{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KEQYCJCPIIVGLC5PXAIWWHWCOJ","short_pith_number":"pith:KEQYCJCP","canonical_record":{"source":{"id":"1905.06364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2019-05-15T18:13:24Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"e1363ed5eb49f75b0478e50be75916073f1316754af394f1b6df516245475e30","abstract_canon_sha256":"842b644d367b84f697f99042f3908a52db8955af373ec9775d70c22c2844d23e"},"schema_version":"1.0"},"canonical_sha256":"512181244f422a658bafb8116b1ec27272f2fb667216a5e770c5fe1b413d9f4f","source":{"kind":"arxiv","id":"1905.06364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06364","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06364v1","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06364","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"KEQYCJCPIIVG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KEQYCJCPIIVGLC5P","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KEQYCJCP","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KEQYCJCPIIVGLC5PXAIWWHWCOJ","target":"record","payload":{"canonical_record":{"source":{"id":"1905.06364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2019-05-15T18:13:24Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"e1363ed5eb49f75b0478e50be75916073f1316754af394f1b6df516245475e30","abstract_canon_sha256":"842b644d367b84f697f99042f3908a52db8955af373ec9775d70c22c2844d23e"},"schema_version":"1.0"},"canonical_sha256":"512181244f422a658bafb8116b1ec27272f2fb667216a5e770c5fe1b413d9f4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:02.643502Z","signature_b64":"C6SoFtzpyw2bQbrxfUCyfhJplUbouC4m+m8tgHtLG93nrzW7slfCJblRSOtp/xmcDO53G4d2WPNefVJXGOAUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512181244f422a658bafb8116b1ec27272f2fb667216a5e770c5fe1b413d9f4f","last_reissued_at":"2026-05-17T23:46:02.641848Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:02.641848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.06364","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":"2026-05-17T23:46:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdYrBSmtPuuTeMiA4D5bZspBg7OSKJMtTcHbmymmPJwEDH4DuPEwimcRmKd5t8cp1jn1qaYFTon3LkCYq0a7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:49:37.948829Z"},"content_sha256":"6c38dbbbfd70752aa7a84c98aed9320a66c6e492a58e91ec33480ad093267f3d","schema_version":"1.0","event_id":"sha256:6c38dbbbfd70752aa7a84c98aed9320a66c6e492a58e91ec33480ad093267f3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KEQYCJCPIIVGLC5PXAIWWHWCOJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic model of firms competitive interaction on the market with taxation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"q-fin.GN","authors_text":"Andrey Shulga, Eduard Abramyan, Oleg Malafeyev","submitted_at":"2019-05-15T18:13:24Z","abstract_excerpt":"In this article three models of firms interaction on the market are described. One of these models is described by using a differential equation and by Lotka-Volterra model, where the equation has a different form. Also, there are models of non-competing and competing firms. The article presents an algorithm for solving the interaction of competing firms in taxation and the calculation of a compromise point. Besides, the article presents a compromise between the interests of a state and an enterprise."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06364","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":"2026-05-17T23:46:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/gz/oJxnMPOC96pqVHqYt796x/bCEprQBW6WmhRBxByyQx9yz3chPG2FsXAUq6Pf06t4wXLAkTJRVZ9m/t7DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:49:37.949557Z"},"content_sha256":"1f38a2a0fce24ae402a0d5a59ff524cefef615b120972cd62fa139fca68cbd33","schema_version":"1.0","event_id":"sha256:1f38a2a0fce24ae402a0d5a59ff524cefef615b120972cd62fa139fca68cbd33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ/bundle.json","state_url":"https://pith.science/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ/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":"2026-06-06T12:49:37Z","links":{"resolver":"https://pith.science/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ","bundle":"https://pith.science/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ/bundle.json","state":"https://pith.science/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEQYCJCPIIVGLC5PXAIWWHWCOJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KEQYCJCPIIVGLC5PXAIWWHWCOJ","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":"842b644d367b84f697f99042f3908a52db8955af373ec9775d70c22c2844d23e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2019-05-15T18:13:24Z","title_canon_sha256":"e1363ed5eb49f75b0478e50be75916073f1316754af394f1b6df516245475e30"},"schema_version":"1.0","source":{"id":"1905.06364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06364","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06364v1","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06364","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"KEQYCJCPIIVG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KEQYCJCPIIVGLC5P","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KEQYCJCP","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:1f38a2a0fce24ae402a0d5a59ff524cefef615b120972cd62fa139fca68cbd33","target":"graph","created_at":"2026-05-17T23:46:02Z","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 three models of firms interaction on the market are described. One of these models is described by using a differential equation and by Lotka-Volterra model, where the equation has a different form. Also, there are models of non-competing and competing firms. The article presents an algorithm for solving the interaction of competing firms in taxation and the calculation of a compromise point. Besides, the article presents a compromise between the interests of a state and an enterprise.","authors_text":"Andrey Shulga, Eduard Abramyan, Oleg Malafeyev","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2019-05-15T18:13:24Z","title":"Dynamic model of firms competitive interaction on the market with taxation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06364","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":"sha256:6c38dbbbfd70752aa7a84c98aed9320a66c6e492a58e91ec33480ad093267f3d","target":"record","created_at":"2026-05-17T23:46:02Z","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":"842b644d367b84f697f99042f3908a52db8955af373ec9775d70c22c2844d23e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2019-05-15T18:13:24Z","title_canon_sha256":"e1363ed5eb49f75b0478e50be75916073f1316754af394f1b6df516245475e30"},"schema_version":"1.0","source":{"id":"1905.06364","kind":"arxiv","version":1}},"canonical_sha256":"512181244f422a658bafb8116b1ec27272f2fb667216a5e770c5fe1b413d9f4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"512181244f422a658bafb8116b1ec27272f2fb667216a5e770c5fe1b413d9f4f","first_computed_at":"2026-05-17T23:46:02.641848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:02.641848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6SoFtzpyw2bQbrxfUCyfhJplUbouC4m+m8tgHtLG93nrzW7slfCJblRSOtp/xmcDO53G4d2WPNefVJXGOAUDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:02.643502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c38dbbbfd70752aa7a84c98aed9320a66c6e492a58e91ec33480ad093267f3d","sha256:1f38a2a0fce24ae402a0d5a59ff524cefef615b120972cd62fa139fca68cbd33"],"state_sha256":"7948e1999925bbc09342490f4ab1a6b8c309b1de5c9d7480bb49290f129806ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9QgoEq4t8zc6F6zDVPinJ58MOPrES3zi3d8SUoR/4dQII9I4wg++K7ssAMTNt28mtQYzZFrzuX9tKehT0gsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:49:37.953621Z","bundle_sha256":"68710f060e1a1451ba21e24b803d8d57f133a1b4d7e24ced8cadb8b60570c677"}}