{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FPV2GEHAWMXGXDVRQAACO32GLG","short_pith_number":"pith:FPV2GEHA","canonical_record":{"source":{"id":"1601.03033","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-12T20:54:16Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d695206b2e0d30eea5b5b5a8dbfe48bae65bb8efbc8502af5385848cecbfe664","abstract_canon_sha256":"f0179b11d412507688a7d61f04947b2fda74ba8519e126436e1720b55460ece5"},"schema_version":"1.0"},"canonical_sha256":"2beba310e0b32e6b8eb18000276f4659b86b2eab886be69c3c5e5bd2c36bd4eb","source":{"kind":"arxiv","id":"1601.03033","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03033","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03033v3","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03033","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"FPV2GEHAWMXG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FPV2GEHAWMXGXDVR","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FPV2GEHA","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FPV2GEHAWMXGXDVRQAACO32GLG","target":"record","payload":{"canonical_record":{"source":{"id":"1601.03033","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-12T20:54:16Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d695206b2e0d30eea5b5b5a8dbfe48bae65bb8efbc8502af5385848cecbfe664","abstract_canon_sha256":"f0179b11d412507688a7d61f04947b2fda74ba8519e126436e1720b55460ece5"},"schema_version":"1.0"},"canonical_sha256":"2beba310e0b32e6b8eb18000276f4659b86b2eab886be69c3c5e5bd2c36bd4eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:21.141609Z","signature_b64":"yOD57yNLDYXniiVxmYhsHXRaUQILt/hyi1gl5oegrX5LY0pQJRMLVx4IxWXVEsLCRlbfpCzFtDFOAAethv/1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2beba310e0b32e6b8eb18000276f4659b86b2eab886be69c3c5e5bd2c36bd4eb","last_reissued_at":"2026-05-18T00:46:21.141106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:21.141106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.03033","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":"2026-05-18T00:46:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fH+0kvNDzsU4P4D7mlhqPS2viMIFVsP3XSCm5f27qk0VJNcvkX3Bg9geZTfSxWn77BUoepG4flJNiWvkQkdXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:57:28.975981Z"},"content_sha256":"63c125f1a03ef3592da982d39c1c6e7a4a7e8a704d2105fc0f9e795b4b273837","schema_version":"1.0","event_id":"sha256:63c125f1a03ef3592da982d39c1c6e7a4a7e8a704d2105fc0f9e795b4b273837"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FPV2GEHAWMXGXDVRQAACO32GLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Points of bounded height on oscillatory sets","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Chris Miller, Georges Comte","submitted_at":"2016-01-12T20:54:16Z","abstract_excerpt":"We show that transcendental curves in $\\mathbb R^n$ (not necessarily compact) have few rational points of bounded height provided that the curves are well behaved with respect to algebraic sets in a certain sense and can be parametrized by functions belonging to a specified algebra of infinitely differentiable functions. Examples of such curves include logarithmic spirals and solutions to Euler equations $x^2y''+xy'+cy=0$ with $c>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03033","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":"2026-05-18T00:46:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SS2SpnWIodUTHp9i2f59nAbY31k+Pcb8dtjnqM+iK+Z1iRm+12PD2YpnZpdpSD0/5ZTb+CRJM7glbahB4R6WDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:57:28.976346Z"},"content_sha256":"4b6f0ff6cc06c97630a9853accdf419888d9d70c824ee1c531f9d20dc2953678","schema_version":"1.0","event_id":"sha256:4b6f0ff6cc06c97630a9853accdf419888d9d70c824ee1c531f9d20dc2953678"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPV2GEHAWMXGXDVRQAACO32GLG/bundle.json","state_url":"https://pith.science/pith/FPV2GEHAWMXGXDVRQAACO32GLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPV2GEHAWMXGXDVRQAACO32GLG/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":"2026-05-28T03:57:28Z","links":{"resolver":"https://pith.science/pith/FPV2GEHAWMXGXDVRQAACO32GLG","bundle":"https://pith.science/pith/FPV2GEHAWMXGXDVRQAACO32GLG/bundle.json","state":"https://pith.science/pith/FPV2GEHAWMXGXDVRQAACO32GLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPV2GEHAWMXGXDVRQAACO32GLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FPV2GEHAWMXGXDVRQAACO32GLG","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":"f0179b11d412507688a7d61f04947b2fda74ba8519e126436e1720b55460ece5","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-12T20:54:16Z","title_canon_sha256":"d695206b2e0d30eea5b5b5a8dbfe48bae65bb8efbc8502af5385848cecbfe664"},"schema_version":"1.0","source":{"id":"1601.03033","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03033","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03033v3","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03033","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"FPV2GEHAWMXG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FPV2GEHAWMXGXDVR","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FPV2GEHA","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:4b6f0ff6cc06c97630a9853accdf419888d9d70c824ee1c531f9d20dc2953678","target":"graph","created_at":"2026-05-18T00:46:21Z","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 show that transcendental curves in $\\mathbb R^n$ (not necessarily compact) have few rational points of bounded height provided that the curves are well behaved with respect to algebraic sets in a certain sense and can be parametrized by functions belonging to a specified algebra of infinitely differentiable functions. Examples of such curves include logarithmic spirals and solutions to Euler equations $x^2y''+xy'+cy=0$ with $c>0$.","authors_text":"Chris Miller, Georges Comte","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-12T20:54:16Z","title":"Points of bounded height on oscillatory sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03033","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":"sha256:63c125f1a03ef3592da982d39c1c6e7a4a7e8a704d2105fc0f9e795b4b273837","target":"record","created_at":"2026-05-18T00:46:21Z","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":"f0179b11d412507688a7d61f04947b2fda74ba8519e126436e1720b55460ece5","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-12T20:54:16Z","title_canon_sha256":"d695206b2e0d30eea5b5b5a8dbfe48bae65bb8efbc8502af5385848cecbfe664"},"schema_version":"1.0","source":{"id":"1601.03033","kind":"arxiv","version":3}},"canonical_sha256":"2beba310e0b32e6b8eb18000276f4659b86b2eab886be69c3c5e5bd2c36bd4eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2beba310e0b32e6b8eb18000276f4659b86b2eab886be69c3c5e5bd2c36bd4eb","first_computed_at":"2026-05-18T00:46:21.141106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:21.141106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yOD57yNLDYXniiVxmYhsHXRaUQILt/hyi1gl5oegrX5LY0pQJRMLVx4IxWXVEsLCRlbfpCzFtDFOAAethv/1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:21.141609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03033","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c125f1a03ef3592da982d39c1c6e7a4a7e8a704d2105fc0f9e795b4b273837","sha256:4b6f0ff6cc06c97630a9853accdf419888d9d70c824ee1c531f9d20dc2953678"],"state_sha256":"abd0f4f221085f1a7328ba8644e3f105ed886bf3a56b415dda89c7b2af959304"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5CaJybDURePshFqpyJWH0YaD4dHh82+481EJ7MfVvsqgcsfPvpKIBSyKneQMKoR+rrGPXCsZd9oncQIoId2NCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:57:28.978325Z","bundle_sha256":"64e11cc13c914995449af142100a153d0dd982ebc32bf5a72f331623c6a86656"}}