{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5O55WCBKPZER5VL3GRFWDSMYMY","short_pith_number":"pith:5O55WCBK","canonical_record":{"source":{"id":"1803.00659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-01T23:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"0f68974dacd64180ea4e8d9fe5f839ea4f5b248b971145f7e42ade2ed4c9f907","abstract_canon_sha256":"f12cbf5066dcd4137b4afe1169e35b8b115a634c810e7af57100b39f26c781af"},"schema_version":"1.0"},"canonical_sha256":"ebbbdb082a7e491ed57b344b61c9986609ba50ad22f731d9841fe93ba4c0aa98","source":{"kind":"arxiv","id":"1803.00659","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00659","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00659v1","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00659","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"5O55WCBKPZER","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5O55WCBKPZER5VL3","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5O55WCBK","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5O55WCBKPZER5VL3GRFWDSMYMY","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-01T23:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"0f68974dacd64180ea4e8d9fe5f839ea4f5b248b971145f7e42ade2ed4c9f907","abstract_canon_sha256":"f12cbf5066dcd4137b4afe1169e35b8b115a634c810e7af57100b39f26c781af"},"schema_version":"1.0"},"canonical_sha256":"ebbbdb082a7e491ed57b344b61c9986609ba50ad22f731d9841fe93ba4c0aa98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:08.230210Z","signature_b64":"xJYY0Z++hLcDR3R7y86SXQ/um550Ji/lC67cEt7KOngJXQxAYAcyCHX/BsmHWSvSLOi3SRDDKw92n20/KmUBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebbbdb082a7e491ed57b344b61c9986609ba50ad22f731d9841fe93ba4c0aa98","last_reissued_at":"2026-05-18T00:22:08.229643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:08.229643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00659","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":"2026-05-18T00:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oD4XO55ifo/PpQ/QfHDFPS/Jemybc25NGtirsza1Gq6IDfHrdQbRMhSVCL8vVD9+B9ftjHhxcjC89Nr2ZQq8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:32:17.344895Z"},"content_sha256":"6128e7b6b7c0ffdb77b73cda0cf85c23f215564e12f5968f1e04660209610c5d","schema_version":"1.0","event_id":"sha256:6128e7b6b7c0ffdb77b73cda0cf85c23f215564e12f5968f1e04660209610c5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5O55WCBKPZER5VL3GRFWDSMYMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of generalized Sidon sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J\\'ozsef Balogh, Lina Li","submitted_at":"2018-03-01T23:28:44Z","abstract_excerpt":"A set $A$ of nonnegative integers is called a Sidon set if there is no Sidon 4-tuple, i.e., $(a,b,c,d)$ in $A$ with $a+b=c+d$ and $\\{a, b\\}\\cap \\{c, d\\}=\\emptyset$. Cameron and Erd\\H os proposed the problem of determining the number of Sidon sets in $[n]$. Results of Kohayakawa, Lee, R\\\" odl and Samotij, and Saxton and Thomason has established that the number of Sidon sets is between $2^{(1.16+o(1))\\sqrt{n}}$ and $2^{(6.442+o(1))\\sqrt{n}}$. An $\\alpha$-generalized Sidon set in $[n]$ is a set with at most $\\alpha$ Sidon 4-tuples. One way to extend the problem of Cameron and Erd\\H os is to estim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00659","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":"2026-05-18T00:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NkGbPswrV4c0W4qeWT+7KnsJacgSQQkyhrQZ3LD8/PHl4Q2e1QuR2+tNkrGF8uaac4xtwdoThN5bvpGwvE1MAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:32:17.345617Z"},"content_sha256":"725a89322fd083ae96bc44aebfdb3afc7b49f00926dbf3148f6aaf898115f4e2","schema_version":"1.0","event_id":"sha256:725a89322fd083ae96bc44aebfdb3afc7b49f00926dbf3148f6aaf898115f4e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5O55WCBKPZER5VL3GRFWDSMYMY/bundle.json","state_url":"https://pith.science/pith/5O55WCBKPZER5VL3GRFWDSMYMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5O55WCBKPZER5VL3GRFWDSMYMY/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":"2026-06-07T17:32:17Z","links":{"resolver":"https://pith.science/pith/5O55WCBKPZER5VL3GRFWDSMYMY","bundle":"https://pith.science/pith/5O55WCBKPZER5VL3GRFWDSMYMY/bundle.json","state":"https://pith.science/pith/5O55WCBKPZER5VL3GRFWDSMYMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5O55WCBKPZER5VL3GRFWDSMYMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5O55WCBKPZER5VL3GRFWDSMYMY","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":"f12cbf5066dcd4137b4afe1169e35b8b115a634c810e7af57100b39f26c781af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-01T23:28:44Z","title_canon_sha256":"0f68974dacd64180ea4e8d9fe5f839ea4f5b248b971145f7e42ade2ed4c9f907"},"schema_version":"1.0","source":{"id":"1803.00659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00659","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00659v1","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00659","created_at":"2026-05-18T00:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"5O55WCBKPZER","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5O55WCBKPZER5VL3","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5O55WCBK","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:725a89322fd083ae96bc44aebfdb3afc7b49f00926dbf3148f6aaf898115f4e2","target":"graph","created_at":"2026-05-18T00:22:08Z","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":"A set $A$ of nonnegative integers is called a Sidon set if there is no Sidon 4-tuple, i.e., $(a,b,c,d)$ in $A$ with $a+b=c+d$ and $\\{a, b\\}\\cap \\{c, d\\}=\\emptyset$. Cameron and Erd\\H os proposed the problem of determining the number of Sidon sets in $[n]$. Results of Kohayakawa, Lee, R\\\" odl and Samotij, and Saxton and Thomason has established that the number of Sidon sets is between $2^{(1.16+o(1))\\sqrt{n}}$ and $2^{(6.442+o(1))\\sqrt{n}}$. An $\\alpha$-generalized Sidon set in $[n]$ is a set with at most $\\alpha$ Sidon 4-tuples. One way to extend the problem of Cameron and Erd\\H os is to estim","authors_text":"J\\'ozsef Balogh, Lina Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-01T23:28:44Z","title":"On the number of generalized Sidon sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00659","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":"sha256:6128e7b6b7c0ffdb77b73cda0cf85c23f215564e12f5968f1e04660209610c5d","target":"record","created_at":"2026-05-18T00:22:08Z","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":"f12cbf5066dcd4137b4afe1169e35b8b115a634c810e7af57100b39f26c781af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-01T23:28:44Z","title_canon_sha256":"0f68974dacd64180ea4e8d9fe5f839ea4f5b248b971145f7e42ade2ed4c9f907"},"schema_version":"1.0","source":{"id":"1803.00659","kind":"arxiv","version":1}},"canonical_sha256":"ebbbdb082a7e491ed57b344b61c9986609ba50ad22f731d9841fe93ba4c0aa98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebbbdb082a7e491ed57b344b61c9986609ba50ad22f731d9841fe93ba4c0aa98","first_computed_at":"2026-05-18T00:22:08.229643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:08.229643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xJYY0Z++hLcDR3R7y86SXQ/um550Ji/lC67cEt7KOngJXQxAYAcyCHX/BsmHWSvSLOi3SRDDKw92n20/KmUBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:08.230210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6128e7b6b7c0ffdb77b73cda0cf85c23f215564e12f5968f1e04660209610c5d","sha256:725a89322fd083ae96bc44aebfdb3afc7b49f00926dbf3148f6aaf898115f4e2"],"state_sha256":"0d97dffc8fda8f18a42781513342cba1d4d8d65744d911e1d96aa788abe63696"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9iL5sDv/r2m2kHZxTvX8FvIx2h4PJUlC3uSEdXXiBjYFcLjQpsQIGNQ9KOMcF48x6ff4cPLrxdPWL2dKFjTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:32:17.349340Z","bundle_sha256":"772e3a9a43b90ce69c95936c740f1da28ea97e722f1c751abc4917c01df97214"}}