{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QA4ELQBH4G3WC72TAPGKW57MOY","short_pith_number":"pith:QA4ELQBH","canonical_record":{"source":{"id":"1303.3600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T20:44:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f3a5e4873a86b34fc4f2a060596ec18685ce3758d9c8521c05c256bf8b493012","abstract_canon_sha256":"f400a4dea9eb9592c56cba932fb56a89b12c3b16b70f2512ab899f281fecb374"},"schema_version":"1.0"},"canonical_sha256":"803845c027e1b7617f5303ccab77ec7638933fc9d8b3f09a258582cebb9e1aef","source":{"kind":"arxiv","id":"1303.3600","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3600","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3600v2","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3600","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"QA4ELQBH4G3W","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QA4ELQBH4G3WC72T","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QA4ELQBH","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QA4ELQBH4G3WC72TAPGKW57MOY","target":"record","payload":{"canonical_record":{"source":{"id":"1303.3600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T20:44:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f3a5e4873a86b34fc4f2a060596ec18685ce3758d9c8521c05c256bf8b493012","abstract_canon_sha256":"f400a4dea9eb9592c56cba932fb56a89b12c3b16b70f2512ab899f281fecb374"},"schema_version":"1.0"},"canonical_sha256":"803845c027e1b7617f5303ccab77ec7638933fc9d8b3f09a258582cebb9e1aef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:33.842460Z","signature_b64":"TmkA78ouVL5rAa4JtdKJJ9erEcEIK8sVT9S5y4lhWtx+e06tQ1yPnA3u1zyw2Gn35dcssqMG/IKRwyIoriN+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"803845c027e1b7617f5303ccab77ec7638933fc9d8b3f09a258582cebb9e1aef","last_reissued_at":"2026-05-18T03:13:33.841633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:33.841633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.3600","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":"2026-05-18T03:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSv6JpxAVawI8ITheFJZ1IhDbDyLu0frW0x6piVEDGnK3kJCmZ9WO4qjUroetaWtO3jS6xdMg8u6grJHunNBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:06:58.603016Z"},"content_sha256":"ed54ad7931f9258d9135d87cc80280b0321d362ddf170042e84d1a11c7402a47","schema_version":"1.0","event_id":"sha256:ed54ad7931f9258d9135d87cc80280b0321d362ddf170042e84d1a11c7402a47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QA4ELQBH4G3WC72TAPGKW57MOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hindman's Coloring Theorem in arbitrary semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Boaz Tsaban, Gili Golan","submitted_at":"2013-03-14T20:44:41Z","abstract_excerpt":"Hindman's Theorem asserts that, for each finite coloring of the natural numbers, there are distinct natural numbers $a_1,a_2,\\dots$ such that all of the sums $a_{i_1}+a_{i_2}+\\dots+a_{i_m}$ ($m\\ge 1$, $i_1<i_2<\\dots<i_m$) have the same color.\n  The celebrated Galvin--Glazer proof of Hindman's Theorem and a classification of semigroups due to Shevrin, imply together that, for each finite coloring of each infinite semigroup $S$, there are distinct elements $a_1,a_2,\\dots$ of $S$ such that all but finitely many of the products $a_{i_1}a_{i_2}\\cdots a_{i_m}$ ($m\\ge 1$, $i_1<i_2<\\dots<i_m$) have th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3600","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":"2026-05-18T03:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrQZMoymj1soS4mFyNOUanxVJOB4LqbeopNMdIZwz4zNjlHUY8N1SXTxPxzOTzmwcQf6yI0thkoiyVgFx4haDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:06:58.603423Z"},"content_sha256":"c3eace261c49ab491c226ddce5916f8e41e4c7350ca428fe06a264a60935e1b3","schema_version":"1.0","event_id":"sha256:c3eace261c49ab491c226ddce5916f8e41e4c7350ca428fe06a264a60935e1b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QA4ELQBH4G3WC72TAPGKW57MOY/bundle.json","state_url":"https://pith.science/pith/QA4ELQBH4G3WC72TAPGKW57MOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QA4ELQBH4G3WC72TAPGKW57MOY/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":"2026-06-01T23:06:58Z","links":{"resolver":"https://pith.science/pith/QA4ELQBH4G3WC72TAPGKW57MOY","bundle":"https://pith.science/pith/QA4ELQBH4G3WC72TAPGKW57MOY/bundle.json","state":"https://pith.science/pith/QA4ELQBH4G3WC72TAPGKW57MOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QA4ELQBH4G3WC72TAPGKW57MOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QA4ELQBH4G3WC72TAPGKW57MOY","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":"f400a4dea9eb9592c56cba932fb56a89b12c3b16b70f2512ab899f281fecb374","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T20:44:41Z","title_canon_sha256":"f3a5e4873a86b34fc4f2a060596ec18685ce3758d9c8521c05c256bf8b493012"},"schema_version":"1.0","source":{"id":"1303.3600","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3600","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3600v2","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3600","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"QA4ELQBH4G3W","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QA4ELQBH4G3WC72T","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QA4ELQBH","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:c3eace261c49ab491c226ddce5916f8e41e4c7350ca428fe06a264a60935e1b3","target":"graph","created_at":"2026-05-18T03:13:33Z","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":"Hindman's Theorem asserts that, for each finite coloring of the natural numbers, there are distinct natural numbers $a_1,a_2,\\dots$ such that all of the sums $a_{i_1}+a_{i_2}+\\dots+a_{i_m}$ ($m\\ge 1$, $i_1<i_2<\\dots<i_m$) have the same color.\n  The celebrated Galvin--Glazer proof of Hindman's Theorem and a classification of semigroups due to Shevrin, imply together that, for each finite coloring of each infinite semigroup $S$, there are distinct elements $a_1,a_2,\\dots$ of $S$ such that all but finitely many of the products $a_{i_1}a_{i_2}\\cdots a_{i_m}$ ($m\\ge 1$, $i_1<i_2<\\dots<i_m$) have th","authors_text":"Boaz Tsaban, Gili Golan","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T20:44:41Z","title":"Hindman's Coloring Theorem in arbitrary semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3600","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:ed54ad7931f9258d9135d87cc80280b0321d362ddf170042e84d1a11c7402a47","target":"record","created_at":"2026-05-18T03:13:33Z","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":"f400a4dea9eb9592c56cba932fb56a89b12c3b16b70f2512ab899f281fecb374","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T20:44:41Z","title_canon_sha256":"f3a5e4873a86b34fc4f2a060596ec18685ce3758d9c8521c05c256bf8b493012"},"schema_version":"1.0","source":{"id":"1303.3600","kind":"arxiv","version":2}},"canonical_sha256":"803845c027e1b7617f5303ccab77ec7638933fc9d8b3f09a258582cebb9e1aef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"803845c027e1b7617f5303ccab77ec7638933fc9d8b3f09a258582cebb9e1aef","first_computed_at":"2026-05-18T03:13:33.841633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:33.841633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TmkA78ouVL5rAa4JtdKJJ9erEcEIK8sVT9S5y4lhWtx+e06tQ1yPnA3u1zyw2Gn35dcssqMG/IKRwyIoriN+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:33.842460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3600","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed54ad7931f9258d9135d87cc80280b0321d362ddf170042e84d1a11c7402a47","sha256:c3eace261c49ab491c226ddce5916f8e41e4c7350ca428fe06a264a60935e1b3"],"state_sha256":"2c66f358e63f6bb8762ff80bc9c19bc7b388f27024a693d973911ccdd74f7c6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wPyAquj/6GZ3S0ezuRaWrUQiYn/R/RctjwCwhTaszrKwVGHLoZFRV7jjGZwqbi2RQ7z6zHIdCAaZc5zZkkAHBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:06:58.605396Z","bundle_sha256":"8d1403f7e32197b222811c9ea556098d40d74138a84e7c376953a027594a4810"}}