{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7SOPFPZYACCHU7GXBRBDAEIREL","short_pith_number":"pith:7SOPFPZY","canonical_record":{"source":{"id":"1503.04704","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-09T02:13:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"8107418d9dda8ca9e4f5f95ae8992ff7845ee13b7f80cc0e69c6be9bc9706480","abstract_canon_sha256":"4e973fe3c77abd1e8e06f4d1002b9f0a3720e03b04aa9359d150344e996df578"},"schema_version":"1.0"},"canonical_sha256":"fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d","source":{"kind":"arxiv","id":"1503.04704","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04704","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04704v3","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04704","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"7SOPFPZYACCH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7SOPFPZYACCHU7GX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7SOPFPZY","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7SOPFPZYACCHU7GXBRBDAEIREL","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04704","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-09T02:13:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"8107418d9dda8ca9e4f5f95ae8992ff7845ee13b7f80cc0e69c6be9bc9706480","abstract_canon_sha256":"4e973fe3c77abd1e8e06f4d1002b9f0a3720e03b04aa9359d150344e996df578"},"schema_version":"1.0"},"canonical_sha256":"fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:59.237164Z","signature_b64":"6x351QycQLS1xEg5388VLgWVK3Sb+qjAK5drchZ1oFatBUtK6PDTL/6lQf7+bbPgLSrZTAQOCJ4BN4I1m5YkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d","last_reissued_at":"2026-05-18T01:20:59.236646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:59.236646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04704","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A9mPVUsvRgmJipVar0leu8WW5A/ng1F0MI1mWlMgfjvE1Y0hZLRpLB+xTU+gH0XHHeAqCsdIzGKmcbb1UfouAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:53:30.943325Z"},"content_sha256":"5fa125172b8bd60141be6e5f79f90f23b62392d87423bb334f931803c51d6206","schema_version":"1.0","event_id":"sha256:5fa125172b8bd60141be6e5f79f90f23b62392d87423bb334f931803c51d6206"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7SOPFPZYACCHU7GXBRBDAEIREL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Applications of Brouwer's Fixed Point Theorem: in Insurance and in Biology Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Muhamed Borogovac","submitted_at":"2015-03-09T02:13:09Z","abstract_excerpt":"In the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation $\\varphi $ of a d-dimensional $(d \\ge 2)$ Euclidean space is introduced that enables us to express the system in the form $f^{t+1}:=\\varphi (f^t),\\, t=0,\\, 1,\\, 2,\\, \\ldots $. Under typical actuarial assumptions, existence of solutions of that system is proven by means of Brouwer's fixed point theorem in normed spaces. In addition, conditions that guarantee uniqueness of a solution are given. The second, smalle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04704","kind":"arxiv","version":3},"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":"2026-05-18T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xL0fTy5X4VS0r1HZgiDwVtYN7vTvE4rvYrqhIstihcl+FYlcP96oz6qCMoTPdxUq3rgLbMd/wRfJCTCgCEODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:53:30.943680Z"},"content_sha256":"acddfa7f16a5cd602e2c2385fbc722a81db1ecd760f44dbd9d773bb5c66a8138","schema_version":"1.0","event_id":"sha256:acddfa7f16a5cd602e2c2385fbc722a81db1ecd760f44dbd9d773bb5c66a8138"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SOPFPZYACCHU7GXBRBDAEIREL/bundle.json","state_url":"https://pith.science/pith/7SOPFPZYACCHU7GXBRBDAEIREL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SOPFPZYACCHU7GXBRBDAEIREL/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":"2026-06-25T11:53:30Z","links":{"resolver":"https://pith.science/pith/7SOPFPZYACCHU7GXBRBDAEIREL","bundle":"https://pith.science/pith/7SOPFPZYACCHU7GXBRBDAEIREL/bundle.json","state":"https://pith.science/pith/7SOPFPZYACCHU7GXBRBDAEIREL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SOPFPZYACCHU7GXBRBDAEIREL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7SOPFPZYACCHU7GXBRBDAEIREL","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":"4e973fe3c77abd1e8e06f4d1002b9f0a3720e03b04aa9359d150344e996df578","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-09T02:13:09Z","title_canon_sha256":"8107418d9dda8ca9e4f5f95ae8992ff7845ee13b7f80cc0e69c6be9bc9706480"},"schema_version":"1.0","source":{"id":"1503.04704","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04704","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04704v3","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04704","created_at":"2026-05-18T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"7SOPFPZYACCH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7SOPFPZYACCHU7GX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7SOPFPZY","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:acddfa7f16a5cd602e2c2385fbc722a81db1ecd760f44dbd9d773bb5c66a8138","target":"graph","created_at":"2026-05-18T01:20:59Z","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 the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation $\\varphi $ of a d-dimensional $(d \\ge 2)$ Euclidean space is introduced that enables us to express the system in the form $f^{t+1}:=\\varphi (f^t),\\, t=0,\\, 1,\\, 2,\\, \\ldots $. Under typical actuarial assumptions, existence of solutions of that system is proven by means of Brouwer's fixed point theorem in normed spaces. In addition, conditions that guarantee uniqueness of a solution are given. The second, smalle","authors_text":"Muhamed Borogovac","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-09T02:13:09Z","title":"Two Applications of Brouwer's Fixed Point Theorem: in Insurance and in Biology Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04704","kind":"arxiv","version":3},"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":"sha256:5fa125172b8bd60141be6e5f79f90f23b62392d87423bb334f931803c51d6206","target":"record","created_at":"2026-05-18T01:20:59Z","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":"4e973fe3c77abd1e8e06f4d1002b9f0a3720e03b04aa9359d150344e996df578","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-09T02:13:09Z","title_canon_sha256":"8107418d9dda8ca9e4f5f95ae8992ff7845ee13b7f80cc0e69c6be9bc9706480"},"schema_version":"1.0","source":{"id":"1503.04704","kind":"arxiv","version":3}},"canonical_sha256":"fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d","first_computed_at":"2026-05-18T01:20:59.236646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:59.236646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6x351QycQLS1xEg5388VLgWVK3Sb+qjAK5drchZ1oFatBUtK6PDTL/6lQf7+bbPgLSrZTAQOCJ4BN4I1m5YkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:59.237164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04704","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa125172b8bd60141be6e5f79f90f23b62392d87423bb334f931803c51d6206","sha256:acddfa7f16a5cd602e2c2385fbc722a81db1ecd760f44dbd9d773bb5c66a8138"],"state_sha256":"b1833a6e1abc07e968e3c46cdaf240fd2cce6a903720e45163af02c658bf5989"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3HQGlpzDeWiHi+jCK7QffpZYnqmqFDrh1BK6zaVBbGn6Y2MR2Hve++iio4oVNjksZW5w2Npxpqaf2WN9XC6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:53:30.945667Z","bundle_sha256":"ab7293bbd103527c163c97c6bdb3fb84314751631fa40138e080f7d81a07110f"}}