{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KCH2Z455BZIZ7CMOCO552MY4NN","short_pith_number":"pith:KCH2Z455","canonical_record":{"source":{"id":"1210.6917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-25T17:24:57Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"5885f640a43c0458ab86f233cadc1dee1389dccaf8cabb6042622d26fdf73a38","abstract_canon_sha256":"93909d9c0c1a9fc4d430041993988baad438c0842195e8e0d9e2201005d03921"},"schema_version":"1.0"},"canonical_sha256":"508facf3bd0e519f898e13bbdd331c6b64838255d5849df8f0349c3f8cd6273f","source":{"kind":"arxiv","id":"1210.6917","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6917","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6917v1","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6917","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"KCH2Z455BZIZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KCH2Z455BZIZ7CMO","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KCH2Z455","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KCH2Z455BZIZ7CMOCO552MY4NN","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-25T17:24:57Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"5885f640a43c0458ab86f233cadc1dee1389dccaf8cabb6042622d26fdf73a38","abstract_canon_sha256":"93909d9c0c1a9fc4d430041993988baad438c0842195e8e0d9e2201005d03921"},"schema_version":"1.0"},"canonical_sha256":"508facf3bd0e519f898e13bbdd331c6b64838255d5849df8f0349c3f8cd6273f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:28.903381Z","signature_b64":"Blpqsuw/slOowceQ7AU6FYKDj3ldcD3s4U9W80pX8Rm8CDoy6sxqwOaIvfuumyg5ThURf8GetURxwFlH7nylAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"508facf3bd0e519f898e13bbdd331c6b64838255d5849df8f0349c3f8cd6273f","last_reissued_at":"2026-05-17T23:43:28.902739Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:28.902739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6917","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":"2026-05-17T23:43:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aj99m03aIrFympHV3I/GJZjt9KuD4F42ts2LqCI4fjXyBtcr+dc56TdF8qtKjZC4icDcUDRihAhOvAyKSOhRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:18:41.562716Z"},"content_sha256":"a9b432a9ac23cf94ffe69e5c6e892b69eb0d7a6dd52836a7eb74ea4a09235174","schema_version":"1.0","event_id":"sha256:a9b432a9ac23cf94ffe69e5c6e892b69eb0d7a6dd52836a7eb74ea4a09235174"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KCH2Z455BZIZ7CMOCO552MY4NN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling-based proofs of almost-periodicity results and algorithmic applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Eli Ben-Sasson, Julia Wolf, Madhur Tulsiani, Noga Ron-Zewi","submitted_at":"2012-10-25T17:24:57Z","abstract_excerpt":"We give new combinatorial proofs of known almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask, whose almost-periodicity lemma has had far-reaching implications in additive combinatorics. We provide an alternative (and L^p-norm free) point of view, which allows for proofs to easily be converted to probabilistic algorithms that decide membership in almost-periodic sumsets of dense subsets of F_2^n.\n  As an application, we give a new algorithmic version of the quasipolynomial Bogolyubov-Ruzsa lemma recently proved by Sanders. Together with the resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6917","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":"2026-05-17T23:43:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"74ZGGCzqZReqlDKfuc++VP6aVUJrkFYiPKSmWMTbgfgDx3goM6LZdFYRNCpqRlymxVTDGLol6AAb+E16eW6LDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:18:41.563429Z"},"content_sha256":"01d2dfab7d47f021425bfa23570037b78e1edc4cd79cc23eb898e45a0810f236","schema_version":"1.0","event_id":"sha256:01d2dfab7d47f021425bfa23570037b78e1edc4cd79cc23eb898e45a0810f236"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCH2Z455BZIZ7CMOCO552MY4NN/bundle.json","state_url":"https://pith.science/pith/KCH2Z455BZIZ7CMOCO552MY4NN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCH2Z455BZIZ7CMOCO552MY4NN/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":"2026-06-11T06:18:41Z","links":{"resolver":"https://pith.science/pith/KCH2Z455BZIZ7CMOCO552MY4NN","bundle":"https://pith.science/pith/KCH2Z455BZIZ7CMOCO552MY4NN/bundle.json","state":"https://pith.science/pith/KCH2Z455BZIZ7CMOCO552MY4NN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCH2Z455BZIZ7CMOCO552MY4NN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KCH2Z455BZIZ7CMOCO552MY4NN","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":"93909d9c0c1a9fc4d430041993988baad438c0842195e8e0d9e2201005d03921","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-25T17:24:57Z","title_canon_sha256":"5885f640a43c0458ab86f233cadc1dee1389dccaf8cabb6042622d26fdf73a38"},"schema_version":"1.0","source":{"id":"1210.6917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6917","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6917v1","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6917","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"KCH2Z455BZIZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KCH2Z455BZIZ7CMO","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KCH2Z455","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:01d2dfab7d47f021425bfa23570037b78e1edc4cd79cc23eb898e45a0810f236","target":"graph","created_at":"2026-05-17T23:43:28Z","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 give new combinatorial proofs of known almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask, whose almost-periodicity lemma has had far-reaching implications in additive combinatorics. We provide an alternative (and L^p-norm free) point of view, which allows for proofs to easily be converted to probabilistic algorithms that decide membership in almost-periodic sumsets of dense subsets of F_2^n.\n  As an application, we give a new algorithmic version of the quasipolynomial Bogolyubov-Ruzsa lemma recently proved by Sanders. Together with the resu","authors_text":"Eli Ben-Sasson, Julia Wolf, Madhur Tulsiani, Noga Ron-Zewi","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-25T17:24:57Z","title":"Sampling-based proofs of almost-periodicity results and algorithmic applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6917","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:a9b432a9ac23cf94ffe69e5c6e892b69eb0d7a6dd52836a7eb74ea4a09235174","target":"record","created_at":"2026-05-17T23:43:28Z","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":"93909d9c0c1a9fc4d430041993988baad438c0842195e8e0d9e2201005d03921","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-25T17:24:57Z","title_canon_sha256":"5885f640a43c0458ab86f233cadc1dee1389dccaf8cabb6042622d26fdf73a38"},"schema_version":"1.0","source":{"id":"1210.6917","kind":"arxiv","version":1}},"canonical_sha256":"508facf3bd0e519f898e13bbdd331c6b64838255d5849df8f0349c3f8cd6273f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"508facf3bd0e519f898e13bbdd331c6b64838255d5849df8f0349c3f8cd6273f","first_computed_at":"2026-05-17T23:43:28.902739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:28.902739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Blpqsuw/slOowceQ7AU6FYKDj3ldcD3s4U9W80pX8Rm8CDoy6sxqwOaIvfuumyg5ThURf8GetURxwFlH7nylAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:28.903381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9b432a9ac23cf94ffe69e5c6e892b69eb0d7a6dd52836a7eb74ea4a09235174","sha256:01d2dfab7d47f021425bfa23570037b78e1edc4cd79cc23eb898e45a0810f236"],"state_sha256":"a56cb79e140927c97b009f7f05682e0299807a1173b25b861c36afc9f3a5b927"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aH86PhCllYh+q1vYnoktG526U5kDXThNF69X93da6ZUkVnrswBya7cuF/7oT6zPR1VC57uhUqEL5R0snhE4KAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:18:41.567493Z","bundle_sha256":"7cbc9fcf7e6625c33f57d720d4a064b820ff0fa996097765ef509ec38d6ee4be"}}