{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZA6SO72VKZVTD42PFFGRWF2V3V","short_pith_number":"pith:ZA6SO72V","canonical_record":{"source":{"id":"1309.5682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-23T02:10:42Z","cross_cats_sorted":[],"title_canon_sha256":"7050f9f6f932a6a560e829f7c5de7ad7d08c1268ca071450e3b032940063ad0d","abstract_canon_sha256":"829356804eecc7d6339c42bb779e507bf02012a72374b96a7cfe7455e7bff8fb"},"schema_version":"1.0"},"canonical_sha256":"c83d277f55566b31f34f294d1b1755dd66357c46155cdd449b57a35899a8ae15","source":{"kind":"arxiv","id":"1309.5682","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5682","created_at":"2026-05-18T03:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5682v1","created_at":"2026-05-18T03:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5682","created_at":"2026-05-18T03:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZA6SO72VKZVT","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZA6SO72VKZVTD42P","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZA6SO72V","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZA6SO72VKZVTD42PFFGRWF2V3V","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-23T02:10:42Z","cross_cats_sorted":[],"title_canon_sha256":"7050f9f6f932a6a560e829f7c5de7ad7d08c1268ca071450e3b032940063ad0d","abstract_canon_sha256":"829356804eecc7d6339c42bb779e507bf02012a72374b96a7cfe7455e7bff8fb"},"schema_version":"1.0"},"canonical_sha256":"c83d277f55566b31f34f294d1b1755dd66357c46155cdd449b57a35899a8ae15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:34.508235Z","signature_b64":"n2knWk7LITNBj0609SPWdTioMYJZSYHknm7yrS70q1/FGkC1c9v708zvyWXV0hNEeqwtGM3quUhz5qqIms/JCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c83d277f55566b31f34f294d1b1755dd66357c46155cdd449b57a35899a8ae15","last_reissued_at":"2026-05-18T03:12:34.507432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:34.507432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5682","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":"2026-05-18T03:12:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ZTsdwkV8J7ZHTyYP5djSrzT0o8LxdC0Kt422E88+rZRTAvyQ9lwKRfZ7ltO+JKqM4+u5Ox3s7CdGzlzL/i1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:41:34.829766Z"},"content_sha256":"cd223593b7be5fa531aa75a735e9dc6cbb70e06c933c6779e4adc36219c56cc1","schema_version":"1.0","event_id":"sha256:cd223593b7be5fa531aa75a735e9dc6cbb70e06c933c6779e4adc36219c56cc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZA6SO72VKZVTD42PFFGRWF2V3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variation of the canonical height in a family of rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Niki Myrto Mavraki","submitted_at":"2013-09-23T02:10:42Z","abstract_excerpt":"Let $d\\ge 2$ be an integer, let $c(t)$ be any rational map, and let $f_t(z) := (z^d+t)/z$ be a family of rational maps indexed by t. For each algebraic number $t$, we let $h_{f_t}(c(t))$ be the canonical height of $c(t)$ with respect to the rational map $f_t$. We prove that the map $H(t):=h_{f_t}(c(t))$ (as $t$ varies among the algebraic numbers) is a Weil height."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5682","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":"2026-05-18T03:12:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWLyriXSv4yFrmv6SEXZo++9/l3t0EIX7liy3TfqzRhuwxELK6PQoqpm/IsSBJJy7X+GSHJKEM2DdRZ2dBU5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:41:34.830092Z"},"content_sha256":"3bd3b2ccc79713670d771303838fee52ba5caa4c11b6edd0e720c8e5c41cabf5","schema_version":"1.0","event_id":"sha256:3bd3b2ccc79713670d771303838fee52ba5caa4c11b6edd0e720c8e5c41cabf5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZA6SO72VKZVTD42PFFGRWF2V3V/bundle.json","state_url":"https://pith.science/pith/ZA6SO72VKZVTD42PFFGRWF2V3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZA6SO72VKZVTD42PFFGRWF2V3V/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":"2026-06-19T23:41:34Z","links":{"resolver":"https://pith.science/pith/ZA6SO72VKZVTD42PFFGRWF2V3V","bundle":"https://pith.science/pith/ZA6SO72VKZVTD42PFFGRWF2V3V/bundle.json","state":"https://pith.science/pith/ZA6SO72VKZVTD42PFFGRWF2V3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZA6SO72VKZVTD42PFFGRWF2V3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZA6SO72VKZVTD42PFFGRWF2V3V","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":"829356804eecc7d6339c42bb779e507bf02012a72374b96a7cfe7455e7bff8fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-23T02:10:42Z","title_canon_sha256":"7050f9f6f932a6a560e829f7c5de7ad7d08c1268ca071450e3b032940063ad0d"},"schema_version":"1.0","source":{"id":"1309.5682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5682","created_at":"2026-05-18T03:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5682v1","created_at":"2026-05-18T03:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5682","created_at":"2026-05-18T03:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZA6SO72VKZVT","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZA6SO72VKZVTD42P","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZA6SO72V","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:3bd3b2ccc79713670d771303838fee52ba5caa4c11b6edd0e720c8e5c41cabf5","target":"graph","created_at":"2026-05-18T03:12:34Z","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":"Let $d\\ge 2$ be an integer, let $c(t)$ be any rational map, and let $f_t(z) := (z^d+t)/z$ be a family of rational maps indexed by t. For each algebraic number $t$, we let $h_{f_t}(c(t))$ be the canonical height of $c(t)$ with respect to the rational map $f_t$. We prove that the map $H(t):=h_{f_t}(c(t))$ (as $t$ varies among the algebraic numbers) is a Weil height.","authors_text":"Dragos Ghioca, Niki Myrto Mavraki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-23T02:10:42Z","title":"Variation of the canonical height in a family of rational maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5682","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:cd223593b7be5fa531aa75a735e9dc6cbb70e06c933c6779e4adc36219c56cc1","target":"record","created_at":"2026-05-18T03:12:34Z","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":"829356804eecc7d6339c42bb779e507bf02012a72374b96a7cfe7455e7bff8fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-23T02:10:42Z","title_canon_sha256":"7050f9f6f932a6a560e829f7c5de7ad7d08c1268ca071450e3b032940063ad0d"},"schema_version":"1.0","source":{"id":"1309.5682","kind":"arxiv","version":1}},"canonical_sha256":"c83d277f55566b31f34f294d1b1755dd66357c46155cdd449b57a35899a8ae15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c83d277f55566b31f34f294d1b1755dd66357c46155cdd449b57a35899a8ae15","first_computed_at":"2026-05-18T03:12:34.507432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:34.507432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n2knWk7LITNBj0609SPWdTioMYJZSYHknm7yrS70q1/FGkC1c9v708zvyWXV0hNEeqwtGM3quUhz5qqIms/JCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:34.508235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd223593b7be5fa531aa75a735e9dc6cbb70e06c933c6779e4adc36219c56cc1","sha256:3bd3b2ccc79713670d771303838fee52ba5caa4c11b6edd0e720c8e5c41cabf5"],"state_sha256":"01b47082302a764cd5819501224810817f05069096e4820c2da95433e0414dc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z1ppCb+P8a4POSVCrKKvLSPxoaTLh94DYszyi1bXDOLGSyTIIwL46Ext6cHhGp8LM6rDEKIq1exTzU4fnRxiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:41:34.831914Z","bundle_sha256":"7e31a5ca4e05269ed9259213d41c1a5699f4d5ec3307cc7e90a96f69bbb9cea8"}}