{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HEZT3MUGMKDFX4OP5ETVQXXOD7","short_pith_number":"pith:HEZT3MUG","canonical_record":{"source":{"id":"1301.4702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-20T22:34:33Z","cross_cats_sorted":[],"title_canon_sha256":"34655b2a20c31acda6fc0430782eae326d90524341e88a2e43799cf841f3ab12","abstract_canon_sha256":"2b2fc0eb8ed7d460cbf5936cc6e01fa7f86e80cd644a974ad098af2af6dd6df5"},"schema_version":"1.0"},"canonical_sha256":"39333db28662865bf1cfe927585eee1fd6d7d64caa94b2dada1ca3bbae128f77","source":{"kind":"arxiv","id":"1301.4702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4702","created_at":"2026-05-18T03:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4702v1","created_at":"2026-05-18T03:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4702","created_at":"2026-05-18T03:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"HEZT3MUGMKDF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HEZT3MUGMKDFX4OP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HEZT3MUG","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HEZT3MUGMKDFX4OP5ETVQXXOD7","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-20T22:34:33Z","cross_cats_sorted":[],"title_canon_sha256":"34655b2a20c31acda6fc0430782eae326d90524341e88a2e43799cf841f3ab12","abstract_canon_sha256":"2b2fc0eb8ed7d460cbf5936cc6e01fa7f86e80cd644a974ad098af2af6dd6df5"},"schema_version":"1.0"},"canonical_sha256":"39333db28662865bf1cfe927585eee1fd6d7d64caa94b2dada1ca3bbae128f77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:55.872273Z","signature_b64":"roKkpTf3aPsQuxduzj7kI4sXLyW7nWYa2frF3miI4W2b8QEyr+2glWMJZhJL8Q9HfsnMgcq12cqYqtGn/aV+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39333db28662865bf1cfe927585eee1fd6d7d64caa94b2dada1ca3bbae128f77","last_reissued_at":"2026-05-18T03:35:55.871482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:55.871482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4702","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":"2026-05-18T03:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4md4lZwm5Ca/P32Py2tPBFipmpwzRPzL8K3KSQxMc65cDRKuYJXS7iGjhYlfrsc4ULaiEYUaNRLEZTwQ43vLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:33:51.382764Z"},"content_sha256":"434fb40114aa6ef5ffe6894867daf7e7398ec134c09b593d77854c20fda32bdd","schema_version":"1.0","event_id":"sha256:434fb40114aa6ef5ffe6894867daf7e7398ec134c09b593d77854c20fda32bdd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HEZT3MUGMKDFX4OP5ETVQXXOD7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measures in Mice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Farmer Schlutzenberg","submitted_at":"2013-01-20T22:34:33Z","abstract_excerpt":"This thesis analyses extenders in fine structural mice. Kunen showed that in the inner model for one measurable cardinal, there is a unique measure. This result is generalized, in various ways, to mice below a superstrong cardinal.\n  The analysis is then used to show that certain tame mice satisfy $V=\\mathsf{HOD}$. In particular, the approach proides a new proof of this result for the inner model $M_n$ for $n$ Woodin cardinals. It is also shown that in $M_n$, all homogeneously Suslin sets of reals are $\\mathbf{\\Delta}^1_{n+1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4702","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":"2026-05-18T03:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uSoLKAb/LGDzr6RhdlOf0KEaGTLm/ft0ZRDwOAJSTZcG4+7xGVjzu5wKVchYaRdrEklMLVWFoqrCvrtGbegKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:33:51.383614Z"},"content_sha256":"40f9eeddaf9afb307eef9f0d3c37b2d53bd1f2017523a56fa66c0429548a8e01","schema_version":"1.0","event_id":"sha256:40f9eeddaf9afb307eef9f0d3c37b2d53bd1f2017523a56fa66c0429548a8e01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7/bundle.json","state_url":"https://pith.science/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7/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":"2026-05-31T04:33:51Z","links":{"resolver":"https://pith.science/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7","bundle":"https://pith.science/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7/bundle.json","state":"https://pith.science/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HEZT3MUGMKDFX4OP5ETVQXXOD7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HEZT3MUGMKDFX4OP5ETVQXXOD7","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":"2b2fc0eb8ed7d460cbf5936cc6e01fa7f86e80cd644a974ad098af2af6dd6df5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-20T22:34:33Z","title_canon_sha256":"34655b2a20c31acda6fc0430782eae326d90524341e88a2e43799cf841f3ab12"},"schema_version":"1.0","source":{"id":"1301.4702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4702","created_at":"2026-05-18T03:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4702v1","created_at":"2026-05-18T03:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4702","created_at":"2026-05-18T03:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"HEZT3MUGMKDF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HEZT3MUGMKDFX4OP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HEZT3MUG","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:40f9eeddaf9afb307eef9f0d3c37b2d53bd1f2017523a56fa66c0429548a8e01","target":"graph","created_at":"2026-05-18T03:35:55Z","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":"This thesis analyses extenders in fine structural mice. Kunen showed that in the inner model for one measurable cardinal, there is a unique measure. This result is generalized, in various ways, to mice below a superstrong cardinal.\n  The analysis is then used to show that certain tame mice satisfy $V=\\mathsf{HOD}$. In particular, the approach proides a new proof of this result for the inner model $M_n$ for $n$ Woodin cardinals. It is also shown that in $M_n$, all homogeneously Suslin sets of reals are $\\mathbf{\\Delta}^1_{n+1}$.","authors_text":"Farmer Schlutzenberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-20T22:34:33Z","title":"Measures in Mice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4702","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":"sha256:434fb40114aa6ef5ffe6894867daf7e7398ec134c09b593d77854c20fda32bdd","target":"record","created_at":"2026-05-18T03:35:55Z","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":"2b2fc0eb8ed7d460cbf5936cc6e01fa7f86e80cd644a974ad098af2af6dd6df5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-20T22:34:33Z","title_canon_sha256":"34655b2a20c31acda6fc0430782eae326d90524341e88a2e43799cf841f3ab12"},"schema_version":"1.0","source":{"id":"1301.4702","kind":"arxiv","version":1}},"canonical_sha256":"39333db28662865bf1cfe927585eee1fd6d7d64caa94b2dada1ca3bbae128f77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39333db28662865bf1cfe927585eee1fd6d7d64caa94b2dada1ca3bbae128f77","first_computed_at":"2026-05-18T03:35:55.871482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:55.871482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"roKkpTf3aPsQuxduzj7kI4sXLyW7nWYa2frF3miI4W2b8QEyr+2glWMJZhJL8Q9HfsnMgcq12cqYqtGn/aV+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:55.872273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:434fb40114aa6ef5ffe6894867daf7e7398ec134c09b593d77854c20fda32bdd","sha256:40f9eeddaf9afb307eef9f0d3c37b2d53bd1f2017523a56fa66c0429548a8e01"],"state_sha256":"f290b7a2bda85666ff7ba96fe5650bf65cf6ba136a08c8d6e293072477a13108"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tl+gjX3H16OKsAo3bxsPUFY2qRTZTEIlqROpnFqISwckE3eye448Kz2ywckMTkg/B6uDazVeVQzi0i/LcWj9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:33:51.389395Z","bundle_sha256":"b04098d63ada170fb605e670474ba699297768b2a31af9a43f2549cc64ec861e"}}