{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FVKVYWTUWNJFO7X6GAGIQ7PMES","short_pith_number":"pith:FVKVYWTU","canonical_record":{"source":{"id":"2603.27163","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-03-28T06:59:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"68670f24c2eeb81c31e3ec7359fd037013a158ae4c8c6c8300bec6e2b55d5439","abstract_canon_sha256":"03f6e76b51c5c5f27166f07b710e808049bcf4c04ecdde3847e26a4f956ba4e9"},"schema_version":"1.0"},"canonical_sha256":"2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a","source":{"kind":"arxiv","id":"2603.27163","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.27163","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2603.27163v4","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27163","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVKVYWTUWNJF","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"FVKVYWTUWNJFO7X6","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"FVKVYWTU","created_at":"2026-05-22T01:04:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FVKVYWTUWNJFO7X6GAGIQ7PMES","target":"record","payload":{"canonical_record":{"source":{"id":"2603.27163","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-03-28T06:59:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"68670f24c2eeb81c31e3ec7359fd037013a158ae4c8c6c8300bec6e2b55d5439","abstract_canon_sha256":"03f6e76b51c5c5f27166f07b710e808049bcf4c04ecdde3847e26a4f956ba4e9"},"schema_version":"1.0"},"canonical_sha256":"2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:00.957802Z","signature_b64":"L1GB5lyBc0LlZ7d/srrfixaLgb/Ao8XcN7yVDiUqjyNlsVb7YR59jiuvsUyG13jb3ZvszZopzD+PcWloIMWhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a","last_reissued_at":"2026-05-22T01:04:00.956988Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:00.956988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.27163","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXdAU7MacCBBgD+az+OA8sRzTpVBKAdQ3fAlDekA6iN4BxcP6ZOGB1ervcQJVzPqwVIuOnHsEKL0oqcNNAJPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:38:50.441816Z"},"content_sha256":"94967f23caa088553aed453dc5d62fa39bcbc552dfc9d56722bd264fb25b9ac3","schema_version":"1.0","event_id":"sha256:94967f23caa088553aed453dc5d62fa39bcbc552dfc9d56722bd264fb25b9ac3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FVKVYWTUWNJFO7X6GAGIQ7PMES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hindman and Owings-like theorems without the Axiom of Choice","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable.","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"David J. Fern\\'andez Bret\\'on, Eliseo Sarmiento Rosales, Jos\\'e A. Guzm\\'an-Vega","submitted_at":"2026-03-28T06:59:02Z","abstract_excerpt":"We investigate Hindman- and Owings-type Ramsey-theoretic statements in Zermelo-Fraenkel set theory without the Axiom of Choice, with some occasional extra assumptions (such as the Axiom of Dependent Choice and/or the Axiom of Determinacy). We study several variations of Hindman's theorem on $\\mathbb Q$-vector spaces; notably, we show that the uncountable analog of Hindman's theorem fails for the additive group of $\\mathbb R$ (under ZF), and for $\\mathbb Q$-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable), among other results. In contrast, for Owings-typ"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the uncountable analog of Hindman's theorem fails for the additive group of R (under ZF), and for Q-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable)","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the uncountable dimension is not well-orderable when working under DC; if every set of reals is well-orderable then the negative result may not hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Uncountable Hindman theorems fail in ZF and under DC for non-well-orderable dimensions, while Owings configurations hold under AD.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"38c0f26d8aa6ed24ec9edca5b58bd0132429f416c51af5cd70e7527e29d21055"},"source":{"id":"2603.27163","kind":"arxiv","version":4},"verdict":{"id":"fb368cbc-fed9-4589-a9b5-5711d8301dd3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T22:19:22.789226Z","strongest_claim":"the uncountable analog of Hindman's theorem fails for the additive group of R (under ZF), and for Q-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable)","one_line_summary":"Uncountable Hindman theorems fail in ZF and under DC for non-well-orderable dimensions, while Owings configurations hold under AD.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the uncountable dimension is not well-orderable when working under DC; if every set of reals is well-orderable then the negative result may not hold.","pith_extraction_headline":"The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.27163/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":3,"snapshot_sha256":"46a0b7f6421d2a81ab66e2907e3f7c56361eb6466859ab992c51549a707503ac"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"fb368cbc-fed9-4589-a9b5-5711d8301dd3"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNdjp8VlphRJQMNDov4wPMb9RvmbLDS/9j/fG+yzO6NYOSblKm6UL1Wm2qniD5s8u6QQi3y5+PJG5SECXQCgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:38:50.442803Z"},"content_sha256":"88c3797b5ba0a430f673be3c620cc171aaf5bca0544d827c020459aa68e91dd2","schema_version":"1.0","event_id":"sha256:88c3797b5ba0a430f673be3c620cc171aaf5bca0544d827c020459aa68e91dd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES/bundle.json","state_url":"https://pith.science/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES/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":"2026-06-10T05:38:50Z","links":{"resolver":"https://pith.science/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES","bundle":"https://pith.science/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES/bundle.json","state":"https://pith.science/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVKVYWTUWNJFO7X6GAGIQ7PMES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FVKVYWTUWNJFO7X6GAGIQ7PMES","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":"03f6e76b51c5c5f27166f07b710e808049bcf4c04ecdde3847e26a4f956ba4e9","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-03-28T06:59:02Z","title_canon_sha256":"68670f24c2eeb81c31e3ec7359fd037013a158ae4c8c6c8300bec6e2b55d5439"},"schema_version":"1.0","source":{"id":"2603.27163","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.27163","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2603.27163v4","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27163","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVKVYWTUWNJF","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"FVKVYWTUWNJFO7X6","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"FVKVYWTU","created_at":"2026-05-22T01:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:88c3797b5ba0a430f673be3c620cc171aaf5bca0544d827c020459aa68e91dd2","target":"graph","created_at":"2026-05-22T01:04:00Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"the uncountable analog of Hindman's theorem fails for the additive group of R (under ZF), and for Q-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable)"},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the uncountable dimension is not well-orderable when working under DC; if every set of reals is well-orderable then the negative result may not hold."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Uncountable Hindman theorems fail in ZF and under DC for non-well-orderable dimensions, while Owings configurations hold under AD."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable."}],"snapshot_sha256":"38c0f26d8aa6ed24ec9edca5b58bd0132429f416c51af5cd70e7527e29d21055"},"formal_canon":{"evidence_count":3,"snapshot_sha256":"46a0b7f6421d2a81ab66e2907e3f7c56361eb6466859ab992c51549a707503ac"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.27163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate Hindman- and Owings-type Ramsey-theoretic statements in Zermelo-Fraenkel set theory without the Axiom of Choice, with some occasional extra assumptions (such as the Axiom of Dependent Choice and/or the Axiom of Determinacy). We study several variations of Hindman's theorem on $\\mathbb Q$-vector spaces; notably, we show that the uncountable analog of Hindman's theorem fails for the additive group of $\\mathbb R$ (under ZF), and for $\\mathbb Q$-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable), among other results. In contrast, for Owings-typ","authors_text":"David J. Fern\\'andez Bret\\'on, Eliseo Sarmiento Rosales, Jos\\'e A. Guzm\\'an-Vega","cross_cats":["math.CO"],"headline":"The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-03-28T06:59:02Z","title":"Hindman and Owings-like theorems without the Axiom of Choice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.27163","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-14T22:19:22.789226Z","id":"fb368cbc-fed9-4589-a9b5-5711d8301dd3","model_set":{"reader":"grok-4.3"},"one_line_summary":"Uncountable Hindman theorems fail in ZF and under DC for non-well-orderable dimensions, while Owings configurations hold under AD.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The uncountable analog of Hindman's theorem fails for the additive group of the reals under ZF and for Q-vector spaces of uncountable dimension under DC when the dimension is not well-orderable.","strongest_claim":"the uncountable analog of Hindman's theorem fails for the additive group of R (under ZF), and for Q-vector spaces of uncountable dimension (under DC if such dimension is not well-orderable)","weakest_assumption":"That the uncountable dimension is not well-orderable when working under DC; if every set of reals is well-orderable then the negative result may not hold."}},"verdict_id":"fb368cbc-fed9-4589-a9b5-5711d8301dd3"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:94967f23caa088553aed453dc5d62fa39bcbc552dfc9d56722bd264fb25b9ac3","target":"record","created_at":"2026-05-22T01:04:00Z","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":"03f6e76b51c5c5f27166f07b710e808049bcf4c04ecdde3847e26a4f956ba4e9","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-03-28T06:59:02Z","title_canon_sha256":"68670f24c2eeb81c31e3ec7359fd037013a158ae4c8c6c8300bec6e2b55d5439"},"schema_version":"1.0","source":{"id":"2603.27163","kind":"arxiv","version":4}},"canonical_sha256":"2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d555c5a74b352577efe300c887dec248e8250ac42c230453bf8d2a9cb44224a","first_computed_at":"2026-05-22T01:04:00.956988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:00.956988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L1GB5lyBc0LlZ7d/srrfixaLgb/Ao8XcN7yVDiUqjyNlsVb7YR59jiuvsUyG13jb3ZvszZopzD+PcWloIMWhDw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:00.957802Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.27163","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94967f23caa088553aed453dc5d62fa39bcbc552dfc9d56722bd264fb25b9ac3","sha256:88c3797b5ba0a430f673be3c620cc171aaf5bca0544d827c020459aa68e91dd2"],"state_sha256":"399079a9ab3d9ba2be150e015d13d585eb900e0f880fd78522f2ccd81ddaa2e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7idcpPiNAvFNCg7+vlkDrszJt/ZCgy8aBJ9IQqjLuADaAfTI+KskhzQE1+LYEcK0aAagepmBEFB3Ti3dfDlFDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:38:50.447621Z","bundle_sha256":"40f726c4345cafe2183c4ea29868545a9def314fa58cf9b502b40d044a53c91e"}}