{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PGWWFLI3H4R46XRXIMCFMDVMLD","short_pith_number":"pith:PGWWFLI3","canonical_record":{"source":{"id":"1411.7896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-11-28T15:11:20Z","cross_cats_sorted":["q-bio.CB"],"title_canon_sha256":"2880a3bc3c42a770c3669c8ec6a58604c6ae329e074bad4299257bfa207134b2","abstract_canon_sha256":"1714dbc5aed1850e627581d99789e5f856712793209e50b26370bc1260a7d179"},"schema_version":"1.0"},"canonical_sha256":"79ad62ad1b3f23cf5e374304560eac58f3649e3010e845577a5860dd1f5de16a","source":{"kind":"arxiv","id":"1411.7896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7896","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7896v1","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7896","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"PGWWFLI3H4R4","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PGWWFLI3H4R46XRX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PGWWFLI3","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PGWWFLI3H4R46XRXIMCFMDVMLD","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-11-28T15:11:20Z","cross_cats_sorted":["q-bio.CB"],"title_canon_sha256":"2880a3bc3c42a770c3669c8ec6a58604c6ae329e074bad4299257bfa207134b2","abstract_canon_sha256":"1714dbc5aed1850e627581d99789e5f856712793209e50b26370bc1260a7d179"},"schema_version":"1.0"},"canonical_sha256":"79ad62ad1b3f23cf5e374304560eac58f3649e3010e845577a5860dd1f5de16a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:37.029699Z","signature_b64":"KS35B7fNwBaYFV2aEVxseSIfPIxf2x1Ow/zSc+HVvAm6rQc8G53jvgWyKah6pqOUoqDPMkaJtNxM5WoZIeTfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79ad62ad1b3f23cf5e374304560eac58f3649e3010e845577a5860dd1f5de16a","last_reissued_at":"2026-05-18T02:32:37.029285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:37.029285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7896","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":"2026-05-18T02:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlVyaza3pRv9RLo0AfvsDVjhKFy08a7nchnqKt6/gNHIa+GUet8xblfiayuVWLQTsgESjVTQ06bYB9PPc/ydDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:01:34.654811Z"},"content_sha256":"4d65764c29d38868c112b17a60002ffd654090b5bf0d35621fe40b41e5d0d614","schema_version":"1.0","event_id":"sha256:4d65764c29d38868c112b17a60002ffd654090b5bf0d35621fe40b41e5d0d614"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PGWWFLI3H4R46XRXIMCFMDVMLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.CB"],"primary_cat":"nlin.CD","authors_text":"Carla Rodrigues, Cristina Janu\\'ario, Gabriel Gil-G\\'omez, Jorge Duarte, Josep Sardany\\'es, Nuno Martins","submitted_at":"2014-11-28T15:11:20Z","abstract_excerpt":"In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems - the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7896","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":"2026-05-18T02:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3clRSRbZ1Rze+dhAhsmYg5B5rx6GRC4G5q37rH78v0Mb6pt60qdUO0rrPAkv3wCErtRCajTEA8VXix1e2MdHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:01:34.655459Z"},"content_sha256":"4d53317346a6e4a2a91ba9cbaa813537e3d5973a6d55bf233e57b1cd0a7aed58","schema_version":"1.0","event_id":"sha256:4d53317346a6e4a2a91ba9cbaa813537e3d5973a6d55bf233e57b1cd0a7aed58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGWWFLI3H4R46XRXIMCFMDVMLD/bundle.json","state_url":"https://pith.science/pith/PGWWFLI3H4R46XRXIMCFMDVMLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGWWFLI3H4R46XRXIMCFMDVMLD/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":"2026-05-31T15:01:34Z","links":{"resolver":"https://pith.science/pith/PGWWFLI3H4R46XRXIMCFMDVMLD","bundle":"https://pith.science/pith/PGWWFLI3H4R46XRXIMCFMDVMLD/bundle.json","state":"https://pith.science/pith/PGWWFLI3H4R46XRXIMCFMDVMLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGWWFLI3H4R46XRXIMCFMDVMLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PGWWFLI3H4R46XRXIMCFMDVMLD","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":"1714dbc5aed1850e627581d99789e5f856712793209e50b26370bc1260a7d179","cross_cats_sorted":["q-bio.CB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-11-28T15:11:20Z","title_canon_sha256":"2880a3bc3c42a770c3669c8ec6a58604c6ae329e074bad4299257bfa207134b2"},"schema_version":"1.0","source":{"id":"1411.7896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7896","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7896v1","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7896","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"PGWWFLI3H4R4","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PGWWFLI3H4R46XRX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PGWWFLI3","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:4d53317346a6e4a2a91ba9cbaa813537e3d5973a6d55bf233e57b1cd0a7aed58","target":"graph","created_at":"2026-05-18T02:32:37Z","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":"In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems - the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, sho","authors_text":"Carla Rodrigues, Cristina Janu\\'ario, Gabriel Gil-G\\'omez, Jorge Duarte, Josep Sardany\\'es, Nuno Martins","cross_cats":["q-bio.CB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-11-28T15:11:20Z","title":"Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7896","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":"sha256:4d65764c29d38868c112b17a60002ffd654090b5bf0d35621fe40b41e5d0d614","target":"record","created_at":"2026-05-18T02:32:37Z","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":"1714dbc5aed1850e627581d99789e5f856712793209e50b26370bc1260a7d179","cross_cats_sorted":["q-bio.CB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-11-28T15:11:20Z","title_canon_sha256":"2880a3bc3c42a770c3669c8ec6a58604c6ae329e074bad4299257bfa207134b2"},"schema_version":"1.0","source":{"id":"1411.7896","kind":"arxiv","version":1}},"canonical_sha256":"79ad62ad1b3f23cf5e374304560eac58f3649e3010e845577a5860dd1f5de16a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79ad62ad1b3f23cf5e374304560eac58f3649e3010e845577a5860dd1f5de16a","first_computed_at":"2026-05-18T02:32:37.029285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:37.029285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KS35B7fNwBaYFV2aEVxseSIfPIxf2x1Ow/zSc+HVvAm6rQc8G53jvgWyKah6pqOUoqDPMkaJtNxM5WoZIeTfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:37.029699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d65764c29d38868c112b17a60002ffd654090b5bf0d35621fe40b41e5d0d614","sha256:4d53317346a6e4a2a91ba9cbaa813537e3d5973a6d55bf233e57b1cd0a7aed58"],"state_sha256":"b595ad5b35b51f6d93aee95164836efb8c7341b8b80d86ec5344265cfb496d2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n3dWxjupbrCplBr9ksQIRTlVYgxVtLbsw5mZUB/ZdTsWCE4CD41QcbRk0ohi5WaViYbzb4wEga/3KBjSKFF/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:01:34.658998Z","bundle_sha256":"63bff3ad8c5531538491e8f286c948816a7fd5d3322ac0c6fcc26d3b14de6abe"}}