{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3RJQNWKPCVLGOKA7U57XDG7NTP","short_pith_number":"pith:3RJQNWKP","canonical_record":{"source":{"id":"2004.06611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-14T15:52:07Z","cross_cats_sorted":["math.CA","math.NT"],"title_canon_sha256":"f252547eebcc5d4d76fadbd6c7ba50f7880f516354d4ee1c119903de3bfd28ec","abstract_canon_sha256":"4bb4d21db37517ea5a5117123207102fb8fe38b65da8a0d89c37cda3bb69040c"},"schema_version":"1.0"},"canonical_sha256":"dc5306d94f155667281fa77f719bed9bc501f542e2d7d0ebdec2699a6e1a8f6b","source":{"kind":"arxiv","id":"2004.06611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.06611","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"2004.06611v1","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.06611","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"3RJQNWKPCVLG","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"3RJQNWKPCVLGOKA7","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"3RJQNWKP","created_at":"2026-07-05T00:54:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3RJQNWKPCVLGOKA7U57XDG7NTP","target":"record","payload":{"canonical_record":{"source":{"id":"2004.06611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-14T15:52:07Z","cross_cats_sorted":["math.CA","math.NT"],"title_canon_sha256":"f252547eebcc5d4d76fadbd6c7ba50f7880f516354d4ee1c119903de3bfd28ec","abstract_canon_sha256":"4bb4d21db37517ea5a5117123207102fb8fe38b65da8a0d89c37cda3bb69040c"},"schema_version":"1.0"},"canonical_sha256":"dc5306d94f155667281fa77f719bed9bc501f542e2d7d0ebdec2699a6e1a8f6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:53.937554Z","signature_b64":"jelzmIxls/Lk+cIiWJYEVu7UwkGVP+dHDBnzKoNe3tNHK3q9sEFNO2apdSbG5ndt0mnDrU4LpN6gUrMCQnKTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc5306d94f155667281fa77f719bed9bc501f542e2d7d0ebdec2699a6e1a8f6b","last_reissued_at":"2026-07-05T00:54:53.937079Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:53.937079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.06611","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":"2026-07-05T00:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2xOABC7PO/SF2ayDXUfOSg+tb2ymteiRStXShXL7szhTqcXojMFgo6Bs+wOHFucSMznE17+kPeUcRL98oPi+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:30:10.882281Z"},"content_sha256":"c52311ae1fca1d601526fc171ac345e2e9fba433229b3f08a0a3121ee197de10","schema_version":"1.0","event_id":"sha256:c52311ae1fca1d601526fc171ac345e2e9fba433229b3f08a0a3121ee197de10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3RJQNWKPCVLGOKA7U57XDG7NTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized difference sets and autocorrelation integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.CO","authors_text":"Noah Kravitz","submitted_at":"2020-04-14T15:52:07Z","abstract_excerpt":"In 2010, Cilleruelo, Ruzsa, and Vinuesa established a surprising connection between the maximum possible size of a generalized Sidon set in the first $N$ natural numbers and the optimal constant in an ``analogous'' problem concerning nonnegative-valued functions on $[0,1]$ with autoconvolution integral uniformly bounded above. Answering a recent question of Barnard and Steinerberger, we prove the corresponding dual result about the minimum size of a so-called generalized difference set that covers the first $N$ natural numbers and the optimal constant in an analogous problem concerning nonnega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.06611","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/2004.06611/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":"2026-07-05T00:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDCsUJviQVuTpbAp3YKUaniCcFRKaXNwoPstA2zV2//9uKm6X99sQaF6ggFDI7PIIIoVjVXBodUxDRAhUR9MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:30:10.882668Z"},"content_sha256":"8be0356bf730d713cb77f5b5620416adec9341492e9041acd5886a3a639f7294","schema_version":"1.0","event_id":"sha256:8be0356bf730d713cb77f5b5620416adec9341492e9041acd5886a3a639f7294"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RJQNWKPCVLGOKA7U57XDG7NTP/bundle.json","state_url":"https://pith.science/pith/3RJQNWKPCVLGOKA7U57XDG7NTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RJQNWKPCVLGOKA7U57XDG7NTP/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":"2026-08-19T14:30:10Z","links":{"resolver":"https://pith.science/pith/3RJQNWKPCVLGOKA7U57XDG7NTP","bundle":"https://pith.science/pith/3RJQNWKPCVLGOKA7U57XDG7NTP/bundle.json","state":"https://pith.science/pith/3RJQNWKPCVLGOKA7U57XDG7NTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RJQNWKPCVLGOKA7U57XDG7NTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3RJQNWKPCVLGOKA7U57XDG7NTP","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":"4bb4d21db37517ea5a5117123207102fb8fe38b65da8a0d89c37cda3bb69040c","cross_cats_sorted":["math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-14T15:52:07Z","title_canon_sha256":"f252547eebcc5d4d76fadbd6c7ba50f7880f516354d4ee1c119903de3bfd28ec"},"schema_version":"1.0","source":{"id":"2004.06611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.06611","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"2004.06611v1","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.06611","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"3RJQNWKPCVLG","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"3RJQNWKPCVLGOKA7","created_at":"2026-07-05T00:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"3RJQNWKP","created_at":"2026-07-05T00:54:53Z"}],"graph_snapshots":[{"event_id":"sha256:8be0356bf730d713cb77f5b5620416adec9341492e9041acd5886a3a639f7294","target":"graph","created_at":"2026-07-05T00:54:53Z","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/2004.06611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 2010, Cilleruelo, Ruzsa, and Vinuesa established a surprising connection between the maximum possible size of a generalized Sidon set in the first $N$ natural numbers and the optimal constant in an ``analogous'' problem concerning nonnegative-valued functions on $[0,1]$ with autoconvolution integral uniformly bounded above. Answering a recent question of Barnard and Steinerberger, we prove the corresponding dual result about the minimum size of a so-called generalized difference set that covers the first $N$ natural numbers and the optimal constant in an analogous problem concerning nonnega","authors_text":"Noah Kravitz","cross_cats":["math.CA","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-14T15:52:07Z","title":"Generalized difference sets and autocorrelation integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.06611","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:c52311ae1fca1d601526fc171ac345e2e9fba433229b3f08a0a3121ee197de10","target":"record","created_at":"2026-07-05T00:54:53Z","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":"4bb4d21db37517ea5a5117123207102fb8fe38b65da8a0d89c37cda3bb69040c","cross_cats_sorted":["math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-14T15:52:07Z","title_canon_sha256":"f252547eebcc5d4d76fadbd6c7ba50f7880f516354d4ee1c119903de3bfd28ec"},"schema_version":"1.0","source":{"id":"2004.06611","kind":"arxiv","version":1}},"canonical_sha256":"dc5306d94f155667281fa77f719bed9bc501f542e2d7d0ebdec2699a6e1a8f6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc5306d94f155667281fa77f719bed9bc501f542e2d7d0ebdec2699a6e1a8f6b","first_computed_at":"2026-07-05T00:54:53.937079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:53.937079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jelzmIxls/Lk+cIiWJYEVu7UwkGVP+dHDBnzKoNe3tNHK3q9sEFNO2apdSbG5ndt0mnDrU4LpN6gUrMCQnKTAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:53.937554Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.06611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c52311ae1fca1d601526fc171ac345e2e9fba433229b3f08a0a3121ee197de10","sha256:8be0356bf730d713cb77f5b5620416adec9341492e9041acd5886a3a639f7294"],"state_sha256":"79bba982b5b3429d2d8ac4313c3da97678d03a57e11bd0f32f53fe69fb652406"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8bQJzP0pzVWkYPNgQsBBe7jP2t7RsoQfQbQ6ymNcd8vE9gI1SsVm+Ns/qwwlPjh2GEaVPJCLU5jJJEzME7TMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T14:30:10.886750Z","bundle_sha256":"a36a4d4cb75830ce52d855e46c159d69e502406db0477588329d0925e0fae3a7"}}