{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WA56BUNVL4TYNJEYTXF3EZLV5Y","short_pith_number":"pith:WA56BUNV","canonical_record":{"source":{"id":"1512.04368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-14T15:45:15Z","cross_cats_sorted":["math.DS","math.MG","math.MP","math.PR"],"title_canon_sha256":"0059073a9b22c92e23d08326b37cea50754697a6dbd5fa4a2fa7138ef60ea802","abstract_canon_sha256":"8e78ef4630a7d6da3080a7592a7edbfc61b36c3ffe49de7386b17e051b4ed51e"},"schema_version":"1.0"},"canonical_sha256":"b03be0d1b55f2786a4989dcbb26575ee2e082a4f88d666bc3cd9f775b7d1db9a","source":{"kind":"arxiv","id":"1512.04368","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04368","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04368v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04368","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"WA56BUNVL4TY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WA56BUNVL4TYNJEY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WA56BUNV","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WA56BUNVL4TYNJEYTXF3EZLV5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-14T15:45:15Z","cross_cats_sorted":["math.DS","math.MG","math.MP","math.PR"],"title_canon_sha256":"0059073a9b22c92e23d08326b37cea50754697a6dbd5fa4a2fa7138ef60ea802","abstract_canon_sha256":"8e78ef4630a7d6da3080a7592a7edbfc61b36c3ffe49de7386b17e051b4ed51e"},"schema_version":"1.0"},"canonical_sha256":"b03be0d1b55f2786a4989dcbb26575ee2e082a4f88d666bc3cd9f775b7d1db9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:22.376087Z","signature_b64":"c/zTD+cDOe0e06yPFtSR54teEWwc3D9LtZ6uROhCqEjnAErvOxYbKytZJAVwsNpDSvaKuNkqMfvtKkFMy3C1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b03be0d1b55f2786a4989dcbb26575ee2e082a4f88d666bc3cd9f775b7d1db9a","last_reissued_at":"2026-05-18T01:24:22.375521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:22.375521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04368","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":"2026-05-18T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6apZe6nN2E8wUExAozLoVjYTuk6qFLZ6czCYNhXSQR8vzGrC9uhmyaeTUzW/goXqQkoDc61tAi/NGKbQjEYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:54:14.065029Z"},"content_sha256":"4101d37d89a87725beb4c618d8bbe89c448cb774869bd5274fb6a0fbc9b6f46a","schema_version":"1.0","event_id":"sha256:4101d37d89a87725beb4c618d8bbe89c448cb774869bd5274fb6a0fbc9b6f46a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WA56BUNVL4TYNJEYTXF3EZLV5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random sparse sampling in a Gibbs weighted tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Julien Barral, St\\'ephane Seuret","submitted_at":"2015-12-14T15:45:15Z","abstract_excerpt":"Let $\\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\\Sigma=\\{0,1\\}^{\\mathbb{N}}$ associated with a H\\\"older potential. The thermodynamic and multifractal properties of $\\mu$ are well known to be linked via the multifractal formalism. In this article, the impact of a random sampling procedure on this structure is studied.\n  More precisely, let $\\{I_w\\}_{w\\in \\Sigma^*}$ stand for the collection of dyadic subintervals of $[0,1]$ naturally indexed by the set of finite dyadic words $\\Sigma^*$. Fix $\\eta\\in(0,1)$, and a sequence $(p_w)_{w\\in \\Sigma^*}$ of independent Bernoulli v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04368","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":"2026-05-18T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"haWb0rHNaQcVHzG/wHcpNdBn7bVpMgkEaeLgcSjP9tlt59XzASzoANm1bygt0yGZED6A9h9Zf5FcUNJUcdkuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:54:14.065413Z"},"content_sha256":"37848bbec71fbf21068837e434e5c084b6741bae8dc063ed38cb28f745945f46","schema_version":"1.0","event_id":"sha256:37848bbec71fbf21068837e434e5c084b6741bae8dc063ed38cb28f745945f46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y/bundle.json","state_url":"https://pith.science/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y/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":"2026-07-01T16:54:14Z","links":{"resolver":"https://pith.science/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y","bundle":"https://pith.science/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y/bundle.json","state":"https://pith.science/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WA56BUNVL4TYNJEYTXF3EZLV5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WA56BUNVL4TYNJEYTXF3EZLV5Y","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":"8e78ef4630a7d6da3080a7592a7edbfc61b36c3ffe49de7386b17e051b4ed51e","cross_cats_sorted":["math.DS","math.MG","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-14T15:45:15Z","title_canon_sha256":"0059073a9b22c92e23d08326b37cea50754697a6dbd5fa4a2fa7138ef60ea802"},"schema_version":"1.0","source":{"id":"1512.04368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04368","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04368v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04368","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"WA56BUNVL4TY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WA56BUNVL4TYNJEY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WA56BUNV","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:37848bbec71fbf21068837e434e5c084b6741bae8dc063ed38cb28f745945f46","target":"graph","created_at":"2026-05-18T01:24:22Z","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":"Let $\\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\\Sigma=\\{0,1\\}^{\\mathbb{N}}$ associated with a H\\\"older potential. The thermodynamic and multifractal properties of $\\mu$ are well known to be linked via the multifractal formalism. In this article, the impact of a random sampling procedure on this structure is studied.\n  More precisely, let $\\{I_w\\}_{w\\in \\Sigma^*}$ stand for the collection of dyadic subintervals of $[0,1]$ naturally indexed by the set of finite dyadic words $\\Sigma^*$. Fix $\\eta\\in(0,1)$, and a sequence $(p_w)_{w\\in \\Sigma^*}$ of independent Bernoulli v","authors_text":"Julien Barral, St\\'ephane Seuret","cross_cats":["math.DS","math.MG","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-14T15:45:15Z","title":"Random sparse sampling in a Gibbs weighted tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04368","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":"sha256:4101d37d89a87725beb4c618d8bbe89c448cb774869bd5274fb6a0fbc9b6f46a","target":"record","created_at":"2026-05-18T01:24:22Z","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":"8e78ef4630a7d6da3080a7592a7edbfc61b36c3ffe49de7386b17e051b4ed51e","cross_cats_sorted":["math.DS","math.MG","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-14T15:45:15Z","title_canon_sha256":"0059073a9b22c92e23d08326b37cea50754697a6dbd5fa4a2fa7138ef60ea802"},"schema_version":"1.0","source":{"id":"1512.04368","kind":"arxiv","version":1}},"canonical_sha256":"b03be0d1b55f2786a4989dcbb26575ee2e082a4f88d666bc3cd9f775b7d1db9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b03be0d1b55f2786a4989dcbb26575ee2e082a4f88d666bc3cd9f775b7d1db9a","first_computed_at":"2026-05-18T01:24:22.375521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:22.375521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/zTD+cDOe0e06yPFtSR54teEWwc3D9LtZ6uROhCqEjnAErvOxYbKytZJAVwsNpDSvaKuNkqMfvtKkFMy3C1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:22.376087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4101d37d89a87725beb4c618d8bbe89c448cb774869bd5274fb6a0fbc9b6f46a","sha256:37848bbec71fbf21068837e434e5c084b6741bae8dc063ed38cb28f745945f46"],"state_sha256":"e7f23fa85ae30ab86f65b37ea49df8f78b9c7819ec1592b4f74eb905534c5de0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ySavJYul5eD86AP0t+kEYB9NZYNHC7IMAu0AgcpClQbSeHd2Egut0KUpGUwXr0SIaUA3Ldl465YhGlSQNHADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T16:54:14.067439Z","bundle_sha256":"2c3572a5f085e87d4ac1ce7bd9bf9ef0dd70be39769a0c418581283a5eb7541a"}}