{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:VTGELSQEZFXGFBQBBOBPGKR4AA","short_pith_number":"pith:VTGELSQE","schema_version":"1.0","canonical_sha256":"accc45ca04c96e6286010b82f32a3c000e658f427f6dbc63588c24f3a5ae601b","source":{"kind":"arxiv","id":"cond-mat/9709101","version":1},"attestation_state":"computed","paper":{"title":"Linear stochastic dynamics with nonlinear fractal properties","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"D. Sornette","submitted_at":"1997-09-09T08:04:47Z","abstract_excerpt":"Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications on population dynamics, epidemics, finance and insurance applications with relation to ARCH(1) process, immigration and investment portfolios and the internet. We highlight the common physical mechanis"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"cond-mat/9709101","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-09-09T08:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"c13dc5cfd7af428dbdb09881233443cb17ec7b2abe89742dff4de8eed3f390cb","abstract_canon_sha256":"c07f634af76f240cfa3173fad719dad12741d482ac01f3b5af85a7f969e312a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:33.151445Z","signature_b64":"lq+TcAAYqEfguecSCoGh44mG+WSEBwoAzb2Ijdj51zy+gwvDQ7PzUjuYtFjPw2q2ukG02ZVQbNl9AKODIlCdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"accc45ca04c96e6286010b82f32a3c000e658f427f6dbc63588c24f3a5ae601b","last_reissued_at":"2026-05-18T01:39:33.151112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:33.151112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear stochastic dynamics with nonlinear fractal properties","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"D. Sornette","submitted_at":"1997-09-09T08:04:47Z","abstract_excerpt":"Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications on population dynamics, epidemics, finance and insurance applications with relation to ARCH(1) process, immigration and investment portfolios and the internet. We highlight the common physical mechanis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9709101","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9709101","created_at":"2026-05-18T01:39:33.151161+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9709101v1","created_at":"2026-05-18T01:39:33.151161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9709101","created_at":"2026-05-18T01:39:33.151161+00:00"},{"alias_kind":"pith_short_12","alias_value":"VTGELSQEZFXG","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"VTGELSQEZFXGFBQB","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"VTGELSQE","created_at":"2026-05-18T12:25:48.327863+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA","json":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA.json","graph_json":"https://pith.science/api/pith-number/VTGELSQEZFXGFBQBBOBPGKR4AA/graph.json","events_json":"https://pith.science/api/pith-number/VTGELSQEZFXGFBQBBOBPGKR4AA/events.json","paper":"https://pith.science/paper/VTGELSQE"},"agent_actions":{"view_html":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA","download_json":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA.json","view_paper":"https://pith.science/paper/VTGELSQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/9709101&json=true","fetch_graph":"https://pith.science/api/pith-number/VTGELSQEZFXGFBQBBOBPGKR4AA/graph.json","fetch_events":"https://pith.science/api/pith-number/VTGELSQEZFXGFBQBBOBPGKR4AA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA/action/storage_attestation","attest_author":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA/action/author_attestation","sign_citation":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA/action/citation_signature","submit_replication":"https://pith.science/pith/VTGELSQEZFXGFBQBBOBPGKR4AA/action/replication_record"}},"created_at":"2026-05-18T01:39:33.151161+00:00","updated_at":"2026-05-18T01:39:33.151161+00:00"}