. Under suitable assumptions, this yields a dynamics $\\T$ on laws invariant by random weighted means (the so called fixed points of smoothing transformations) and which have a finite moment of order 2. Moreover, we can exhibit two main behaviors: If the weights are conservative, i.e., sum up to~1 almost surely, we find a domain for the initial law $\\mu$ such that a non-standard (functional) central limit theorem is valid for the orbit $(\\T^n\\mu)_{n\\ge 0}$ (this completes in a non trivial way our previous result i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6275","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":"2026-05-18T02:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aar3uslD869ClpACdALYtmIFkXIyVbqMcGNzY1KMaha9oW5gEphlzjnXtNftc+ruLXqJbIYPMTekEcEDJ5JwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:04:44.982481Z"},"content_sha256":"7c29089c81c443dfbe75f7e731b037e2295c16b60e2bfe9dbaf362d6087c780a","schema_version":"1.0","event_id":"sha256:7c29089c81c443dfbe75f7e731b037e2295c16b60e2bfe9dbaf362d6087c780a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4/bundle.json","state_url":"https://pith.science/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4/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":"2026-06-23T05:04:44Z","links":{"resolver":"https://pith.science/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4","bundle":"https://pith.science/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4/bundle.json","state":"https://pith.science/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJVIZKJBUJTCY3GBIZFLQQUBT4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SJVIZKJBUJTCY3GBIZFLQQUBT4","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":"dc65785f6d8c6e9a1dcab5b382be28fdad1f6ea31c64e037838ce4fcc0d82f6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T15:52:12Z","title_canon_sha256":"10ae00047f173c33c3f20b619841992dd187bb5b1a45329894896920203adede"},"schema_version":"1.0","source":{"id":"1407.6275","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6275","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6275v2","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6275","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"SJVIZKJBUJTC","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SJVIZKJBUJTCY3GB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SJVIZKJB","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:7c29089c81c443dfbe75f7e731b037e2295c16b60e2bfe9dbaf362d6087c780a","target":"graph","created_at":"2026-05-18T02:30:40Z","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 consider complex Mandelbrot multiplicative cascades on a random weigh\\-ted tree. Under suitable assumptions, this yields a dynamics $\\T$ on laws invariant by random weighted means (the so called fixed points of smoothing transformations) and which have a finite moment of order 2. Moreover, we can exhibit two main behaviors: If the weights are conservative, i.e., sum up to~1 almost surely, we find a domain for the initial law $\\mu$ such that a non-standard (functional) central limit theorem is valid for the orbit $(\\T^n\\mu)_{n\\ge 0}$ (this completes in a non trivial way our previous result i","authors_text":"Jacques Peyri\\`ere, Julien Barral","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T15:52:12Z","title":"Mandelbrot cascades on random weighted trees and nonlinear smoothing transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6275","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":"sha256:321b0a394ed01988476b0263939112aadbeaf67cc8e0a0b0dffdfa5de291a241","target":"record","created_at":"2026-05-18T02:30:40Z","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":"dc65785f6d8c6e9a1dcab5b382be28fdad1f6ea31c64e037838ce4fcc0d82f6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T15:52:12Z","title_canon_sha256":"10ae00047f173c33c3f20b619841992dd187bb5b1a45329894896920203adede"},"schema_version":"1.0","source":{"id":"1407.6275","kind":"arxiv","version":2}},"canonical_sha256":"926a8ca921a2662c6cc1464ab842819f2da1d00ecdd3df51b3d275a0566dfeb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"926a8ca921a2662c6cc1464ab842819f2da1d00ecdd3df51b3d275a0566dfeb3","first_computed_at":"2026-05-18T02:30:40.103026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:40.103026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ojzyrUhevHAKVbmAsQh0hUBz3ISQIkgeRC9D8xZKOz34jqKp1FOK0plLY2JNFL6dFn0bAEXOUcHJ504yf7UXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:40.103541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6275","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:321b0a394ed01988476b0263939112aadbeaf67cc8e0a0b0dffdfa5de291a241","sha256:7c29089c81c443dfbe75f7e731b037e2295c16b60e2bfe9dbaf362d6087c780a"],"state_sha256":"3bde7d3849b9023dd68e163ef83a0b2fc27d50257456713bb29e5f8050d2d67d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c513fWUCKQtROma4BuoVSiJsneEBKoKUgvJg8vesC528K+tI0hYrWG6hoIRqveij6gmoXzhtGQ0i3i8JnekXAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:04:44.984424Z","bundle_sha256":"c0d568daa3234b03afa35e6a0feedd42077fabd846682fe6b1b58968e3f73334"}}