{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:RXRJRX3QG3KD2EGJAUX3EJPUJ6","short_pith_number":"pith:RXRJRX3Q","canonical_record":{"source":{"id":"math/9702206","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1997-02-18T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"092b9f0fc1068021d80cc523a49fcc98cafddb204c331c9b4cf54a234ccb1bb5","abstract_canon_sha256":"bdec3a8de33b3e8c7a8601b0ecfb44415dcdc302f32fbe6c0e01c61489aabfa3"},"schema_version":"1.0"},"canonical_sha256":"8de298df7036d43d10c9052fb225f44f8da4bfe5cb5ce2d0d873bef3563cbb5b","source":{"kind":"arxiv","id":"math/9702206","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9702206","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/9702206v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9702206","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"RXRJRX3QG3KD","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"RXRJRX3QG3KD2EGJ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"RXRJRX3Q","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:RXRJRX3QG3KD2EGJAUX3EJPUJ6","target":"record","payload":{"canonical_record":{"source":{"id":"math/9702206","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1997-02-18T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"092b9f0fc1068021d80cc523a49fcc98cafddb204c331c9b4cf54a234ccb1bb5","abstract_canon_sha256":"bdec3a8de33b3e8c7a8601b0ecfb44415dcdc302f32fbe6c0e01c61489aabfa3"},"schema_version":"1.0"},"canonical_sha256":"8de298df7036d43d10c9052fb225f44f8da4bfe5cb5ce2d0d873bef3563cbb5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:37.204059Z","signature_b64":"QQGrQjwj5T6NcSInOATG9l8/GjiFkaAxB3GCIcLrOC3RqMm74f2X7htF6sUUnvGIVpwEvt8wquF+FI6WBZ7vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8de298df7036d43d10c9052fb225f44f8da4bfe5cb5ce2d0d873bef3563cbb5b","last_reissued_at":"2026-05-18T01:05:37.203424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:37.203424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9702206","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":"2026-05-18T01:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bG4OnnnFBxemD15PGEmwBrd4h6AYwbHnGSrptrN8X2f61eF7Av58nzTavMsVVTbH8HewkXvHYv6y2CD2CRzqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:19:21.228338Z"},"content_sha256":"de94d217a83c2a39edec20e67ece6b7ccf983a94093d2570a306a9e9d148db65","schema_version":"1.0","event_id":"sha256:de94d217a83c2a39edec20e67ece6b7ccf983a94093d2570a306a9e9d148db65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:RXRJRX3QG3KD2EGJAUX3EJPUJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The maximality of the core model","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ernest Schimmerling, John R. Steel","submitted_at":"1997-02-18T00:00:00Z","abstract_excerpt":"If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T.  Several applications of maximality are proved, including:\n o K computes successors of weakly compact cardinals correctly.\n o K^c is an iterate of K.\n o (with Mitchell) If alpha is a cardinal > aleph_1, then K-restriction-alpha is universal for mice of height alpha.\n  Other results in this paper, when combined with work of Woodin, imply:\n o If square-kappa-finite fails and kappa is a singular, strong limit cardinal, then Indu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9702206","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":"2026-05-18T01:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTkpP6fDOdkN+QTB6hZtgAgVJMoQ1whdbCU9JL9hOm7iItYv1vMVvc+SmltQHLsqhQ1AM9Ji4joKuxNhbgHTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:19:21.229021Z"},"content_sha256":"6cbc7e12ec5df1300766623c05e56e9094faac884cbf97b39b9110e88aa3001c","schema_version":"1.0","event_id":"sha256:6cbc7e12ec5df1300766623c05e56e9094faac884cbf97b39b9110e88aa3001c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6/bundle.json","state_url":"https://pith.science/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6/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":"2026-06-06T06:19:21Z","links":{"resolver":"https://pith.science/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6","bundle":"https://pith.science/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6/bundle.json","state":"https://pith.science/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXRJRX3QG3KD2EGJAUX3EJPUJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:RXRJRX3QG3KD2EGJAUX3EJPUJ6","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":"bdec3a8de33b3e8c7a8601b0ecfb44415dcdc302f32fbe6c0e01c61489aabfa3","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1997-02-18T00:00:00Z","title_canon_sha256":"092b9f0fc1068021d80cc523a49fcc98cafddb204c331c9b4cf54a234ccb1bb5"},"schema_version":"1.0","source":{"id":"math/9702206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9702206","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/9702206v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9702206","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"RXRJRX3QG3KD","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"RXRJRX3QG3KD2EGJ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"RXRJRX3Q","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:6cbc7e12ec5df1300766623c05e56e9094faac884cbf97b39b9110e88aa3001c","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T.  Several applications of maximality are proved, including:\n o K computes successors of weakly compact cardinals correctly.\n o K^c is an iterate of K.\n o (with Mitchell) If alpha is a cardinal > aleph_1, then K-restriction-alpha is universal for mice of height alpha.\n  Other results in this paper, when combined with work of Woodin, imply:\n o If square-kappa-finite fails and kappa is a singular, strong limit cardinal, then Indu","authors_text":"Ernest Schimmerling, John R. Steel","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1997-02-18T00:00:00Z","title":"The maximality of the core model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9702206","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:de94d217a83c2a39edec20e67ece6b7ccf983a94093d2570a306a9e9d148db65","target":"record","created_at":"2026-05-18T01:05:37Z","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":"bdec3a8de33b3e8c7a8601b0ecfb44415dcdc302f32fbe6c0e01c61489aabfa3","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1997-02-18T00:00:00Z","title_canon_sha256":"092b9f0fc1068021d80cc523a49fcc98cafddb204c331c9b4cf54a234ccb1bb5"},"schema_version":"1.0","source":{"id":"math/9702206","kind":"arxiv","version":1}},"canonical_sha256":"8de298df7036d43d10c9052fb225f44f8da4bfe5cb5ce2d0d873bef3563cbb5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8de298df7036d43d10c9052fb225f44f8da4bfe5cb5ce2d0d873bef3563cbb5b","first_computed_at":"2026-05-18T01:05:37.203424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.203424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QQGrQjwj5T6NcSInOATG9l8/GjiFkaAxB3GCIcLrOC3RqMm74f2X7htF6sUUnvGIVpwEvt8wquF+FI6WBZ7vDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.204059Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9702206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de94d217a83c2a39edec20e67ece6b7ccf983a94093d2570a306a9e9d148db65","sha256:6cbc7e12ec5df1300766623c05e56e9094faac884cbf97b39b9110e88aa3001c"],"state_sha256":"991c932c32ba9f236a6e9021b0fdd930bfadd3e3c6f160f01d4ef7c6776147ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"niA3dqiw6ff0eaet8BexNEDES9CUx9cl3jfPkKYrsR1kLXT/d3SgljyglfvwSdwpWVClr3Us04piJUylZVR/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:19:21.233080Z","bundle_sha256":"96f65a3baab06845893c8f98e1ac25aa34fbe56c5894215a68d369c805cd9125"}}