{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H323VF2LRLPP5Q2VQ6NK77OGUG","short_pith_number":"pith:H323VF2L","canonical_record":{"source":{"id":"1710.03385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T03:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"1bf3400c5e9992afaf87aacf97f9585dc5c00b3395eef2529d7d16299bb729a9","abstract_canon_sha256":"270c2c9679a25d0f9cb9ca1900be1be7b69f36da5bd44e1237299a88bac72902"},"schema_version":"1.0"},"canonical_sha256":"3ef5ba974b8adefec355879aaffdc6a19fa99ea792507bcdd9afeaee6ee80447","source":{"kind":"arxiv","id":"1710.03385","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03385","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03385v1","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03385","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"H323VF2LRLPP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H323VF2LRLPP5Q2V","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H323VF2L","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H323VF2LRLPP5Q2VQ6NK77OGUG","target":"record","payload":{"canonical_record":{"source":{"id":"1710.03385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T03:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"1bf3400c5e9992afaf87aacf97f9585dc5c00b3395eef2529d7d16299bb729a9","abstract_canon_sha256":"270c2c9679a25d0f9cb9ca1900be1be7b69f36da5bd44e1237299a88bac72902"},"schema_version":"1.0"},"canonical_sha256":"3ef5ba974b8adefec355879aaffdc6a19fa99ea792507bcdd9afeaee6ee80447","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:12.110630Z","signature_b64":"t3J6Uy3Yc+mDOk4n3NibGRelLUgd4AYq/f8UxnRIRxgZBwGRluxqfr9Za/kJwCGqdIdsVpK3agwihUR/du/mDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ef5ba974b8adefec355879aaffdc6a19fa99ea792507bcdd9afeaee6ee80447","last_reissued_at":"2026-05-18T00:33:12.110052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:12.110052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.03385","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":"2026-05-18T00:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81/9iETBPu/UrDr/VRvNcB5a3U0WgRhE2ws20AnzMIj8oLaOwlqfThDN7hL60/T0PiGHkQgtp5xJMvSpQDuADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:11:06.104088Z"},"content_sha256":"f85e88a15ecbc6f66b7ae5e26a00e2994d0b1432507f6cd73f7ef207c022d25f","schema_version":"1.0","event_id":"sha256:f85e88a15ecbc6f66b7ae5e26a00e2994d0b1432507f6cd73f7ef207c022d25f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H323VF2LRLPP5Q2VQ6NK77OGUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correspondences in complex dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Siqueira, Luna Lomonaco, Shaun Bullett","submitted_at":"2017-10-10T03:06:34Z","abstract_excerpt":"This paper surveys some recent results concerning the dynamics of two families of holomorphic correspondences, namely ${\\mathcal F}_a:z \\to w$ defined by the relation $$\\left( \\frac{aw-1}{w-1} \\right)^2 + \\left( \\frac{aw-1}{w-1} \\right) \\left( \\frac{az +1}{z+1} \\right) + \\left( \\frac{az+1}{z+1} \\right)^2 =3,$$ and $$\\mathbf{f}_c(z)=z^{\\beta} +c, \\mbox{ where } 1<\\beta=p/q \\in \\mathbb{Q},$$ which is the correspondence $\\mathbf{f}_c:z \\to w$ defined by the relation $$(w-c)^q=z^p.$$ Both can be regarded as generalizations of the family of quadratic maps $f_c(z)=z^2+c$. We describe dynamical prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03385","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":"2026-05-18T00:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HO2XzOZSNbhz/WmTHrJrGdBmoVaBCLVcG/HW8W+wEMdH/3ucuueJQ7cvJuDtvlVODVfl3K71McXk23dtxhahDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:11:06.104451Z"},"content_sha256":"6687f61e88dbd79379818e2fc918fe89786bebb053e8513baa1f9a30dfdfc013","schema_version":"1.0","event_id":"sha256:6687f61e88dbd79379818e2fc918fe89786bebb053e8513baa1f9a30dfdfc013"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H323VF2LRLPP5Q2VQ6NK77OGUG/bundle.json","state_url":"https://pith.science/pith/H323VF2LRLPP5Q2VQ6NK77OGUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H323VF2LRLPP5Q2VQ6NK77OGUG/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":"2026-06-22T11:11:06Z","links":{"resolver":"https://pith.science/pith/H323VF2LRLPP5Q2VQ6NK77OGUG","bundle":"https://pith.science/pith/H323VF2LRLPP5Q2VQ6NK77OGUG/bundle.json","state":"https://pith.science/pith/H323VF2LRLPP5Q2VQ6NK77OGUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H323VF2LRLPP5Q2VQ6NK77OGUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H323VF2LRLPP5Q2VQ6NK77OGUG","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":"270c2c9679a25d0f9cb9ca1900be1be7b69f36da5bd44e1237299a88bac72902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T03:06:34Z","title_canon_sha256":"1bf3400c5e9992afaf87aacf97f9585dc5c00b3395eef2529d7d16299bb729a9"},"schema_version":"1.0","source":{"id":"1710.03385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03385","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03385v1","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03385","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"H323VF2LRLPP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H323VF2LRLPP5Q2V","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H323VF2L","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:6687f61e88dbd79379818e2fc918fe89786bebb053e8513baa1f9a30dfdfc013","target":"graph","created_at":"2026-05-18T00:33:12Z","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":"This paper surveys some recent results concerning the dynamics of two families of holomorphic correspondences, namely ${\\mathcal F}_a:z \\to w$ defined by the relation $$\\left( \\frac{aw-1}{w-1} \\right)^2 + \\left( \\frac{aw-1}{w-1} \\right) \\left( \\frac{az +1}{z+1} \\right) + \\left( \\frac{az+1}{z+1} \\right)^2 =3,$$ and $$\\mathbf{f}_c(z)=z^{\\beta} +c, \\mbox{ where } 1<\\beta=p/q \\in \\mathbb{Q},$$ which is the correspondence $\\mathbf{f}_c:z \\to w$ defined by the relation $$(w-c)^q=z^p.$$ Both can be regarded as generalizations of the family of quadratic maps $f_c(z)=z^2+c$. We describe dynamical prope","authors_text":"Carlos Siqueira, Luna Lomonaco, Shaun Bullett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T03:06:34Z","title":"Correspondences in complex dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03385","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:f85e88a15ecbc6f66b7ae5e26a00e2994d0b1432507f6cd73f7ef207c022d25f","target":"record","created_at":"2026-05-18T00:33:12Z","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":"270c2c9679a25d0f9cb9ca1900be1be7b69f36da5bd44e1237299a88bac72902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T03:06:34Z","title_canon_sha256":"1bf3400c5e9992afaf87aacf97f9585dc5c00b3395eef2529d7d16299bb729a9"},"schema_version":"1.0","source":{"id":"1710.03385","kind":"arxiv","version":1}},"canonical_sha256":"3ef5ba974b8adefec355879aaffdc6a19fa99ea792507bcdd9afeaee6ee80447","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ef5ba974b8adefec355879aaffdc6a19fa99ea792507bcdd9afeaee6ee80447","first_computed_at":"2026-05-18T00:33:12.110052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:12.110052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t3J6Uy3Yc+mDOk4n3NibGRelLUgd4AYq/f8UxnRIRxgZBwGRluxqfr9Za/kJwCGqdIdsVpK3agwihUR/du/mDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:12.110630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f85e88a15ecbc6f66b7ae5e26a00e2994d0b1432507f6cd73f7ef207c022d25f","sha256:6687f61e88dbd79379818e2fc918fe89786bebb053e8513baa1f9a30dfdfc013"],"state_sha256":"e8095c46512aa01f3cb1d14862ec12a34b57d423e285e781ab3dec0092ee4e11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3T2j7cBIYeqy17ziNdUmKnr9bBmRbUOaYaYirXuzdmsADo6yARroUcDvMWGrMe+MmMyTahRXF8Qs6Vc8hmTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:11:06.106480Z","bundle_sha256":"65b6bf7cf8f6f2f17eae1548b6e24054fd4c2a146c2cc696107e13421173488c"}}