{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EONRHXIUVNDROPQLHN4HBSGAKR","short_pith_number":"pith:EONRHXIU","canonical_record":{"source":{"id":"1304.5173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-18T16:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"a9e60d94cdcac7d914e63f5356a05c6937c4f28c62fac535c7d1641dea4498eb","abstract_canon_sha256":"73c698a2a28183a93ba4b688d3478064193363b57a0b297d8699fa8b43430db5"},"schema_version":"1.0"},"canonical_sha256":"239b13dd14ab47173e0b3b7870c8c05447881f62d293e1a0d5d2e13ea0c910be","source":{"kind":"arxiv","id":"1304.5173","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5173","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5173v2","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5173","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"EONRHXIUVNDR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EONRHXIUVNDROPQL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EONRHXIU","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EONRHXIUVNDROPQLHN4HBSGAKR","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-18T16:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"a9e60d94cdcac7d914e63f5356a05c6937c4f28c62fac535c7d1641dea4498eb","abstract_canon_sha256":"73c698a2a28183a93ba4b688d3478064193363b57a0b297d8699fa8b43430db5"},"schema_version":"1.0"},"canonical_sha256":"239b13dd14ab47173e0b3b7870c8c05447881f62d293e1a0d5d2e13ea0c910be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:15.413557Z","signature_b64":"d0DYjdQ67pUpkRnn5iOlThPwaVwfSTSVlOIkRdlcC1um0qpyjMMeGyemWo5ETKh8C17glU6hJS8jSEXFMbOYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"239b13dd14ab47173e0b3b7870c8c05447881f62d293e1a0d5d2e13ea0c910be","last_reissued_at":"2026-05-18T03:04:15.412979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:15.412979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5173","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BrDpSLN3wF5Vr2zOVN7Tzqty2T8A6gQMJ1btkyuNan0QYiKbMeTn0GCsf6xd5IouRXCWyW4o2+Jx1BexE/lzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:57:49.087249Z"},"content_sha256":"802324bd3f997c05884e3d15d47162a73c3545b67dc6c0a242eb8e25a63065b6","schema_version":"1.0","event_id":"sha256:802324bd3f997c05884e3d15d47162a73c3545b67dc6c0a242eb8e25a63065b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EONRHXIUVNDROPQLHN4HBSGAKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partition regularity with congruence conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Barber, Imre Leader","submitted_at":"2013-04-18T16:04:49Z","abstract_excerpt":"An infinite integer matrix A is called image partition regular if, whenever the natural numbers are finitely coloured, there is an integer vector x such that Ax is monochromatic. Given an image partition regular matrix A, can we also insist that each variable x_i is a multiple of some given d_i? This is a question of Hindman, Leader and Strauss.\n  Our aim in this short note is to show that the answer is negative. As an application, we disprove a conjectured equivalence between the two main forms of partition regularity, namely image partition regularity and kernel partition regularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5173","kind":"arxiv","version":2},"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":"2026-05-18T03:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AdM1ODTinMu691rvIHWNYtQPwtCVNDDK1wRqA2DVzyd/l/FTe8Mrqc8gu/NdQyX4OhYZyKxMPc6WT/rauaEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:57:49.087605Z"},"content_sha256":"d6427bba644ec99ebde012c3a2a2baaf15539b00836f18de7f20ff3ed490c153","schema_version":"1.0","event_id":"sha256:d6427bba644ec99ebde012c3a2a2baaf15539b00836f18de7f20ff3ed490c153"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EONRHXIUVNDROPQLHN4HBSGAKR/bundle.json","state_url":"https://pith.science/pith/EONRHXIUVNDROPQLHN4HBSGAKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EONRHXIUVNDROPQLHN4HBSGAKR/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":"2026-06-02T15:57:49Z","links":{"resolver":"https://pith.science/pith/EONRHXIUVNDROPQLHN4HBSGAKR","bundle":"https://pith.science/pith/EONRHXIUVNDROPQLHN4HBSGAKR/bundle.json","state":"https://pith.science/pith/EONRHXIUVNDROPQLHN4HBSGAKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EONRHXIUVNDROPQLHN4HBSGAKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EONRHXIUVNDROPQLHN4HBSGAKR","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":"73c698a2a28183a93ba4b688d3478064193363b57a0b297d8699fa8b43430db5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-18T16:04:49Z","title_canon_sha256":"a9e60d94cdcac7d914e63f5356a05c6937c4f28c62fac535c7d1641dea4498eb"},"schema_version":"1.0","source":{"id":"1304.5173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5173","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5173v2","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5173","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"EONRHXIUVNDR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EONRHXIUVNDROPQL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EONRHXIU","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:d6427bba644ec99ebde012c3a2a2baaf15539b00836f18de7f20ff3ed490c153","target":"graph","created_at":"2026-05-18T03:04:15Z","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":"An infinite integer matrix A is called image partition regular if, whenever the natural numbers are finitely coloured, there is an integer vector x such that Ax is monochromatic. Given an image partition regular matrix A, can we also insist that each variable x_i is a multiple of some given d_i? This is a question of Hindman, Leader and Strauss.\n  Our aim in this short note is to show that the answer is negative. As an application, we disprove a conjectured equivalence between the two main forms of partition regularity, namely image partition regularity and kernel partition regularity.","authors_text":"Ben Barber, Imre Leader","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-18T16:04:49Z","title":"Partition regularity with congruence conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5173","kind":"arxiv","version":2},"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":"sha256:802324bd3f997c05884e3d15d47162a73c3545b67dc6c0a242eb8e25a63065b6","target":"record","created_at":"2026-05-18T03:04:15Z","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":"73c698a2a28183a93ba4b688d3478064193363b57a0b297d8699fa8b43430db5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-18T16:04:49Z","title_canon_sha256":"a9e60d94cdcac7d914e63f5356a05c6937c4f28c62fac535c7d1641dea4498eb"},"schema_version":"1.0","source":{"id":"1304.5173","kind":"arxiv","version":2}},"canonical_sha256":"239b13dd14ab47173e0b3b7870c8c05447881f62d293e1a0d5d2e13ea0c910be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"239b13dd14ab47173e0b3b7870c8c05447881f62d293e1a0d5d2e13ea0c910be","first_computed_at":"2026-05-18T03:04:15.412979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:15.412979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d0DYjdQ67pUpkRnn5iOlThPwaVwfSTSVlOIkRdlcC1um0qpyjMMeGyemWo5ETKh8C17glU6hJS8jSEXFMbOYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:15.413557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:802324bd3f997c05884e3d15d47162a73c3545b67dc6c0a242eb8e25a63065b6","sha256:d6427bba644ec99ebde012c3a2a2baaf15539b00836f18de7f20ff3ed490c153"],"state_sha256":"c574286f3fb3afbf79fead9ac13a2e3c5a5ae766305465d42c3a7893e5b2685a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMwT6roR3Q25n+TcdomWEx6hFc5kV1BiNQ2HD7oBPLzYfQE7F7AgIvr4CVUKJEszUBBHe+O9pmb8zXRfm7LoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:57:49.089484Z","bundle_sha256":"e722cbded2d164b3a8080775b8a2bbc3615b1fd494a99a67f7b62a620e87d124"}}