{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:IDZ563XRPMNHXHXJ6Y7ECPVUUF","short_pith_number":"pith:IDZ563XR","canonical_record":{"source":{"id":"math/9611209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1996-11-13T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"c14d726c7c0e04dea156e381b9320767a6c2a0e13a8509d59aa489f9363f7f1f","abstract_canon_sha256":"676beaf3824065e128c5c71aa0733733824d4cad26223b3ce9bce7f66d8790e1"},"schema_version":"1.0"},"canonical_sha256":"40f3df6ef17b1a7b9ee9f63e413eb4a144f3f3bec6a9b5319c8464de51c8ee6f","source":{"kind":"arxiv","id":"math/9611209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9611209","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/9611209v1","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9611209","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"IDZ563XRPMNH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"IDZ563XRPMNHXHXJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"IDZ563XR","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:IDZ563XRPMNHXHXJ6Y7ECPVUUF","target":"record","payload":{"canonical_record":{"source":{"id":"math/9611209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1996-11-13T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"c14d726c7c0e04dea156e381b9320767a6c2a0e13a8509d59aa489f9363f7f1f","abstract_canon_sha256":"676beaf3824065e128c5c71aa0733733824d4cad26223b3ce9bce7f66d8790e1"},"schema_version":"1.0"},"canonical_sha256":"40f3df6ef17b1a7b9ee9f63e413eb4a144f3f3bec6a9b5319c8464de51c8ee6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.932955Z","signature_b64":"IYgBMkZll5iy0PK5V1PmobGljpINpi3sCVKjJ8RC9jbNHETVQC8qxK96Y5Oci+PzF4Lch6OhTViY3fMqVfG2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f3df6ef17b1a7b9ee9f63e413eb4a144f3f3bec6a9b5319c8464de51c8ee6f","last_reissued_at":"2026-05-18T01:05:46.932383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.932383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9611209","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6A1ycAQA+xqYGM6cKPITyDrsNd7WWnMN8uoM2+Dc6Gn17e8v1gB6C4UcqNbiKVVWWQ0Tv0ddbR/nqU/b5cMSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:36:53.334348Z"},"content_sha256":"c652c4607e2d576005d0b62b719240a3dc61e86ff6d4701e9fcdc3987189b1bb","schema_version":"1.0","event_id":"sha256:c652c4607e2d576005d0b62b719240a3dc61e86ff6d4701e9fcdc3987189b1bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:IDZ563XRPMNHXHXJ6Y7ECPVUUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chains of End Elementary Extensions of Models of Set Theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andres Villaveces","submitted_at":"1996-11-13T00:00:00Z","abstract_excerpt":"Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained that way (`Unfoldable cardinals') behave as a `boundary' between properties consistent with `V=L' and existence of indiscernibles. We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various different forcings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9611209","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uF5r8xMlVM56jRYSoWaoUZNCnHeDd+EBNIKX88ef9zaFT7GYFLI/g3b/soOk7nZ/HVrtsSM5cHWP583p0AfJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:36:53.334970Z"},"content_sha256":"9b01b33f0f73a34597243a9c6d3bf1b0ecd94e2a9c60d70076442d9577d7b1fa","schema_version":"1.0","event_id":"sha256:9b01b33f0f73a34597243a9c6d3bf1b0ecd94e2a9c60d70076442d9577d7b1fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF/bundle.json","state_url":"https://pith.science/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF/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":"2026-06-01T01:36:53Z","links":{"resolver":"https://pith.science/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF","bundle":"https://pith.science/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF/bundle.json","state":"https://pith.science/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDZ563XRPMNHXHXJ6Y7ECPVUUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:IDZ563XRPMNHXHXJ6Y7ECPVUUF","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":"676beaf3824065e128c5c71aa0733733824d4cad26223b3ce9bce7f66d8790e1","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1996-11-13T00:00:00Z","title_canon_sha256":"c14d726c7c0e04dea156e381b9320767a6c2a0e13a8509d59aa489f9363f7f1f"},"schema_version":"1.0","source":{"id":"math/9611209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9611209","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/9611209v1","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9611209","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"IDZ563XRPMNH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"IDZ563XRPMNHXHXJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"IDZ563XR","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:9b01b33f0f73a34597243a9c6d3bf1b0ecd94e2a9c60d70076442d9577d7b1fa","target":"graph","created_at":"2026-05-18T01:05:46Z","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":"Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained that way (`Unfoldable cardinals') behave as a `boundary' between properties consistent with `V=L' and existence of indiscernibles. We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various different forcings.","authors_text":"Andres Villaveces","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1996-11-13T00:00:00Z","title":"Chains of End Elementary Extensions of Models of Set Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9611209","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:c652c4607e2d576005d0b62b719240a3dc61e86ff6d4701e9fcdc3987189b1bb","target":"record","created_at":"2026-05-18T01:05:46Z","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":"676beaf3824065e128c5c71aa0733733824d4cad26223b3ce9bce7f66d8790e1","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1996-11-13T00:00:00Z","title_canon_sha256":"c14d726c7c0e04dea156e381b9320767a6c2a0e13a8509d59aa489f9363f7f1f"},"schema_version":"1.0","source":{"id":"math/9611209","kind":"arxiv","version":1}},"canonical_sha256":"40f3df6ef17b1a7b9ee9f63e413eb4a144f3f3bec6a9b5319c8464de51c8ee6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40f3df6ef17b1a7b9ee9f63e413eb4a144f3f3bec6a9b5319c8464de51c8ee6f","first_computed_at":"2026-05-18T01:05:46.932383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:46.932383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IYgBMkZll5iy0PK5V1PmobGljpINpi3sCVKjJ8RC9jbNHETVQC8qxK96Y5Oci+PzF4Lch6OhTViY3fMqVfG2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:46.932955Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9611209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c652c4607e2d576005d0b62b719240a3dc61e86ff6d4701e9fcdc3987189b1bb","sha256:9b01b33f0f73a34597243a9c6d3bf1b0ecd94e2a9c60d70076442d9577d7b1fa"],"state_sha256":"0ef57de53298b74e00abfc4cc100e8666b9f448ee321e64151e9b3367ba18a69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eou6LZrDh+c4sbrY05aRLj/fNN6vh4Tar3w0rlHlduy1fUdXdID2G9dehO+pcYINLG+R+aLIpeECjEIzNxGbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:36:53.338408Z","bundle_sha256":"cc78169fda68c25916bc6f6e3cc7622951170fd0432b811c56d1fd3765c52681"}}