{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LCYOC4BVHLGDMUP7LNWRTLAHHV","short_pith_number":"pith:LCYOC4BV","canonical_record":{"source":{"id":"2309.00427","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T12:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"33cdf6146686caeb1f699463ff0ac6df047ed771b859f9425b53349f588d2a65","abstract_canon_sha256":"39a09062e72e26a02eb88e86ee6fd3439b06001e4c0e6ee94cddb2c09dfa5c56"},"schema_version":"1.0"},"canonical_sha256":"58b0e170353acc3651ff5b6d19ac073d412228c8443a782ebd956becab45a366","source":{"kind":"arxiv","id":"2309.00427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.00427","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"2309.00427v1","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.00427","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"LCYOC4BVHLGD","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"pith_short_16","alias_value":"LCYOC4BVHLGDMUP7","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"pith_short_8","alias_value":"LCYOC4BV","created_at":"2026-07-05T06:46:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LCYOC4BVHLGDMUP7LNWRTLAHHV","target":"record","payload":{"canonical_record":{"source":{"id":"2309.00427","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T12:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"33cdf6146686caeb1f699463ff0ac6df047ed771b859f9425b53349f588d2a65","abstract_canon_sha256":"39a09062e72e26a02eb88e86ee6fd3439b06001e4c0e6ee94cddb2c09dfa5c56"},"schema_version":"1.0"},"canonical_sha256":"58b0e170353acc3651ff5b6d19ac073d412228c8443a782ebd956becab45a366","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:46:56.843763Z","signature_b64":"q8OtJw/hwhhlmQR5MNYzUr9S6NoJf6tttA73iDHjAw2lPYybmlGt9jSYH46wXz14zEUB2LzU2gRjCQ6VpEnPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58b0e170353acc3651ff5b6d19ac073d412228c8443a782ebd956becab45a366","last_reissued_at":"2026-07-05T06:46:56.843291Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:46:56.843291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.00427","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":"2026-07-05T06:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PYjVbXzXOW7iR4KxBnGIbeWLGI5kqAtmx64iYx7UUAHf5L6c1uJ/TOWL8+514M5p2McwdrT/9npq3SAzmL+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:24:01.068006Z"},"content_sha256":"cde4c333612a4ce951f62942762aa73165d606880eee3b169129e5e2d6c5b8dc","schema_version":"1.0","event_id":"sha256:cde4c333612a4ce951f62942762aa73165d606880eee3b169129e5e2d6c5b8dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LCYOC4BVHLGDMUP7LNWRTLAHHV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite families of solutions for $A^3 + B^3 = C^3 + D^3$ and $A^4 + B^4 + C^4 + D^4 + E^4 = F^4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Archit Agarwal, Meghali Garg","submitted_at":"2023-09-01T12:39:49Z","abstract_excerpt":"Ramanujan, in his lost notebook, gave an interesting identity, which generates infinite families of solutions to Euler's Diophantine equation $A^3 + B^3 = C^3 + D^3$. In this paper, we produce a few infinite families of solutions to the aforementioned Diophantine equation as well as for the Diophantine equation $A^4 + B^4 + C^4 + D^4 + E^4 = F^4$ in the spirit of Ramanujan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.00427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XNq2kKxi3Doay502Ugyr8N93+/htP6exLDbiLnJn4NWi5FYuuLimEPTV7apHjRm4TO22BuzhGw/K/iCg9B1sDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:24:01.068386Z"},"content_sha256":"ab4e6d99d0bc32f433a463f0bfb44bf37b68877dce16a33d0bb937b55df2c67e","schema_version":"1.0","event_id":"sha256:ab4e6d99d0bc32f433a463f0bfb44bf37b68877dce16a33d0bb937b55df2c67e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV/bundle.json","state_url":"https://pith.science/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV/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":"2026-07-09T04:24:01Z","links":{"resolver":"https://pith.science/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV","bundle":"https://pith.science/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV/bundle.json","state":"https://pith.science/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCYOC4BVHLGDMUP7LNWRTLAHHV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LCYOC4BVHLGDMUP7LNWRTLAHHV","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":"39a09062e72e26a02eb88e86ee6fd3439b06001e4c0e6ee94cddb2c09dfa5c56","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T12:39:49Z","title_canon_sha256":"33cdf6146686caeb1f699463ff0ac6df047ed771b859f9425b53349f588d2a65"},"schema_version":"1.0","source":{"id":"2309.00427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.00427","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"2309.00427v1","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.00427","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"LCYOC4BVHLGD","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"pith_short_16","alias_value":"LCYOC4BVHLGDMUP7","created_at":"2026-07-05T06:46:56Z"},{"alias_kind":"pith_short_8","alias_value":"LCYOC4BV","created_at":"2026-07-05T06:46:56Z"}],"graph_snapshots":[{"event_id":"sha256:ab4e6d99d0bc32f433a463f0bfb44bf37b68877dce16a33d0bb937b55df2c67e","target":"graph","created_at":"2026-07-05T06:46:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.00427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ramanujan, in his lost notebook, gave an interesting identity, which generates infinite families of solutions to Euler's Diophantine equation $A^3 + B^3 = C^3 + D^3$. In this paper, we produce a few infinite families of solutions to the aforementioned Diophantine equation as well as for the Diophantine equation $A^4 + B^4 + C^4 + D^4 + E^4 = F^4$ in the spirit of Ramanujan.","authors_text":"Archit Agarwal, Meghali Garg","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T12:39:49Z","title":"Infinite families of solutions for $A^3 + B^3 = C^3 + D^3$ and $A^4 + B^4 + C^4 + D^4 + E^4 = F^4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00427","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:cde4c333612a4ce951f62942762aa73165d606880eee3b169129e5e2d6c5b8dc","target":"record","created_at":"2026-07-05T06:46:56Z","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":"39a09062e72e26a02eb88e86ee6fd3439b06001e4c0e6ee94cddb2c09dfa5c56","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T12:39:49Z","title_canon_sha256":"33cdf6146686caeb1f699463ff0ac6df047ed771b859f9425b53349f588d2a65"},"schema_version":"1.0","source":{"id":"2309.00427","kind":"arxiv","version":1}},"canonical_sha256":"58b0e170353acc3651ff5b6d19ac073d412228c8443a782ebd956becab45a366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58b0e170353acc3651ff5b6d19ac073d412228c8443a782ebd956becab45a366","first_computed_at":"2026-07-05T06:46:56.843291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:46:56.843291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q8OtJw/hwhhlmQR5MNYzUr9S6NoJf6tttA73iDHjAw2lPYybmlGt9jSYH46wXz14zEUB2LzU2gRjCQ6VpEnPAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:46:56.843763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.00427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cde4c333612a4ce951f62942762aa73165d606880eee3b169129e5e2d6c5b8dc","sha256:ab4e6d99d0bc32f433a463f0bfb44bf37b68877dce16a33d0bb937b55df2c67e"],"state_sha256":"487ac7bebadbe5bd68171939339eefac361c229c17423bc631c3e8ca6c52d044"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JMJT7MSYfRz0nL0e/XVSt7bcBy/LMW5LHK1Z1AtaCZzXT9Atoa/QFp9U5sFgfGkkjzIyyF36kN66LkFecLoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T04:24:01.070331Z","bundle_sha256":"8c687d290fb6d581d57cf9d9a3095444f06294360493d6399cb4846bd03b1c8b"}}