{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:OET3WD6MSUISGTTYMTG4N5DF72","short_pith_number":"pith:OET3WD6M","schema_version":"1.0","canonical_sha256":"7127bb0fcc9511234e7864cdc6f465fe9db33dfd332d056ab2a104f96feeb3e9","source":{"kind":"arxiv","id":"math/0402343","version":1},"attestation_state":"computed","paper":{"title":"Dynamics of exponential linear map in functional space","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"David Gamarnik, Grzegorz Swirszcz, Tomasz Nowicki","submitted_at":"2004-02-21T05:48:12Z","abstract_excerpt":"We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the functional space, where we look for a global attractor. We consider the following bifurcation problem: Given a probability measure $\\mu$, which corresponds to the weight distribution of a link of a random graph we form a positive linear operator $\\Phi$\n (convolution) on distribution functions and then we analyze a family of its exponents with a parameter $\\lambda"},"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":"math/0402343","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2004-02-21T05:48:12Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"47497f4d00260c7110cbc614f020bf45f92b1c1d0424e3fb89006f707f623e03","abstract_canon_sha256":"b2961e2073c079f37ebf4c28da547e69b06b7bd173c1dd988de6ab6132d83e2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.562580Z","signature_b64":"W0A7GJe0+ddCHF8S3aiu+Y8o7Hc9YxNLnLHv9TAaj0X/qi+27xEtWeSZuDyHR8HCRIuAgbEn7JCa40JJojS5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7127bb0fcc9511234e7864cdc6f465fe9db33dfd332d056ab2a104f96feeb3e9","last_reissued_at":"2026-05-18T01:05:26.562122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.562122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of exponential linear map in functional space","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"David Gamarnik, Grzegorz Swirszcz, Tomasz Nowicki","submitted_at":"2004-02-21T05:48:12Z","abstract_excerpt":"We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the functional space, where we look for a global attractor. We consider the following bifurcation problem: Given a probability measure $\\mu$, which corresponds to the weight distribution of a link of a random graph we form a positive linear operator $\\Phi$\n (convolution) on distribution functions and then we analyze a family of its exponents with a parameter $\\lambda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402343","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":"math/0402343","created_at":"2026-05-18T01:05:26.562193+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0402343v1","created_at":"2026-05-18T01:05:26.562193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402343","created_at":"2026-05-18T01:05:26.562193+00:00"},{"alias_kind":"pith_short_12","alias_value":"OET3WD6MSUIS","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"OET3WD6MSUISGTTY","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"OET3WD6M","created_at":"2026-05-18T12:25:52.687210+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/OET3WD6MSUISGTTYMTG4N5DF72","json":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72.json","graph_json":"https://pith.science/api/pith-number/OET3WD6MSUISGTTYMTG4N5DF72/graph.json","events_json":"https://pith.science/api/pith-number/OET3WD6MSUISGTTYMTG4N5DF72/events.json","paper":"https://pith.science/paper/OET3WD6M"},"agent_actions":{"view_html":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72","download_json":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72.json","view_paper":"https://pith.science/paper/OET3WD6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0402343&json=true","fetch_graph":"https://pith.science/api/pith-number/OET3WD6MSUISGTTYMTG4N5DF72/graph.json","fetch_events":"https://pith.science/api/pith-number/OET3WD6MSUISGTTYMTG4N5DF72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72/action/storage_attestation","attest_author":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72/action/author_attestation","sign_citation":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72/action/citation_signature","submit_replication":"https://pith.science/pith/OET3WD6MSUISGTTYMTG4N5DF72/action/replication_record"}},"created_at":"2026-05-18T01:05:26.562193+00:00","updated_at":"2026-05-18T01:05:26.562193+00:00"}