{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:FNSE6ECGFX7YVDRWFO74F7E6M4","short_pith_number":"pith:FNSE6ECG","schema_version":"1.0","canonical_sha256":"2b644f10462dff8a8e362bbfc2fc9e673172c6eb0afd9dd58b225d07bae57841","source":{"kind":"arxiv","id":"0808.3352","version":1},"attestation_state":"computed","paper":{"title":"A stochastic model for tumor growth with immunization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.CB","authors_text":"Steffen Trimper, Thomas Bose","submitted_at":"2008-08-25T13:24:26Z","abstract_excerpt":"We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution Ps is derived depending "},"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":"0808.3352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.CB","submitted_at":"2008-08-25T13:24:26Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"be31c1524b9b17440c5188b4524246156985803a896d8273a17bb978b235f4fa","abstract_canon_sha256":"bb8ba2798db1e5a8fe07d167aee890a6910f73b3c078f120a58a8316c96c88eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:42.796992Z","signature_b64":"wx03jRQh7VPvTwH6hU42zTAFwmYO79oiw8B+JTc2P8iwtJhd8Qe83tGlYaXaRwYfRUs3WW6oENg6dR1YIOshBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b644f10462dff8a8e362bbfc2fc9e673172c6eb0afd9dd58b225d07bae57841","last_reissued_at":"2026-05-18T02:15:42.796347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:42.796347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stochastic model for tumor growth with immunization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.CB","authors_text":"Steffen Trimper, Thomas Bose","submitted_at":"2008-08-25T13:24:26Z","abstract_excerpt":"We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution Ps is derived depending "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3352","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":"0808.3352","created_at":"2026-05-18T02:15:42.796452+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.3352v1","created_at":"2026-05-18T02:15:42.796452+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3352","created_at":"2026-05-18T02:15:42.796452+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNSE6ECGFX7Y","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNSE6ECGFX7YVDRW","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNSE6ECG","created_at":"2026-05-18T12:25:57.157939+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/FNSE6ECGFX7YVDRWFO74F7E6M4","json":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4.json","graph_json":"https://pith.science/api/pith-number/FNSE6ECGFX7YVDRWFO74F7E6M4/graph.json","events_json":"https://pith.science/api/pith-number/FNSE6ECGFX7YVDRWFO74F7E6M4/events.json","paper":"https://pith.science/paper/FNSE6ECG"},"agent_actions":{"view_html":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4","download_json":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4.json","view_paper":"https://pith.science/paper/FNSE6ECG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.3352&json=true","fetch_graph":"https://pith.science/api/pith-number/FNSE6ECGFX7YVDRWFO74F7E6M4/graph.json","fetch_events":"https://pith.science/api/pith-number/FNSE6ECGFX7YVDRWFO74F7E6M4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4/action/storage_attestation","attest_author":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4/action/author_attestation","sign_citation":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4/action/citation_signature","submit_replication":"https://pith.science/pith/FNSE6ECGFX7YVDRWFO74F7E6M4/action/replication_record"}},"created_at":"2026-05-18T02:15:42.796452+00:00","updated_at":"2026-05-18T02:15:42.796452+00:00"}