{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:IIL2FYR63K75XKPPVA76O6RGAE","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":"c9bf0e8299f497903b263e215612ec05ba7f143bb6650cbd3eed886dc491a7dd","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-10-14T19:00:54Z","title_canon_sha256":"13cf69bb4cbda537de98849e73af01263133a33bc4bead877c9ced5a85ae1d78"},"schema_version":"1.0","source":{"id":"quant-ph/9910067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9910067","created_at":"2026-07-04T16:16:25Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9910067v1","created_at":"2026-07-04T16:16:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9910067","created_at":"2026-07-04T16:16:25Z"},{"alias_kind":"pith_short_12","alias_value":"IIL2FYR63K75","created_at":"2026-07-04T16:16:25Z"},{"alias_kind":"pith_short_16","alias_value":"IIL2FYR63K75XKPP","created_at":"2026-07-04T16:16:25Z"},{"alias_kind":"pith_short_8","alias_value":"IIL2FYR6","created_at":"2026-07-04T16:16:25Z"}],"graph_snapshots":[{"event_id":"sha256:4106b79f6313fb41eb256e00c7843b3878a32cec4fb2e94aa80af1992a4ff6a1","target":"graph","created_at":"2026-07-04T16:16:25Z","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/quant-ph/9910067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In ","authors_text":"Daniel Gottesman","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1999-10-14T19:00:54Z","title":"On the Theory of Quantum Secret Sharing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9910067","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:ef2344e40cbc3d058c434153ac08eb561daac20e6d0ee9bffd50f8fb061d95b8","target":"record","created_at":"2026-07-04T16:16:25Z","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":"c9bf0e8299f497903b263e215612ec05ba7f143bb6650cbd3eed886dc491a7dd","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-10-14T19:00:54Z","title_canon_sha256":"13cf69bb4cbda537de98849e73af01263133a33bc4bead877c9ced5a85ae1d78"},"schema_version":"1.0","source":{"id":"quant-ph/9910067","kind":"arxiv","version":1}},"canonical_sha256":"4217a2e23edabfdba9efa83fe77a26012d7e8465fc3bda6a9540eebeb5991923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4217a2e23edabfdba9efa83fe77a26012d7e8465fc3bda6a9540eebeb5991923","first_computed_at":"2026-07-04T16:16:25.799636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:16:25.799636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jvVvXJViOZG831EpNYrjxgeTdaceYRRZ96TL3piMaS7HrlH0jQrkxqYvfTHvlX9sDCoHYyO3ECiVAZrBJNXzDA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:16:25.800092Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9910067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef2344e40cbc3d058c434153ac08eb561daac20e6d0ee9bffd50f8fb061d95b8","sha256:4106b79f6313fb41eb256e00c7843b3878a32cec4fb2e94aa80af1992a4ff6a1"],"state_sha256":"67693308c2d99e22c04e8a9742b621543c94185e94bebf8890287f9431646f00"}