{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BK2WZ4YHVE2ERQUQYIKVMKGXAW","short_pith_number":"pith:BK2WZ4YH","canonical_record":{"source":{"id":"1303.4125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-18T00:09:09Z","cross_cats_sorted":[],"title_canon_sha256":"d69652c2aa7db09992a8e520a85d9c250adc2bfb300cd5c08d96bd60d3bf9a7b","abstract_canon_sha256":"465ff545dc8452a730d604984064408d15e422aa096553c169b15acb5f615329"},"schema_version":"1.0"},"canonical_sha256":"0ab56cf307a93448c290c2155628d7058454c3090045f0b12ee078f875baa811","source":{"kind":"arxiv","id":"1303.4125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4125","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4125v1","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4125","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"BK2WZ4YHVE2E","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BK2WZ4YHVE2ERQUQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BK2WZ4YH","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BK2WZ4YHVE2ERQUQYIKVMKGXAW","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-18T00:09:09Z","cross_cats_sorted":[],"title_canon_sha256":"d69652c2aa7db09992a8e520a85d9c250adc2bfb300cd5c08d96bd60d3bf9a7b","abstract_canon_sha256":"465ff545dc8452a730d604984064408d15e422aa096553c169b15acb5f615329"},"schema_version":"1.0"},"canonical_sha256":"0ab56cf307a93448c290c2155628d7058454c3090045f0b12ee078f875baa811","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:25.579478Z","signature_b64":"FBre84i374UsXH6tngMzLsDsNIiu4DAN1SAlSF5Su0LxjfA9EF5bELWZoxcvgA8lWtmHc6IrnWf7rexm6rVpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ab56cf307a93448c290c2155628d7058454c3090045f0b12ee078f875baa811","last_reissued_at":"2026-05-18T01:22:25.578871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:25.578871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4125","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":"2026-05-18T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmWISn6NhII2VJiXSDRq6zDAk7oIY2+Qb1jfw3gX896O3bdWEYXTSONHvPXzbDOzLE0DS2Gwk/TS68XBlLLEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:59:58.324541Z"},"content_sha256":"1ec0f666ed3608b84d8ac6a442c7874d071e03529b66a7059cd56dcedc59d448","schema_version":"1.0","event_id":"sha256:1ec0f666ed3608b84d8ac6a442c7874d071e03529b66a7059cd56dcedc59d448"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BK2WZ4YHVE2ERQUQYIKVMKGXAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear forms in logarithms and integral points on higher-dimensional varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aaron Levin","submitted_at":"2013-03-18T00:09:09Z","abstract_excerpt":"We apply inequalities from the theory of linear forms in logarithms to deduce effective results on S-integral points on certain higher-dimensional varieties when the cardinality of S is sufficiently small. These results may be viewed as a higher-dimensional version of an effective result of Bilu on integral points on curves. In particular, we prove a completely explicit result for integral points on certain affine subsets of the projective plane. As an application, we generalize an effective result of Vojta on the three-variable unit equation by giving an effective solution of the polynomial u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4125","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":"2026-05-18T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0w73WFNLyf4AqTOpmSL0bAeGssy9tYEw79eGx6cHpzoK0RbpWW10gPfltfdcEOUT6VTHvQ9OI881y4tMo3ZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:59:58.324879Z"},"content_sha256":"452cf65a78fd4bfeff9b33b6093f6480b8c442fee8895aa45297c95ec1a245ae","schema_version":"1.0","event_id":"sha256:452cf65a78fd4bfeff9b33b6093f6480b8c442fee8895aa45297c95ec1a245ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW/bundle.json","state_url":"https://pith.science/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW/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":"2026-06-20T05:59:58Z","links":{"resolver":"https://pith.science/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW","bundle":"https://pith.science/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW/bundle.json","state":"https://pith.science/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BK2WZ4YHVE2ERQUQYIKVMKGXAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BK2WZ4YHVE2ERQUQYIKVMKGXAW","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":"465ff545dc8452a730d604984064408d15e422aa096553c169b15acb5f615329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-18T00:09:09Z","title_canon_sha256":"d69652c2aa7db09992a8e520a85d9c250adc2bfb300cd5c08d96bd60d3bf9a7b"},"schema_version":"1.0","source":{"id":"1303.4125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4125","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4125v1","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4125","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"BK2WZ4YHVE2E","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BK2WZ4YHVE2ERQUQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BK2WZ4YH","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:452cf65a78fd4bfeff9b33b6093f6480b8c442fee8895aa45297c95ec1a245ae","target":"graph","created_at":"2026-05-18T01:22:25Z","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 apply inequalities from the theory of linear forms in logarithms to deduce effective results on S-integral points on certain higher-dimensional varieties when the cardinality of S is sufficiently small. These results may be viewed as a higher-dimensional version of an effective result of Bilu on integral points on curves. In particular, we prove a completely explicit result for integral points on certain affine subsets of the projective plane. As an application, we generalize an effective result of Vojta on the three-variable unit equation by giving an effective solution of the polynomial u","authors_text":"Aaron Levin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-18T00:09:09Z","title":"Linear forms in logarithms and integral points on higher-dimensional varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4125","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":"sha256:1ec0f666ed3608b84d8ac6a442c7874d071e03529b66a7059cd56dcedc59d448","target":"record","created_at":"2026-05-18T01:22:25Z","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":"465ff545dc8452a730d604984064408d15e422aa096553c169b15acb5f615329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-18T00:09:09Z","title_canon_sha256":"d69652c2aa7db09992a8e520a85d9c250adc2bfb300cd5c08d96bd60d3bf9a7b"},"schema_version":"1.0","source":{"id":"1303.4125","kind":"arxiv","version":1}},"canonical_sha256":"0ab56cf307a93448c290c2155628d7058454c3090045f0b12ee078f875baa811","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ab56cf307a93448c290c2155628d7058454c3090045f0b12ee078f875baa811","first_computed_at":"2026-05-18T01:22:25.578871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.578871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FBre84i374UsXH6tngMzLsDsNIiu4DAN1SAlSF5Su0LxjfA9EF5bELWZoxcvgA8lWtmHc6IrnWf7rexm6rVpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.579478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ec0f666ed3608b84d8ac6a442c7874d071e03529b66a7059cd56dcedc59d448","sha256:452cf65a78fd4bfeff9b33b6093f6480b8c442fee8895aa45297c95ec1a245ae"],"state_sha256":"80fa5c38007b2c451654118d3b9feb196a91f3c4754303255e9c405217e33781"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mO74K4AboV62opDD+G9ZA6+5/0wkMkBFpq4sK0e9DgaY/0TKd53ctIp40dBpGL9xr+1miFa/s9Kk/xXNb9kdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:59:58.326765Z","bundle_sha256":"f27970bbc05f1aa920ff7614ee051afa6ed24bf75120fab1e1f2f6c6960af3af"}}