{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QJF6H2X4LG4LMFJA6MFYLJQIGQ","short_pith_number":"pith:QJF6H2X4","canonical_record":{"source":{"id":"1404.5669","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-22T23:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"d86a6b86637cded846440fa971a3e6df0bd0a2192f85622d7607cdd697efd4c5","abstract_canon_sha256":"17e3da23aee1ad61725e427c70654788318e7cf2f65da84f4c3711771c6d3338"},"schema_version":"1.0"},"canonical_sha256":"824be3eafc59b8b61520f30b85a6083433a37f0c5e58b19bc279a30d28dd0a63","source":{"kind":"arxiv","id":"1404.5669","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5669","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5669v2","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5669","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"QJF6H2X4LG4L","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QJF6H2X4LG4LMFJA","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QJF6H2X4","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QJF6H2X4LG4LMFJA6MFYLJQIGQ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5669","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-22T23:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"d86a6b86637cded846440fa971a3e6df0bd0a2192f85622d7607cdd697efd4c5","abstract_canon_sha256":"17e3da23aee1ad61725e427c70654788318e7cf2f65da84f4c3711771c6d3338"},"schema_version":"1.0"},"canonical_sha256":"824be3eafc59b8b61520f30b85a6083433a37f0c5e58b19bc279a30d28dd0a63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:33.106264Z","signature_b64":"JBbOXj/4g9+2uuu5Vp1xf9oe5jW6bmqpamzM6+oJZxlcHfKaOF2mIw5PhSGnZEC1+tY7k9C1ywVOCgjcDhuiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"824be3eafc59b8b61520f30b85a6083433a37f0c5e58b19bc279a30d28dd0a63","last_reissued_at":"2026-05-18T01:37:33.105756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:33.105756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5669","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnnjPHygUyAB1qFT0h0mxRTCD+6SBG4V8mWLyLq6u4GzwfAJV7lHoFUcjP9vUgngrrfcDAkXaGg1BM0Tvvv+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:57:03.016491Z"},"content_sha256":"8b68fd21a456daff99026ea8d889f63da52f2ee8a8d21e3760e143a661797837","schema_version":"1.0","event_id":"sha256:8b68fd21a456daff99026ea8d889f63da52f2ee8a8d21e3760e143a661797837"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QJF6H2X4LG4LMFJA6MFYLJQIGQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linnik's approximation to Goldbach's conjecture, and other problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dave Platt, Tim Trudgian","submitted_at":"2014-04-22T23:28:17Z","abstract_excerpt":"We examine the problem of writing every sufficiently large even number as the sum of two primes and at most $K$ powers of 2. We outline an approach that only just falls short of improving the current bounds on $K$. Finally, we improve the estimates in other Waring--Goldbach problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5669","kind":"arxiv","version":2},"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":"2026-05-18T01:37:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZL4XY5WThgMUgePV5ZH8fzBhJ2VSWXOAgO+EcQGe9VZ0o5TO+9yi4D3btEIVtvwclbBN6UZLRvmezqzD8EtBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:57:03.016829Z"},"content_sha256":"e67285e43cf44091cce1f3c476f0dd874a7d701cca659493338fc390cb347e4f","schema_version":"1.0","event_id":"sha256:e67285e43cf44091cce1f3c476f0dd874a7d701cca659493338fc390cb347e4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ/bundle.json","state_url":"https://pith.science/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ/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":"2026-06-27T14:57:03Z","links":{"resolver":"https://pith.science/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ","bundle":"https://pith.science/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ/bundle.json","state":"https://pith.science/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJF6H2X4LG4LMFJA6MFYLJQIGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QJF6H2X4LG4LMFJA6MFYLJQIGQ","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":"17e3da23aee1ad61725e427c70654788318e7cf2f65da84f4c3711771c6d3338","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-22T23:28:17Z","title_canon_sha256":"d86a6b86637cded846440fa971a3e6df0bd0a2192f85622d7607cdd697efd4c5"},"schema_version":"1.0","source":{"id":"1404.5669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5669","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5669v2","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5669","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"QJF6H2X4LG4L","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QJF6H2X4LG4LMFJA","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QJF6H2X4","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:e67285e43cf44091cce1f3c476f0dd874a7d701cca659493338fc390cb347e4f","target":"graph","created_at":"2026-05-18T01:37:33Z","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 examine the problem of writing every sufficiently large even number as the sum of two primes and at most $K$ powers of 2. We outline an approach that only just falls short of improving the current bounds on $K$. Finally, we improve the estimates in other Waring--Goldbach problems.","authors_text":"Dave Platt, Tim Trudgian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-22T23:28:17Z","title":"Linnik's approximation to Goldbach's conjecture, and other problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5669","kind":"arxiv","version":2},"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":"sha256:8b68fd21a456daff99026ea8d889f63da52f2ee8a8d21e3760e143a661797837","target":"record","created_at":"2026-05-18T01:37:33Z","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":"17e3da23aee1ad61725e427c70654788318e7cf2f65da84f4c3711771c6d3338","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-22T23:28:17Z","title_canon_sha256":"d86a6b86637cded846440fa971a3e6df0bd0a2192f85622d7607cdd697efd4c5"},"schema_version":"1.0","source":{"id":"1404.5669","kind":"arxiv","version":2}},"canonical_sha256":"824be3eafc59b8b61520f30b85a6083433a37f0c5e58b19bc279a30d28dd0a63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"824be3eafc59b8b61520f30b85a6083433a37f0c5e58b19bc279a30d28dd0a63","first_computed_at":"2026-05-18T01:37:33.105756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:33.105756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JBbOXj/4g9+2uuu5Vp1xf9oe5jW6bmqpamzM6+oJZxlcHfKaOF2mIw5PhSGnZEC1+tY7k9C1ywVOCgjcDhuiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:33.106264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b68fd21a456daff99026ea8d889f63da52f2ee8a8d21e3760e143a661797837","sha256:e67285e43cf44091cce1f3c476f0dd874a7d701cca659493338fc390cb347e4f"],"state_sha256":"5afb377a34ba99d3fb1c355e36ffb9169aab9dfe155fbdb3dd300997620e815a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opCVrVEWjZsL6PCdIKy1H/EjlYFiGtTPV/b+CtHXbam7GyibfycsIb8GsHJX4NLq3Z4ezaeHdAXB8sG8y3gXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:57:03.018786Z","bundle_sha256":"10114053a23b61d6e9ce5ff8dffc05d3f02db12657b95ed3c7a833221b168f8c"}}