{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CFJBQTB73VDCRFLRDIFUTQRQRZ","short_pith_number":"pith:CFJBQTB7","canonical_record":{"source":{"id":"1805.06847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-17T16:32:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b0c5861ce182d4d4de3e327299e59b63206817f2f3781d9b6c8bff6ca1e79152","abstract_canon_sha256":"edc9edd9e115c2c85bcabe0616d603c2b9e9309031a9e570b9fe0fb359c77465"},"schema_version":"1.0"},"canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","source":{"kind":"arxiv","id":"1805.06847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06847","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06847v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06847","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"CFJBQTB73VDC","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFJBQTB73VDCRFLR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFJBQTB7","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CFJBQTB73VDCRFLRDIFUTQRQRZ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-17T16:32:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b0c5861ce182d4d4de3e327299e59b63206817f2f3781d9b6c8bff6ca1e79152","abstract_canon_sha256":"edc9edd9e115c2c85bcabe0616d603c2b9e9309031a9e570b9fe0fb359c77465"},"schema_version":"1.0"},"canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:43.146638Z","signature_b64":"qZiGz4y+sPI/g2bMLOISXmABN/mI1/Ec7cLFAIlBaOutqQKwU4OleD0rErlBUJcIDRvLusRzQW2GRLdagDoCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","last_reissued_at":"2026-05-18T00:15:43.146041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:43.146041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06847","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":"2026-05-18T00:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jimOPmL32XcPx+OWmMs5sy5eNIA9oKgrkCrkXpmQdy5g/QVPxk5tyDdDdZb04XamTP/1jbx5a2lkGC9sqJISBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:44:16.619233Z"},"content_sha256":"c78551366a450319e3305c77d0849c0d6a107a37f6d49a1b91f8388aeebebf81","schema_version":"1.0","event_id":"sha256:c78551366a450319e3305c77d0849c0d6a107a37f6d49a1b91f8388aeebebf81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CFJBQTB73VDCRFLRDIFUTQRQRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative structure of stable sets in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"C. Terry, J. Wolf","submitted_at":"2018-05-17T16:32:15Z","abstract_excerpt":"We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06847","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":"2026-05-18T00:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPQddoN5TVXSvd+HbIyg5/lJWYDARqs22xhyty4yYMhc6KtC7YGi+4uvDl60qNHZRc99N2R7Ger2MNyhrg6+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:44:16.619591Z"},"content_sha256":"09177496a8f6331c09f66443456b0994857a64dd5bba1b10fee8623bb07cc7aa","schema_version":"1.0","event_id":"sha256:09177496a8f6331c09f66443456b0994857a64dd5bba1b10fee8623bb07cc7aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/bundle.json","state_url":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/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":"2026-06-02T15:44:16Z","links":{"resolver":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ","bundle":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/bundle.json","state":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CFJBQTB73VDCRFLRDIFUTQRQRZ","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":"edc9edd9e115c2c85bcabe0616d603c2b9e9309031a9e570b9fe0fb359c77465","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-17T16:32:15Z","title_canon_sha256":"b0c5861ce182d4d4de3e327299e59b63206817f2f3781d9b6c8bff6ca1e79152"},"schema_version":"1.0","source":{"id":"1805.06847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06847","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06847v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06847","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"CFJBQTB73VDC","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFJBQTB73VDCRFLR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFJBQTB7","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:09177496a8f6331c09f66443456b0994857a64dd5bba1b10fee8623bb07cc7aa","target":"graph","created_at":"2026-05-18T00:15:43Z","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 prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics.","authors_text":"C. Terry, J. Wolf","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-17T16:32:15Z","title":"Quantitative structure of stable sets in finite abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06847","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:c78551366a450319e3305c77d0849c0d6a107a37f6d49a1b91f8388aeebebf81","target":"record","created_at":"2026-05-18T00:15:43Z","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":"edc9edd9e115c2c85bcabe0616d603c2b9e9309031a9e570b9fe0fb359c77465","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-17T16:32:15Z","title_canon_sha256":"b0c5861ce182d4d4de3e327299e59b63206817f2f3781d9b6c8bff6ca1e79152"},"schema_version":"1.0","source":{"id":"1805.06847","kind":"arxiv","version":1}},"canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","first_computed_at":"2026-05-18T00:15:43.146041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:43.146041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZiGz4y+sPI/g2bMLOISXmABN/mI1/Ec7cLFAIlBaOutqQKwU4OleD0rErlBUJcIDRvLusRzQW2GRLdagDoCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:43.146638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c78551366a450319e3305c77d0849c0d6a107a37f6d49a1b91f8388aeebebf81","sha256:09177496a8f6331c09f66443456b0994857a64dd5bba1b10fee8623bb07cc7aa"],"state_sha256":"a83e5352638cde1535f5e6908c4d81dd44db0caa3cc65e9585703597e7987b25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GeDn2svKja6RkalmDuoE2Lt6Oi55A7EJUJDnh6bvlDvRGSa//eFs1NwJ/QzAI8XjjxNIye3yBKOQLnpTh3GjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:44:16.622619Z","bundle_sha256":"54d2b1804ea8780f3b0fa2e6ecc9aa31eefddb8ed5d0d21f3e989c4f3ec8ce81"}}