{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2NJXWOYQ2TIZ4OU6DCO5Z2ABDA","short_pith_number":"pith:2NJXWOYQ","canonical_record":{"source":{"id":"1611.08988","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-28T05:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"920a0b4e878f3852e818c3beacac755623349740c42d26311a551405c5cf9066","abstract_canon_sha256":"4a2836a50b5dc846fe6ce85326d6e30bbd431fbe18e58b5c608d3b4a8745737b"},"schema_version":"1.0"},"canonical_sha256":"d3537b3b10d4d19e3a9e189ddce801182de84271e8d71d97251805d3ceab5a2f","source":{"kind":"arxiv","id":"1611.08988","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08988","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08988v4","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08988","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"2NJXWOYQ2TIZ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2NJXWOYQ2TIZ4OU6","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2NJXWOYQ","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2NJXWOYQ2TIZ4OU6DCO5Z2ABDA","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08988","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-28T05:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"920a0b4e878f3852e818c3beacac755623349740c42d26311a551405c5cf9066","abstract_canon_sha256":"4a2836a50b5dc846fe6ce85326d6e30bbd431fbe18e58b5c608d3b4a8745737b"},"schema_version":"1.0"},"canonical_sha256":"d3537b3b10d4d19e3a9e189ddce801182de84271e8d71d97251805d3ceab5a2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:47.988030Z","signature_b64":"Kkr5g3pQTgLWixUjQwUgzQLOCBdnje/Yl0UibAIbBhiaIbis1koJ9AMogwr2C52Vk8QiCLeuCL+V7kHX0sG8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3537b3b10d4d19e3a9e189ddce801182de84271e8d71d97251805d3ceab5a2f","last_reissued_at":"2026-05-18T00:10:47.987389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:47.987389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08988","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":"2026-05-18T00:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2Ilu/evs1Gr8vO71AKAcQcNQZTXXIDrwgF2kDiaJ+ko3eN9sHanQsMxmS0Jek5KlRDZR5uRjJftkLsyRhQFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:48:13.254968Z"},"content_sha256":"f175d5106eeff2f9daab2b7b2d73523a47aba9a87887a2a5881d193da3cfae3e","schema_version":"1.0","event_id":"sha256:f175d5106eeff2f9daab2b7b2d73523a47aba9a87887a2a5881d193da3cfae3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2NJXWOYQ2TIZ4OU6DCO5Z2ABDA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $\\alpha$-largeness and the Paris-Harrington principle in $\\mathrm{RCA}_0$ and $\\mathrm{RCA}_0^{\\displaystyle{*}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Florian Pelupessy","submitted_at":"2016-11-28T05:37:12Z","abstract_excerpt":"We examine, within $\\mathrm{RCA}_0$, the treatment by Ketonen and Solovay on the use of $\\alpha$-largeness for giving an upper bound for the Paris--Harrington principle. This proof works fine in $\\mathrm{RCA}_0^{\\displaystyle{*}}$ for every fixed standard dimension. We also show how to modify the arguments to work within $\\mathrm{RCA}_0^{\\displaystyle{*}}$ for unrestricted dimensions. To the author's knowledge, this is the first time that it is confirmed that the treatment can be done within $\\mathrm{EFA}$ without some transfinite induction added."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08988","kind":"arxiv","version":4},"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":"2026-05-18T00:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3GB9b7BkCZFjuso8pPuFBSYCRyeSYcXqIFRQi9qUljacFiHzRs95dyvVtAKgYblexfsN7E7kkZNTAtO8nKFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:48:13.255581Z"},"content_sha256":"8b37ed06e2624fc4bf35550d1e71816979b2789724126d25fa2428450857a9cf","schema_version":"1.0","event_id":"sha256:8b37ed06e2624fc4bf35550d1e71816979b2789724126d25fa2428450857a9cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA/bundle.json","state_url":"https://pith.science/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA/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":"2026-05-27T05:48:13Z","links":{"resolver":"https://pith.science/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA","bundle":"https://pith.science/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA/bundle.json","state":"https://pith.science/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NJXWOYQ2TIZ4OU6DCO5Z2ABDA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2NJXWOYQ2TIZ4OU6DCO5Z2ABDA","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":"4a2836a50b5dc846fe6ce85326d6e30bbd431fbe18e58b5c608d3b4a8745737b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-28T05:37:12Z","title_canon_sha256":"920a0b4e878f3852e818c3beacac755623349740c42d26311a551405c5cf9066"},"schema_version":"1.0","source":{"id":"1611.08988","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08988","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08988v4","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08988","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"2NJXWOYQ2TIZ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2NJXWOYQ2TIZ4OU6","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2NJXWOYQ","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:8b37ed06e2624fc4bf35550d1e71816979b2789724126d25fa2428450857a9cf","target":"graph","created_at":"2026-05-18T00:10:47Z","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 examine, within $\\mathrm{RCA}_0$, the treatment by Ketonen and Solovay on the use of $\\alpha$-largeness for giving an upper bound for the Paris--Harrington principle. This proof works fine in $\\mathrm{RCA}_0^{\\displaystyle{*}}$ for every fixed standard dimension. We also show how to modify the arguments to work within $\\mathrm{RCA}_0^{\\displaystyle{*}}$ for unrestricted dimensions. To the author's knowledge, this is the first time that it is confirmed that the treatment can be done within $\\mathrm{EFA}$ without some transfinite induction added.","authors_text":"Florian Pelupessy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-28T05:37:12Z","title":"On $\\alpha$-largeness and the Paris-Harrington principle in $\\mathrm{RCA}_0$ and $\\mathrm{RCA}_0^{\\displaystyle{*}}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08988","kind":"arxiv","version":4},"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:f175d5106eeff2f9daab2b7b2d73523a47aba9a87887a2a5881d193da3cfae3e","target":"record","created_at":"2026-05-18T00:10:47Z","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":"4a2836a50b5dc846fe6ce85326d6e30bbd431fbe18e58b5c608d3b4a8745737b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-28T05:37:12Z","title_canon_sha256":"920a0b4e878f3852e818c3beacac755623349740c42d26311a551405c5cf9066"},"schema_version":"1.0","source":{"id":"1611.08988","kind":"arxiv","version":4}},"canonical_sha256":"d3537b3b10d4d19e3a9e189ddce801182de84271e8d71d97251805d3ceab5a2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3537b3b10d4d19e3a9e189ddce801182de84271e8d71d97251805d3ceab5a2f","first_computed_at":"2026-05-18T00:10:47.987389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:47.987389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kkr5g3pQTgLWixUjQwUgzQLOCBdnje/Yl0UibAIbBhiaIbis1koJ9AMogwr2C52Vk8QiCLeuCL+V7kHX0sG8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:47.988030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08988","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f175d5106eeff2f9daab2b7b2d73523a47aba9a87887a2a5881d193da3cfae3e","sha256:8b37ed06e2624fc4bf35550d1e71816979b2789724126d25fa2428450857a9cf"],"state_sha256":"00ed1fa2b36089400d509e2752cc877848d05329b18a0b3915a2552336ec1e1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s0uRPLLQT0Pbn0Np8JH0iSzQDk4hZCBWfVKXQOgzCXnBQW3GO5uBZ8/K1hHjXoX05/kIZlMdYg68s2VFjAYcBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:48:13.259154Z","bundle_sha256":"d2b1e01afae9de340edb9e1526085144ffbedc70b2fb46d0f625c9761c6e9526"}}