{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:5YC4WQQ2PA2EWG3GVUE4WIEZBK","short_pith_number":"pith:5YC4WQQ2","canonical_record":{"source":{"id":"math/9510216","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"58ed55891078fae6c9528d3ba8865c259379bad64bc7e2bc360d8cc95e3bca60","abstract_canon_sha256":"ed22f06bd896ce76ae97719c0fe23e118130497a3027b7995e1c8532690dc878"},"schema_version":"1.0"},"canonical_sha256":"ee05cb421a78344b1b66ad09cb20990abfc4419dc7b5228da9a6d5b87dbb8263","source":{"kind":"arxiv","id":"math/9510216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9510216","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9510216v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9510216","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"5YC4WQQ2PA2E","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"5YC4WQQ2PA2EWG3G","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"5YC4WQQ2","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:5YC4WQQ2PA2EWG3GVUE4WIEZBK","target":"record","payload":{"canonical_record":{"source":{"id":"math/9510216","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"58ed55891078fae6c9528d3ba8865c259379bad64bc7e2bc360d8cc95e3bca60","abstract_canon_sha256":"ed22f06bd896ce76ae97719c0fe23e118130497a3027b7995e1c8532690dc878"},"schema_version":"1.0"},"canonical_sha256":"ee05cb421a78344b1b66ad09cb20990abfc4419dc7b5228da9a6d5b87dbb8263","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:48.192888Z","signature_b64":"ALarklJ7a3PCMDSObb7mm63et/a2FT8h6MLFM9hfnzdYQDTk7wFTXFG3ZuVnjPFaB/Hel/UAKwm1H3XxiY4TCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee05cb421a78344b1b66ad09cb20990abfc4419dc7b5228da9a6d5b87dbb8263","last_reissued_at":"2026-05-18T01:05:48.192376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:48.192376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9510216","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":"2026-05-18T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6wXIM5JRX9Os+wXouBhDRhItsUlsCmlSMlU/AUxuBKBffmNAswxfzTxrHvh/fOpJjmo0jCzh9wQ2UYoHVQFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:50:33.197892Z"},"content_sha256":"35dfc12306d31c2a81a8132651254085b5659e7fc7c3108abbefd5ad031972df","schema_version":"1.0","event_id":"sha256:35dfc12306d31c2a81a8132651254085b5659e7fc7c3108abbefd5ad031972df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:5YC4WQQ2PA2EWG3GVUE4WIEZBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On squares, outside guessing of clubs and I_{<f}[lambda]","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Mirna D\\v{z}amonja, Saharon Shelah","submitted_at":"1995-10-15T00:00:00Z","abstract_excerpt":"Suppose that lambda = mu^+. We consider two aspects of the square property on subsets of lambda. First, we have results which show e.g. that for aleph_0 <= kappa =cf (kappa)< mu, the equality cf([mu]^{<= kappa}, subseteq)= mu is a sufficient condition for the set of elements of lambda whose cofinality is bounded by kappa, to be split into the union of mu sets with squares. Secondly, we introduce a certain weak version of the square property and prove that if mu is a strong limit, then this weak square property holds on lambda without any additional assumptions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510216","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":"2026-05-18T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v3dMD9rusTbW4GHYY9XfplnlxL9d8hT/N97r1tjBgdf85SwUGmgLY2Kt8Pd2Fwema0MEoUvy+mdugKm7Q7ZyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:50:33.198238Z"},"content_sha256":"b53324be2f6a5bffc314cd3babea1465d708da1d63105cf7c7c251e1b7ff84aa","schema_version":"1.0","event_id":"sha256:b53324be2f6a5bffc314cd3babea1465d708da1d63105cf7c7c251e1b7ff84aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK/bundle.json","state_url":"https://pith.science/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK/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":"2026-06-20T10:50:33Z","links":{"resolver":"https://pith.science/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK","bundle":"https://pith.science/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK/bundle.json","state":"https://pith.science/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YC4WQQ2PA2EWG3GVUE4WIEZBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:5YC4WQQ2PA2EWG3GVUE4WIEZBK","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":"ed22f06bd896ce76ae97719c0fe23e118130497a3027b7995e1c8532690dc878","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","title_canon_sha256":"58ed55891078fae6c9528d3ba8865c259379bad64bc7e2bc360d8cc95e3bca60"},"schema_version":"1.0","source":{"id":"math/9510216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9510216","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9510216v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9510216","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"5YC4WQQ2PA2E","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"5YC4WQQ2PA2EWG3G","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"5YC4WQQ2","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:b53324be2f6a5bffc314cd3babea1465d708da1d63105cf7c7c251e1b7ff84aa","target":"graph","created_at":"2026-05-18T01:05:48Z","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":"Suppose that lambda = mu^+. We consider two aspects of the square property on subsets of lambda. First, we have results which show e.g. that for aleph_0 <= kappa =cf (kappa)< mu, the equality cf([mu]^{<= kappa}, subseteq)= mu is a sufficient condition for the set of elements of lambda whose cofinality is bounded by kappa, to be split into the union of mu sets with squares. Secondly, we introduce a certain weak version of the square property and prove that if mu is a strong limit, then this weak square property holds on lambda without any additional assumptions","authors_text":"Mirna D\\v{z}amonja, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","title":"On squares, outside guessing of clubs and I_{<f}[lambda]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510216","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":"sha256:35dfc12306d31c2a81a8132651254085b5659e7fc7c3108abbefd5ad031972df","target":"record","created_at":"2026-05-18T01:05:48Z","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":"ed22f06bd896ce76ae97719c0fe23e118130497a3027b7995e1c8532690dc878","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","title_canon_sha256":"58ed55891078fae6c9528d3ba8865c259379bad64bc7e2bc360d8cc95e3bca60"},"schema_version":"1.0","source":{"id":"math/9510216","kind":"arxiv","version":1}},"canonical_sha256":"ee05cb421a78344b1b66ad09cb20990abfc4419dc7b5228da9a6d5b87dbb8263","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee05cb421a78344b1b66ad09cb20990abfc4419dc7b5228da9a6d5b87dbb8263","first_computed_at":"2026-05-18T01:05:48.192376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.192376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ALarklJ7a3PCMDSObb7mm63et/a2FT8h6MLFM9hfnzdYQDTk7wFTXFG3ZuVnjPFaB/Hel/UAKwm1H3XxiY4TCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.192888Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9510216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35dfc12306d31c2a81a8132651254085b5659e7fc7c3108abbefd5ad031972df","sha256:b53324be2f6a5bffc314cd3babea1465d708da1d63105cf7c7c251e1b7ff84aa"],"state_sha256":"1bd330f6e499d97fcfb2fa701f3d15269ef0862dcc93869e674fcd487440b8eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hMe5g4Dgv2DyKQziGmts7X/yLPj1wiwP5cm+MTFiWIeUJQr9v10nTvqS5YFWS2oRSQqmnfJvIoLRh2x0i4EyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:50:33.200228Z","bundle_sha256":"3ddcab97e29d4bcce7f2047394bbed43623f91fb6bfacb93103123860620f53d"}}