{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:36ZDKDU6OJ3UAGFJWQABPXPS5J","short_pith_number":"pith:36ZDKDU6","canonical_record":{"source":{"id":"1112.2461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T07:26:07Z","cross_cats_sorted":[],"title_canon_sha256":"bd9cf207e67fbfb09af9fe196bb22be43328894ef14d62348870abdcd074ee3e","abstract_canon_sha256":"339b974bb63d9ca337d35a4fb5a62ed93564575137a89683898232b953a60856"},"schema_version":"1.0"},"canonical_sha256":"dfb2350e9e72774018a9b40017ddf2ea7d7df51671343d9586a21667d60a7432","source":{"kind":"arxiv","id":"1112.2461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2461","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2461v1","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2461","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"pith_short_12","alias_value":"36ZDKDU6OJ3U","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"36ZDKDU6OJ3UAGFJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"36ZDKDU6","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:36ZDKDU6OJ3UAGFJWQABPXPS5J","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T07:26:07Z","cross_cats_sorted":[],"title_canon_sha256":"bd9cf207e67fbfb09af9fe196bb22be43328894ef14d62348870abdcd074ee3e","abstract_canon_sha256":"339b974bb63d9ca337d35a4fb5a62ed93564575137a89683898232b953a60856"},"schema_version":"1.0"},"canonical_sha256":"dfb2350e9e72774018a9b40017ddf2ea7d7df51671343d9586a21667d60a7432","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:34.333951Z","signature_b64":"xD+hIhReQx359a7eZ0MBfzemIzY2Nkj7P85FjOIheSyhyNvVMuDQ5+Z44ukqQSE0cucCeRGttf3o7wfFkMaTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfb2350e9e72774018a9b40017ddf2ea7d7df51671343d9586a21667d60a7432","last_reissued_at":"2026-05-18T04:06:34.333236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:34.333236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2461","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":"2026-05-18T04:06:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgncydsnJSeGdYkLfiDLbMKLC8bzInoug8BDMyGkNen2Hb2EmNIDnnuqh5bw/TuRTkr/30a6XJolYU0N771xBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:25:05.754199Z"},"content_sha256":"d80807b7b52912ae81e57759731cc51e30b41ad7926a47778cce7be89073001a","schema_version":"1.0","event_id":"sha256:d80807b7b52912ae81e57759731cc51e30b41ad7926a47778cce7be89073001a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:36ZDKDU6OJ3UAGFJWQABPXPS5J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Baker's Explicit abc-Conjecture and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shanta Laishram, T. N. Shorey","submitted_at":"2011-12-12T07:26:07Z","abstract_excerpt":"The conjecture of Masser-Oesterl\\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2461","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":"2026-05-18T04:06:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C5vBO5pTUqmgFBamEXB7LMRV/zEQUA88UrznAyfeEOYeAwvsmnzxtx63zhH5R4Wb5SYz/ifP1KE1Y+wmyIFdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:25:05.754832Z"},"content_sha256":"51f1930268971945a450cdf423e8a3590dc03a49459eaf1e86644fb9403ca796","schema_version":"1.0","event_id":"sha256:51f1930268971945a450cdf423e8a3590dc03a49459eaf1e86644fb9403ca796"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J/bundle.json","state_url":"https://pith.science/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J/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":"2026-06-12T05:25:05Z","links":{"resolver":"https://pith.science/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J","bundle":"https://pith.science/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J/bundle.json","state":"https://pith.science/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/36ZDKDU6OJ3UAGFJWQABPXPS5J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:36ZDKDU6OJ3UAGFJWQABPXPS5J","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":"339b974bb63d9ca337d35a4fb5a62ed93564575137a89683898232b953a60856","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T07:26:07Z","title_canon_sha256":"bd9cf207e67fbfb09af9fe196bb22be43328894ef14d62348870abdcd074ee3e"},"schema_version":"1.0","source":{"id":"1112.2461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2461","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2461v1","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2461","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"pith_short_12","alias_value":"36ZDKDU6OJ3U","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"36ZDKDU6OJ3UAGFJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"36ZDKDU6","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:51f1930268971945a450cdf423e8a3590dc03a49459eaf1e86644fb9403ca796","target":"graph","created_at":"2026-05-18T04:06:34Z","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":"The conjecture of Masser-Oesterl\\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures.","authors_text":"Shanta Laishram, T. N. Shorey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T07:26:07Z","title":"Baker's Explicit abc-Conjecture and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2461","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:d80807b7b52912ae81e57759731cc51e30b41ad7926a47778cce7be89073001a","target":"record","created_at":"2026-05-18T04:06:34Z","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":"339b974bb63d9ca337d35a4fb5a62ed93564575137a89683898232b953a60856","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T07:26:07Z","title_canon_sha256":"bd9cf207e67fbfb09af9fe196bb22be43328894ef14d62348870abdcd074ee3e"},"schema_version":"1.0","source":{"id":"1112.2461","kind":"arxiv","version":1}},"canonical_sha256":"dfb2350e9e72774018a9b40017ddf2ea7d7df51671343d9586a21667d60a7432","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfb2350e9e72774018a9b40017ddf2ea7d7df51671343d9586a21667d60a7432","first_computed_at":"2026-05-18T04:06:34.333236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:34.333236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xD+hIhReQx359a7eZ0MBfzemIzY2Nkj7P85FjOIheSyhyNvVMuDQ5+Z44ukqQSE0cucCeRGttf3o7wfFkMaTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:34.333951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d80807b7b52912ae81e57759731cc51e30b41ad7926a47778cce7be89073001a","sha256:51f1930268971945a450cdf423e8a3590dc03a49459eaf1e86644fb9403ca796"],"state_sha256":"cf2843abbdba20b4c485fa1ee665d22357c49d32485ef8ecabdad9e999f27674"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NsrdOPKMJ9xejjIwj3XGsn3ADrwO5QGvm31WeWcBLizjjuCRUCq5KranPmfHhR211LTilcf4HUxUFf3DFBcHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:25:05.757947Z","bundle_sha256":"09e944ef140e97f3f04caa14547fde6ba0b22e33e618beb1a845a1dd2dd757ff"}}