{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:L2THZ4YE3GM4B2TW2D3EXQBI7L","short_pith_number":"pith:L2THZ4YE","canonical_record":{"source":{"id":"1603.03340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-10T17:27:53Z","cross_cats_sorted":[],"title_canon_sha256":"bc1ececf37263ab939cf42afe0febe5748a2a9ce80221494348e39255fa18e6f","abstract_canon_sha256":"d9892de715fa83abafdac4efdac1635efbe78a441951f67dc11f178c7091778e"},"schema_version":"1.0"},"canonical_sha256":"5ea67cf304d999c0ea76d0f64bc028fac5364b66840198a24492f70b954ca409","source":{"kind":"arxiv","id":"1603.03340","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03340","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03340v3","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03340","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"L2THZ4YE3GM4","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L2THZ4YE3GM4B2TW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L2THZ4YE","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:L2THZ4YE3GM4B2TW2D3EXQBI7L","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-10T17:27:53Z","cross_cats_sorted":[],"title_canon_sha256":"bc1ececf37263ab939cf42afe0febe5748a2a9ce80221494348e39255fa18e6f","abstract_canon_sha256":"d9892de715fa83abafdac4efdac1635efbe78a441951f67dc11f178c7091778e"},"schema_version":"1.0"},"canonical_sha256":"5ea67cf304d999c0ea76d0f64bc028fac5364b66840198a24492f70b954ca409","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:57.303513Z","signature_b64":"BQ+z8wjoD3V3dgrhHlkL5pyj+7eBRKXPa4lRGC1tREExcB48yZK0ZnQihOflVuk4abRc5cduOFq1H8H3DKxyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ea67cf304d999c0ea76d0f64bc028fac5364b66840198a24492f70b954ca409","last_reissued_at":"2026-05-18T00:50:57.302739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:57.302739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03340","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":"2026-05-18T00:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4L+UvT0KK8+25VOl0EZG5ywQ+v30Z2NYlHL1S8kyp/A/2QFKqqpdfnQOBkv7ReyrhE76QCtyYnJpD0WCkhpZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:21:49.103256Z"},"content_sha256":"4430fb36f91428e28ea5e730e2bff4dff41cdc1d948d596cc4133e29e5be898b","schema_version":"1.0","event_id":"sha256:4430fb36f91428e28ea5e730e2bff4dff41cdc1d948d596cc4133e29e5be898b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:L2THZ4YE3GM4B2TW2D3EXQBI7L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thue's inequalities and the hypergeometric method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Divyum Sharma, N. Saradha, Shabnam Akhtari","submitted_at":"2016-03-10T17:27:53Z","abstract_excerpt":"Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape $0<|F(x, y)| \\leq h$, where $F(x , y) =(\\alpha x + \\beta y)^r -(\\gamma x + \\delta y)^r \\in \\mathbb{Z}[x ,y]$, $\\alpha$, $\\beta$, $\\gamma$ and $\\delta$ are algebraic constants with $\\alpha\\delta-\\beta\\gamma \\neq 0$, and $r \\geq 3$ and $h$ are integers. As an important application, we pay special attention to the binomial Thue's inequaities $|ax^r - by^r| \\leq c$. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03340","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":"2026-05-18T00:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xKM8ucuNBMnJdv+w9jespbXzQC8R84VW7Yu4X0VzI+Hc548dB0xSbZepzxjxq5MiKaMVfipZb3BaCva7EnySDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:21:49.103617Z"},"content_sha256":"4c87276135677d7cf7e01457c38f12171ffd2ec27e749878724227a97dce7756","schema_version":"1.0","event_id":"sha256:4c87276135677d7cf7e01457c38f12171ffd2ec27e749878724227a97dce7756"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L/bundle.json","state_url":"https://pith.science/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L/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":"2026-06-03T11:21:49Z","links":{"resolver":"https://pith.science/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L","bundle":"https://pith.science/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L/bundle.json","state":"https://pith.science/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2THZ4YE3GM4B2TW2D3EXQBI7L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L2THZ4YE3GM4B2TW2D3EXQBI7L","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":"d9892de715fa83abafdac4efdac1635efbe78a441951f67dc11f178c7091778e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-10T17:27:53Z","title_canon_sha256":"bc1ececf37263ab939cf42afe0febe5748a2a9ce80221494348e39255fa18e6f"},"schema_version":"1.0","source":{"id":"1603.03340","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03340","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03340v3","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03340","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"L2THZ4YE3GM4","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L2THZ4YE3GM4B2TW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L2THZ4YE","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:4c87276135677d7cf7e01457c38f12171ffd2ec27e749878724227a97dce7756","target":"graph","created_at":"2026-05-18T00:50:57Z","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":"Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape $0<|F(x, y)| \\leq h$, where $F(x , y) =(\\alpha x + \\beta y)^r -(\\gamma x + \\delta y)^r \\in \\mathbb{Z}[x ,y]$, $\\alpha$, $\\beta$, $\\gamma$ and $\\delta$ are algebraic constants with $\\alpha\\delta-\\beta\\gamma \\neq 0$, and $r \\geq 3$ and $h$ are integers. As an important application, we pay special attention to the binomial Thue's inequaities $|ax^r - by^r| \\leq c$. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement b","authors_text":"Divyum Sharma, N. Saradha, Shabnam Akhtari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-10T17:27:53Z","title":"Thue's inequalities and the hypergeometric method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03340","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":"sha256:4430fb36f91428e28ea5e730e2bff4dff41cdc1d948d596cc4133e29e5be898b","target":"record","created_at":"2026-05-18T00:50:57Z","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":"d9892de715fa83abafdac4efdac1635efbe78a441951f67dc11f178c7091778e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-10T17:27:53Z","title_canon_sha256":"bc1ececf37263ab939cf42afe0febe5748a2a9ce80221494348e39255fa18e6f"},"schema_version":"1.0","source":{"id":"1603.03340","kind":"arxiv","version":3}},"canonical_sha256":"5ea67cf304d999c0ea76d0f64bc028fac5364b66840198a24492f70b954ca409","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ea67cf304d999c0ea76d0f64bc028fac5364b66840198a24492f70b954ca409","first_computed_at":"2026-05-18T00:50:57.302739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:57.302739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BQ+z8wjoD3V3dgrhHlkL5pyj+7eBRKXPa4lRGC1tREExcB48yZK0ZnQihOflVuk4abRc5cduOFq1H8H3DKxyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:57.303513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03340","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4430fb36f91428e28ea5e730e2bff4dff41cdc1d948d596cc4133e29e5be898b","sha256:4c87276135677d7cf7e01457c38f12171ffd2ec27e749878724227a97dce7756"],"state_sha256":"d0711467da4680b64dcabbc1d911982b4f1cebe79e252ac4863608f4f2d29098"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LARLvyvAf3KSMuTxmxojp6qs6WXQWAAUPg0gL9ht26obtwj31Yqb+T6mwms2bNL6Iq8cEIdzQ6IO3C1FXWvQCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:21:49.105595Z","bundle_sha256":"1d3af7beba38f7f828eceeb9d085f96a849a9c2c3f1f53b99f7a2a6cc2d1a379"}}