{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BXAFTLS2YENHIJOBYSRTHLYNKO","short_pith_number":"pith:BXAFTLS2","canonical_record":{"source":{"id":"1209.3233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-14T15:48:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"62a1051ca2529e775895d08821c4cec8c60d678bb153122e6bbfb0fbdeb1664c","abstract_canon_sha256":"3f454efd20c284cf4c6351e8246dff2b038a65d2c72ed6008150a3c42db47c73"},"schema_version":"1.0"},"canonical_sha256":"0dc059ae5ac11a7425c1c4a333af0d53b58262226ab4854047469b4f87082825","source":{"kind":"arxiv","id":"1209.3233","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3233","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3233v2","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3233","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"BXAFTLS2YENH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BXAFTLS2YENHIJOB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BXAFTLS2","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BXAFTLS2YENHIJOBYSRTHLYNKO","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-14T15:48:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"62a1051ca2529e775895d08821c4cec8c60d678bb153122e6bbfb0fbdeb1664c","abstract_canon_sha256":"3f454efd20c284cf4c6351e8246dff2b038a65d2c72ed6008150a3c42db47c73"},"schema_version":"1.0"},"canonical_sha256":"0dc059ae5ac11a7425c1c4a333af0d53b58262226ab4854047469b4f87082825","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:40.077965Z","signature_b64":"eRYfIFHAohLHw7zSkJ6e9TB41PsvqkVoRKHr5z/Jvacvx0LDWPRmBRp3giwTF8wfnzWreCXo6WnKz3xUisC/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dc059ae5ac11a7425c1c4a333af0d53b58262226ab4854047469b4f87082825","last_reissued_at":"2026-05-18T03:41:40.077170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:40.077170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3233","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":"2026-05-18T03:41:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1XIxh43JmtGb3tsl/d7Bp31dgPYh84kYgbVgHT3du343L1qtqRMlmSYIEOVx4Jt2D3dAvMnJf22J2AaEVJyjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:28:48.893404Z"},"content_sha256":"8fc6208f300f3e101c86cf97a29c71f71ad215ef587cfd28ad37b4ad600cb2d1","schema_version":"1.0","event_id":"sha256:8fc6208f300f3e101c86cf97a29c71f71ad215ef587cfd28ad37b4ad600cb2d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BXAFTLS2YENHIJOBYSRTHLYNKO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse Erdos-Fuchs theorem for k-fold sumsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Hao Pan, Li-Xia Dai","submitted_at":"2012-09-14T15:48:13Z","abstract_excerpt":"We generalize a result of Ruzsa on the inverse Erdos-Fuchs theorem for k-fold sumsets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3233","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":"2026-05-18T03:41:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nSSvCwSaEOsqhzQ2Og47tY/tvrzgLyYmOmmS6YdegUxFHIy9yfXHyLGJcsFNtBcONonKAPaYMTUB3EcCXJWBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:28:48.894173Z"},"content_sha256":"bfadab10474813e6b7c5ce865433e70749866db4178032c113c4d39c0a087d58","schema_version":"1.0","event_id":"sha256:bfadab10474813e6b7c5ce865433e70749866db4178032c113c4d39c0a087d58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXAFTLS2YENHIJOBYSRTHLYNKO/bundle.json","state_url":"https://pith.science/pith/BXAFTLS2YENHIJOBYSRTHLYNKO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXAFTLS2YENHIJOBYSRTHLYNKO/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":"2026-05-25T20:28:48Z","links":{"resolver":"https://pith.science/pith/BXAFTLS2YENHIJOBYSRTHLYNKO","bundle":"https://pith.science/pith/BXAFTLS2YENHIJOBYSRTHLYNKO/bundle.json","state":"https://pith.science/pith/BXAFTLS2YENHIJOBYSRTHLYNKO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXAFTLS2YENHIJOBYSRTHLYNKO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BXAFTLS2YENHIJOBYSRTHLYNKO","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":"3f454efd20c284cf4c6351e8246dff2b038a65d2c72ed6008150a3c42db47c73","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-14T15:48:13Z","title_canon_sha256":"62a1051ca2529e775895d08821c4cec8c60d678bb153122e6bbfb0fbdeb1664c"},"schema_version":"1.0","source":{"id":"1209.3233","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3233","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3233v2","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3233","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"BXAFTLS2YENH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BXAFTLS2YENHIJOB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BXAFTLS2","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:bfadab10474813e6b7c5ce865433e70749866db4178032c113c4d39c0a087d58","target":"graph","created_at":"2026-05-18T03:41:40Z","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 generalize a result of Ruzsa on the inverse Erdos-Fuchs theorem for k-fold sumsets.","authors_text":"Hao Pan, Li-Xia Dai","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-14T15:48:13Z","title":"Inverse Erdos-Fuchs theorem for k-fold sumsets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3233","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":"sha256:8fc6208f300f3e101c86cf97a29c71f71ad215ef587cfd28ad37b4ad600cb2d1","target":"record","created_at":"2026-05-18T03:41:40Z","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":"3f454efd20c284cf4c6351e8246dff2b038a65d2c72ed6008150a3c42db47c73","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-14T15:48:13Z","title_canon_sha256":"62a1051ca2529e775895d08821c4cec8c60d678bb153122e6bbfb0fbdeb1664c"},"schema_version":"1.0","source":{"id":"1209.3233","kind":"arxiv","version":2}},"canonical_sha256":"0dc059ae5ac11a7425c1c4a333af0d53b58262226ab4854047469b4f87082825","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dc059ae5ac11a7425c1c4a333af0d53b58262226ab4854047469b4f87082825","first_computed_at":"2026-05-18T03:41:40.077170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:40.077170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eRYfIFHAohLHw7zSkJ6e9TB41PsvqkVoRKHr5z/Jvacvx0LDWPRmBRp3giwTF8wfnzWreCXo6WnKz3xUisC/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:40.077965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3233","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fc6208f300f3e101c86cf97a29c71f71ad215ef587cfd28ad37b4ad600cb2d1","sha256:bfadab10474813e6b7c5ce865433e70749866db4178032c113c4d39c0a087d58"],"state_sha256":"ad238ff5187b7d546b94f534f00551d65145839cce57fd2a862ca70d3388329e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"chrj9yCmiyBAZk0iIfvAIQXpcb/w+RKyOhmHahovztFycDIh3lpQvLn58XlC2Qqz19Fk23rmZ/NEL2uLd9lWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:28:48.898932Z","bundle_sha256":"461c60d3baeae9d43c1d3a21bd0a497d16e97b568a18db2432c49d80d74e3355"}}