{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KG7TXMZ6QN5OAAKQBYKPWDTP5C","short_pith_number":"pith:KG7TXMZ6","canonical_record":{"source":{"id":"2606.17487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T03:57:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e6dc6dfba2e1109fb085017f613997a29e9656d761d268255e9d9df4b24d2ce0","abstract_canon_sha256":"688f97cc8899e23a997cb8e4336202e6cbe2b7f886875503215bf0922a4c7eca"},"schema_version":"1.0"},"canonical_sha256":"51bf3bb33e837ae001500e14fb0e6fe88454caebe461504902941300417f4dfa","source":{"kind":"arxiv","id":"2606.17487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17487","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17487v1","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17487","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"KG7TXMZ6QN5O","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"KG7TXMZ6QN5OAAKQ","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"KG7TXMZ6","created_at":"2026-06-19T16:10:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KG7TXMZ6QN5OAAKQBYKPWDTP5C","target":"record","payload":{"canonical_record":{"source":{"id":"2606.17487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T03:57:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e6dc6dfba2e1109fb085017f613997a29e9656d761d268255e9d9df4b24d2ce0","abstract_canon_sha256":"688f97cc8899e23a997cb8e4336202e6cbe2b7f886875503215bf0922a4c7eca"},"schema_version":"1.0"},"canonical_sha256":"51bf3bb33e837ae001500e14fb0e6fe88454caebe461504902941300417f4dfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:14.282634Z","signature_b64":"2knjBz4XQBxiynuZQ0XF1gWVuQBe/LZSOPv7B7h2HNN7NTa7uiaAMygAC1hyDD9IguWusWjY92NcKTB1LtnoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51bf3bb33e837ae001500e14fb0e6fe88454caebe461504902941300417f4dfa","last_reissued_at":"2026-06-19T16:10:14.282253Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:14.282253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.17487","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":"2026-06-19T16:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yuYXEnmUmjyO77nsx/8bUCbnDbUrdx2gzcg1Bpgn/NdwaCdgL/H03VxDg7ASZhQuWo/qDLZPFZS+9VaNPYanAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:17:15.472643Z"},"content_sha256":"d6f716247d7dbe6130b6cd902a6d2894096f07664fedcedea66329ee89a4b6ac","schema_version":"1.0","event_id":"sha256:d6f716247d7dbe6130b6cd902a6d2894096f07664fedcedea66329ee89a4b6ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KG7TXMZ6QN5OAAKQBYKPWDTP5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A combinatorial large sieve for Sidon sets, distances, and norm forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Adam Sheffer, Chi Hoi Yip, Cosmin Pohoata, Ernie Croot, Junzhe Mao","submitted_at":"2026-06-16T03:57:20Z","abstract_excerpt":"We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence branching produces many modular collisions, while global bounded-multiplicity hypotheses force these collisions to be rare.\n  As a first application, we prove that every Sidon subset $A\\subset\\{1^2,\\ldots,N^2\\}$ satisfies \\[\n  |A|\n  \\le\n  N\\exp\\left(\n  -c\\frac{\\log N}{\\log\\log N}\n  \\right) \\] for some absolute constant $c>0$. This gives the first super-polylogarithmic saving for a classical problem of Alon and Erd\\H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17487","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/2606.17487/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":"2026-06-19T16:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QXuiri98yy5Wff/6A6o1sbCyySdp7kfzqQxiFOhnZ9JvCD42LWO2JzX9N/Grm+fAj4jtHrk5YzXC0bBhYByMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:17:15.473011Z"},"content_sha256":"e7cbd7f691f9116e42290fbf7530bd4a5237ead6ccf3bebb2ce9d233bb926792","schema_version":"1.0","event_id":"sha256:e7cbd7f691f9116e42290fbf7530bd4a5237ead6ccf3bebb2ce9d233bb926792"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C/bundle.json","state_url":"https://pith.science/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C/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":"2026-06-23T06:17:15Z","links":{"resolver":"https://pith.science/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C","bundle":"https://pith.science/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C/bundle.json","state":"https://pith.science/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KG7TXMZ6QN5OAAKQBYKPWDTP5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KG7TXMZ6QN5OAAKQBYKPWDTP5C","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":"688f97cc8899e23a997cb8e4336202e6cbe2b7f886875503215bf0922a4c7eca","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T03:57:20Z","title_canon_sha256":"e6dc6dfba2e1109fb085017f613997a29e9656d761d268255e9d9df4b24d2ce0"},"schema_version":"1.0","source":{"id":"2606.17487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17487","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17487v1","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17487","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"KG7TXMZ6QN5O","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"KG7TXMZ6QN5OAAKQ","created_at":"2026-06-19T16:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"KG7TXMZ6","created_at":"2026-06-19T16:10:14Z"}],"graph_snapshots":[{"event_id":"sha256:e7cbd7f691f9116e42290fbf7530bd4a5237ead6ccf3bebb2ce9d233bb926792","target":"graph","created_at":"2026-06-19T16:10:14Z","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/2606.17487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence branching produces many modular collisions, while global bounded-multiplicity hypotheses force these collisions to be rare.\n  As a first application, we prove that every Sidon subset $A\\subset\\{1^2,\\ldots,N^2\\}$ satisfies \\[\n  |A|\n  \\le\n  N\\exp\\left(\n  -c\\frac{\\log N}{\\log\\log N}\n  \\right) \\] for some absolute constant $c>0$. This gives the first super-polylogarithmic saving for a classical problem of Alon and Erd\\H","authors_text":"Adam Sheffer, Chi Hoi Yip, Cosmin Pohoata, Ernie Croot, Junzhe Mao","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T03:57:20Z","title":"A combinatorial large sieve for Sidon sets, distances, and norm forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17487","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:d6f716247d7dbe6130b6cd902a6d2894096f07664fedcedea66329ee89a4b6ac","target":"record","created_at":"2026-06-19T16:10:14Z","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":"688f97cc8899e23a997cb8e4336202e6cbe2b7f886875503215bf0922a4c7eca","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T03:57:20Z","title_canon_sha256":"e6dc6dfba2e1109fb085017f613997a29e9656d761d268255e9d9df4b24d2ce0"},"schema_version":"1.0","source":{"id":"2606.17487","kind":"arxiv","version":1}},"canonical_sha256":"51bf3bb33e837ae001500e14fb0e6fe88454caebe461504902941300417f4dfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51bf3bb33e837ae001500e14fb0e6fe88454caebe461504902941300417f4dfa","first_computed_at":"2026-06-19T16:10:14.282253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:14.282253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2knjBz4XQBxiynuZQ0XF1gWVuQBe/LZSOPv7B7h2HNN7NTa7uiaAMygAC1hyDD9IguWusWjY92NcKTB1LtnoCQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:14.282634Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6f716247d7dbe6130b6cd902a6d2894096f07664fedcedea66329ee89a4b6ac","sha256:e7cbd7f691f9116e42290fbf7530bd4a5237ead6ccf3bebb2ce9d233bb926792"],"state_sha256":"c2add8a8774a909eb62b9767a984d52d04d9a690572821c62264166356fc1980"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JHkdadBRgIRr+w2rsODKjG4OoljQEytU9EAHbDrdpEuamI2f8Iy+ewhI75WcREQi65iZEtaPrd5VJ5Cpv2yBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:17:15.475386Z","bundle_sha256":"c50dba0e4e283433fcb086a2e626c7b4c7ab3216b554fd7c56ad43a4fe60a834"}}