{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:VRGK7I56T64QMF6CN2DZU53ZJG","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":"d4f010a3f26e011cc9dfa5a171dda44e4ffccdfc53ad5ae27693af27533071b5","cross_cats_sorted":[],"license":"","primary_cat":"math.HO","submitted_at":"2006-11-23T20:58:53Z","title_canon_sha256":"2186217dfbe85e464508ce06721ef31a0e8f476983a96d4cad045ac52449e251"},"schema_version":"1.0","source":{"id":"math/0611740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611740","created_at":"2026-07-04T14:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611740v1","created_at":"2026-07-04T14:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611740","created_at":"2026-07-04T14:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"VRGK7I56T64Q","created_at":"2026-07-04T14:57:41Z"},{"alias_kind":"pith_short_16","alias_value":"VRGK7I56T64QMF6C","created_at":"2026-07-04T14:57:41Z"},{"alias_kind":"pith_short_8","alias_value":"VRGK7I56","created_at":"2026-07-04T14:57:41Z"}],"graph_snapshots":[{"event_id":"sha256:73330be992ac7732afd554c579196e58f1852a866e33b8623f615409c469c75e","target":"graph","created_at":"2026-07-04T14:57:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0611740/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given Monday, October 30, 2006, at the University of Milan.]","authors_text":"G. J. Chaitin (IBM Research)","cross_cats":[],"headline":"","license":"","primary_cat":"math.HO","submitted_at":"2006-11-23T20:58:53Z","title":"The Halting Probability Omega: Irreducible Complexity in Pure Mathematics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611740","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:e0c60af640f90a179353b5f38186f0db5ffd1bc85fb7a4bf1655cb46c4f34b27","target":"record","created_at":"2026-07-04T14:57:41Z","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":"d4f010a3f26e011cc9dfa5a171dda44e4ffccdfc53ad5ae27693af27533071b5","cross_cats_sorted":[],"license":"","primary_cat":"math.HO","submitted_at":"2006-11-23T20:58:53Z","title_canon_sha256":"2186217dfbe85e464508ce06721ef31a0e8f476983a96d4cad045ac52449e251"},"schema_version":"1.0","source":{"id":"math/0611740","kind":"arxiv","version":1}},"canonical_sha256":"ac4cafa3be9fb90617c26e879a777949a4aaf74c804c230d33925c2fd70c09ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4cafa3be9fb90617c26e879a777949a4aaf74c804c230d33925c2fd70c09ac","first_computed_at":"2026-07-04T14:57:41.717525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:57:41.717525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+iYrXisdlTCniT7BLntDEOkV0DXtTPVnukwoShBVEuyNP654BJO+pMTMQytmMWokO01Gal1JRHhuRxlagvoeBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:57:41.717988Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0c60af640f90a179353b5f38186f0db5ffd1bc85fb7a4bf1655cb46c4f34b27","sha256:73330be992ac7732afd554c579196e58f1852a866e33b8623f615409c469c75e"],"state_sha256":"badcea32d6fe87bba62f334676634a9af0602d33f0721b22de497047edc3e220"}