{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NHG3WL2I7VJU66ANHV5UV3MTDB","short_pith_number":"pith:NHG3WL2I","canonical_record":{"source":{"id":"1305.0867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-04T02:01:08Z","cross_cats_sorted":[],"title_canon_sha256":"e9d9d030191613d494881129257d6c6b280dc7ded9ab2d4b792ae652140e502a","abstract_canon_sha256":"ff27d02f5633c0a2f313c9e77173a93f7280192c50888f3896918493bd87ffb4"},"schema_version":"1.0"},"canonical_sha256":"69cdbb2f48fd534f780d3d7b4aed93187c135a0cdcc67df84b6684c3f5fe8bda","source":{"kind":"arxiv","id":"1305.0867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0867","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0867v1","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0867","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"NHG3WL2I7VJU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NHG3WL2I7VJU66AN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NHG3WL2I","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NHG3WL2I7VJU66ANHV5UV3MTDB","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-04T02:01:08Z","cross_cats_sorted":[],"title_canon_sha256":"e9d9d030191613d494881129257d6c6b280dc7ded9ab2d4b792ae652140e502a","abstract_canon_sha256":"ff27d02f5633c0a2f313c9e77173a93f7280192c50888f3896918493bd87ffb4"},"schema_version":"1.0"},"canonical_sha256":"69cdbb2f48fd534f780d3d7b4aed93187c135a0cdcc67df84b6684c3f5fe8bda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:35.649374Z","signature_b64":"r5c7ElZF0q/q/MDFZp1jqO9ew9BdHBSveKXeu1vLiMlONIrkT/RYkRQ1ROaQT0yTTCLDyEqh8GQeimEfs3LDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69cdbb2f48fd534f780d3d7b4aed93187c135a0cdcc67df84b6684c3f5fe8bda","last_reissued_at":"2026-05-17T23:53:35.648670Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:35.648670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0867","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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+V12CCxdU9mRxhpVzXuKc3lgpYxFQqheKQaI8ukw7iaGBuvGc5J1jSxEtU+AR+uu4Eee5F2uSH8bNmq9X5ezAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:44:50.158353Z"},"content_sha256":"f7218495cdbeed0010dcbcf113177fece4a7c614d92f31967bfc83c4dcd01295","schema_version":"1.0","event_id":"sha256:f7218495cdbeed0010dcbcf113177fece4a7c614d92f31967bfc83c4dcd01295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NHG3WL2I7VJU66ANHV5UV3MTDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Igors Gorbovickis","submitted_at":"2013-05-04T02:01:08Z","abstract_excerpt":"We consider a space of complex polynomials of degree $n\\ge 3$ with $n-1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebraic functions on that space, are algebraically independent over the field of complex numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0867","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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvgdXbKJMT9HCaAXicgMMUd4aZXys1O0Ue6n9UDGPt4FR94B0+ASJHxob9kT3j60/fkgVettSPSTbv26PMs0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:44:50.159030Z"},"content_sha256":"2eec4f4f7bc6416519dd488533b92a4497322db1f27ea6b6dbcf9a7d35a492d6","schema_version":"1.0","event_id":"sha256:2eec4f4f7bc6416519dd488533b92a4497322db1f27ea6b6dbcf9a7d35a492d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHG3WL2I7VJU66ANHV5UV3MTDB/bundle.json","state_url":"https://pith.science/pith/NHG3WL2I7VJU66ANHV5UV3MTDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHG3WL2I7VJU66ANHV5UV3MTDB/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":"2026-06-11T00:44:50Z","links":{"resolver":"https://pith.science/pith/NHG3WL2I7VJU66ANHV5UV3MTDB","bundle":"https://pith.science/pith/NHG3WL2I7VJU66ANHV5UV3MTDB/bundle.json","state":"https://pith.science/pith/NHG3WL2I7VJU66ANHV5UV3MTDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHG3WL2I7VJU66ANHV5UV3MTDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NHG3WL2I7VJU66ANHV5UV3MTDB","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":"ff27d02f5633c0a2f313c9e77173a93f7280192c50888f3896918493bd87ffb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-04T02:01:08Z","title_canon_sha256":"e9d9d030191613d494881129257d6c6b280dc7ded9ab2d4b792ae652140e502a"},"schema_version":"1.0","source":{"id":"1305.0867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0867","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0867v1","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0867","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"NHG3WL2I7VJU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NHG3WL2I7VJU66AN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NHG3WL2I","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:2eec4f4f7bc6416519dd488533b92a4497322db1f27ea6b6dbcf9a7d35a492d6","target":"graph","created_at":"2026-05-17T23:53:35Z","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":"We consider a space of complex polynomials of degree $n\\ge 3$ with $n-1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebraic functions on that space, are algebraically independent over the field of complex numbers.","authors_text":"Igors Gorbovickis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-04T02:01:08Z","title":"Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0867","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:f7218495cdbeed0010dcbcf113177fece4a7c614d92f31967bfc83c4dcd01295","target":"record","created_at":"2026-05-17T23:53:35Z","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":"ff27d02f5633c0a2f313c9e77173a93f7280192c50888f3896918493bd87ffb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-04T02:01:08Z","title_canon_sha256":"e9d9d030191613d494881129257d6c6b280dc7ded9ab2d4b792ae652140e502a"},"schema_version":"1.0","source":{"id":"1305.0867","kind":"arxiv","version":1}},"canonical_sha256":"69cdbb2f48fd534f780d3d7b4aed93187c135a0cdcc67df84b6684c3f5fe8bda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69cdbb2f48fd534f780d3d7b4aed93187c135a0cdcc67df84b6684c3f5fe8bda","first_computed_at":"2026-05-17T23:53:35.648670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:35.648670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r5c7ElZF0q/q/MDFZp1jqO9ew9BdHBSveKXeu1vLiMlONIrkT/RYkRQ1ROaQT0yTTCLDyEqh8GQeimEfs3LDDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:35.649374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7218495cdbeed0010dcbcf113177fece4a7c614d92f31967bfc83c4dcd01295","sha256:2eec4f4f7bc6416519dd488533b92a4497322db1f27ea6b6dbcf9a7d35a492d6"],"state_sha256":"e27590c69299311a1b0218ac462f1324574596b5c61ec579967b00a3991308d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/yg/+R6IiQrMphL8gbH2QcLQrqKA3LCOcqTDmBbmte+rBxNkT1VeS3su4br6azn4kKT5uMYyWajo48pc8JAzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:44:50.163275Z","bundle_sha256":"90efa07e77af01a767088d8f713b413a32d6401f9ebf8a5b2b7d06d608a96cf6"}}