{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PCRUTLI237LVQTZLMTATKEEPQD","short_pith_number":"pith:PCRUTLI2","canonical_record":{"source":{"id":"1711.02007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-06T16:47:21Z","cross_cats_sorted":[],"title_canon_sha256":"196fea55672a04dc2d163360883fd4f658f9d64616b54abe9c00fc91134adb01","abstract_canon_sha256":"717747c3de128bec69e2f52a5b17ac008023d39e376767babac783af937b8266"},"schema_version":"1.0"},"canonical_sha256":"78a349ad1adfd7584f2b64c135108f80e60ccf5d075eb30a55bfc5af964cab31","source":{"kind":"arxiv","id":"1711.02007","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02007","created_at":"2026-05-18T00:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02007v2","created_at":"2026-05-18T00:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02007","created_at":"2026-05-18T00:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"PCRUTLI237LV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PCRUTLI237LVQTZL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PCRUTLI2","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PCRUTLI237LVQTZLMTATKEEPQD","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-06T16:47:21Z","cross_cats_sorted":[],"title_canon_sha256":"196fea55672a04dc2d163360883fd4f658f9d64616b54abe9c00fc91134adb01","abstract_canon_sha256":"717747c3de128bec69e2f52a5b17ac008023d39e376767babac783af937b8266"},"schema_version":"1.0"},"canonical_sha256":"78a349ad1adfd7584f2b64c135108f80e60ccf5d075eb30a55bfc5af964cab31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:02.129136Z","signature_b64":"BHIN1Y4LTiwtGgjxsptld9aB+VVQ5QSTwz1stLOzQ326XAIOIZy+sRReniKdFWlXVXVvzkSonj1L5Pe4jU1vBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a349ad1adfd7584f2b64c135108f80e60ccf5d075eb30a55bfc5af964cab31","last_reissued_at":"2026-05-18T00:31:02.128621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:02.128621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02007","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25KZd8m3NHHGqPLrBhKkSBkYYDY5AxZNpToGYbyi3z8VSKuiNDpapvxNoDQW0tjesAmZipXzqtwOZ5FvQlymDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:44:10.985845Z"},"content_sha256":"9a131d1808a6f01be2c365153f6e241674b585febbea930f8d4d41fef499e1ae","schema_version":"1.0","event_id":"sha256:9a131d1808a6f01be2c365153f6e241674b585febbea930f8d4d41fef499e1ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PCRUTLI237LVQTZLMTATKEEPQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The internal structure of $\\mathrm{HOD}^{L[x]}$ up to its Woodin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yizheng Zhu","submitted_at":"2017-11-06T16:47:21Z","abstract_excerpt":"Assume $\\boldsymbol{\\Delta}^1_3$-determinacy. It is shown that for any $x \\geq_T M_1^{\\#}$, $\\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $\\omega_2^{L[x]}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02007","kind":"arxiv","version":2},"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":"2026-05-18T00:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAP6LkOsnGmZqInNF3wS/JXxfGBR8UbtFuPfcP982BxjxGeaqIoEcj+1VYhMJekuaX0OCW0zF5AY3rFP9/BNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:44:10.986197Z"},"content_sha256":"1e28600ede0f3a377ec78b0a3f8ca4cd76da1894b746d5b3969a058094e7aa03","schema_version":"1.0","event_id":"sha256:1e28600ede0f3a377ec78b0a3f8ca4cd76da1894b746d5b3969a058094e7aa03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCRUTLI237LVQTZLMTATKEEPQD/bundle.json","state_url":"https://pith.science/pith/PCRUTLI237LVQTZLMTATKEEPQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCRUTLI237LVQTZLMTATKEEPQD/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":"2026-06-12T10:44:10Z","links":{"resolver":"https://pith.science/pith/PCRUTLI237LVQTZLMTATKEEPQD","bundle":"https://pith.science/pith/PCRUTLI237LVQTZLMTATKEEPQD/bundle.json","state":"https://pith.science/pith/PCRUTLI237LVQTZLMTATKEEPQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCRUTLI237LVQTZLMTATKEEPQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PCRUTLI237LVQTZLMTATKEEPQD","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":"717747c3de128bec69e2f52a5b17ac008023d39e376767babac783af937b8266","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-06T16:47:21Z","title_canon_sha256":"196fea55672a04dc2d163360883fd4f658f9d64616b54abe9c00fc91134adb01"},"schema_version":"1.0","source":{"id":"1711.02007","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02007","created_at":"2026-05-18T00:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02007v2","created_at":"2026-05-18T00:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02007","created_at":"2026-05-18T00:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"PCRUTLI237LV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PCRUTLI237LVQTZL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PCRUTLI2","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:1e28600ede0f3a377ec78b0a3f8ca4cd76da1894b746d5b3969a058094e7aa03","target":"graph","created_at":"2026-05-18T00:31:02Z","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":"Assume $\\boldsymbol{\\Delta}^1_3$-determinacy. It is shown that for any $x \\geq_T M_1^{\\#}$, $\\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $\\omega_2^{L[x]}$.","authors_text":"Yizheng Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-06T16:47:21Z","title":"The internal structure of $\\mathrm{HOD}^{L[x]}$ up to its Woodin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02007","kind":"arxiv","version":2},"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":"sha256:9a131d1808a6f01be2c365153f6e241674b585febbea930f8d4d41fef499e1ae","target":"record","created_at":"2026-05-18T00:31:02Z","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":"717747c3de128bec69e2f52a5b17ac008023d39e376767babac783af937b8266","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-06T16:47:21Z","title_canon_sha256":"196fea55672a04dc2d163360883fd4f658f9d64616b54abe9c00fc91134adb01"},"schema_version":"1.0","source":{"id":"1711.02007","kind":"arxiv","version":2}},"canonical_sha256":"78a349ad1adfd7584f2b64c135108f80e60ccf5d075eb30a55bfc5af964cab31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78a349ad1adfd7584f2b64c135108f80e60ccf5d075eb30a55bfc5af964cab31","first_computed_at":"2026-05-18T00:31:02.128621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:02.128621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BHIN1Y4LTiwtGgjxsptld9aB+VVQ5QSTwz1stLOzQ326XAIOIZy+sRReniKdFWlXVXVvzkSonj1L5Pe4jU1vBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:02.129136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02007","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a131d1808a6f01be2c365153f6e241674b585febbea930f8d4d41fef499e1ae","sha256:1e28600ede0f3a377ec78b0a3f8ca4cd76da1894b746d5b3969a058094e7aa03"],"state_sha256":"dbe419907e640ff4d9890eafea040c060287046df7d712158da1aae93e67006d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zD5Jr8Jmx7ay5Np2jWvgF1EVr/NIREw/VdY7XoDVkQzX0XuLLlJV6GbajG7aPVHWw6kJIlgv1ibLJoUy8h4UAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:44:10.988839Z","bundle_sha256":"0a6f5a63a584abf468b18582039a618a8f3a0b989e6c1116a7e940cf96ac5d99"}}