{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZFHTDDBDTYE46NE25WWU5BCH2C","short_pith_number":"pith:ZFHTDDBD","canonical_record":{"source":{"id":"1104.5213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-04-27T18:51:41Z","cross_cats_sorted":[],"title_canon_sha256":"517bcde20a7b01adcd49fceb88502a8baf0aa3d60229dd266a16da3e6992cfbe","abstract_canon_sha256":"7e8a29b97d9bda70a1d2ebc4782d4cb898f446b92172a6fd78bcf7b9697f11bc"},"schema_version":"1.0"},"canonical_sha256":"c94f318c239e09cf349aedad4e8447d08f0dbdfe59916802dab3972216bce98e","source":{"kind":"arxiv","id":"1104.5213","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5213","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5213v2","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5213","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZFHTDDBDTYE4","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZFHTDDBDTYE46NE2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZFHTDDBD","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZFHTDDBDTYE46NE25WWU5BCH2C","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-04-27T18:51:41Z","cross_cats_sorted":[],"title_canon_sha256":"517bcde20a7b01adcd49fceb88502a8baf0aa3d60229dd266a16da3e6992cfbe","abstract_canon_sha256":"7e8a29b97d9bda70a1d2ebc4782d4cb898f446b92172a6fd78bcf7b9697f11bc"},"schema_version":"1.0"},"canonical_sha256":"c94f318c239e09cf349aedad4e8447d08f0dbdfe59916802dab3972216bce98e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:49.631166Z","signature_b64":"c/A0pN8gBusA9sK+AzEhj5fy6u+AhTXNAwASauqaQpN0vu0iMSyAH3K2j8amky/sttXMIsb9ozZmtW3jjrhNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c94f318c239e09cf349aedad4e8447d08f0dbdfe59916802dab3972216bce98e","last_reissued_at":"2026-05-18T00:20:49.630529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:49.630529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5213","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":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSI2ZJgkpKqYtPRSbPIQQQtssMnTASRWgIZ9NxPqq21Y7Ttv0lI4RRs+X9CjFrO99yErAIW5jvavvieMPplzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T23:27:27.510855Z"},"content_sha256":"6ca063b9f8f408de939c9dd1b8976effe494062a4794243c1bce1dc533755fba","schema_version":"1.0","event_id":"sha256:6ca063b9f8f408de939c9dd1b8976effe494062a4794243c1bce1dc533755fba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZFHTDDBDTYE46NE25WWU5BCH2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Square root voting system, optimal threshold and \\pi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Karol Zyczkowski, Wojciech Slomczynski","submitted_at":"2011-04-27T18:51:41Z","abstract_excerpt":"The problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favour of the square root voting system, where the voting weights of member states are proportional to the square root of their population are discussed and a link between this solution and the random walk in the one-dimensional lattice is established. It is known that the voting power of every member state is approximately equal to its voting weight, if the threshold q for the qualified majority"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5213","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":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0DeXoXuuJ4Zy+TeEJ6I6j2nGJtlFBJ5cs0MFAjpQBALypOJSLQMpoqbhWrveLKDE1YrYaSreirt5nDXSM5lBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T23:27:27.511502Z"},"content_sha256":"610ccbe0f9d2702add2da6d63f193d6b99b5e5fc68ba20e7f2bd83eb1e926467","schema_version":"1.0","event_id":"sha256:610ccbe0f9d2702add2da6d63f193d6b99b5e5fc68ba20e7f2bd83eb1e926467"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFHTDDBDTYE46NE25WWU5BCH2C/bundle.json","state_url":"https://pith.science/pith/ZFHTDDBDTYE46NE25WWU5BCH2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFHTDDBDTYE46NE25WWU5BCH2C/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":"2026-05-24T23:27:27Z","links":{"resolver":"https://pith.science/pith/ZFHTDDBDTYE46NE25WWU5BCH2C","bundle":"https://pith.science/pith/ZFHTDDBDTYE46NE25WWU5BCH2C/bundle.json","state":"https://pith.science/pith/ZFHTDDBDTYE46NE25WWU5BCH2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFHTDDBDTYE46NE25WWU5BCH2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZFHTDDBDTYE46NE25WWU5BCH2C","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":"7e8a29b97d9bda70a1d2ebc4782d4cb898f446b92172a6fd78bcf7b9697f11bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-04-27T18:51:41Z","title_canon_sha256":"517bcde20a7b01adcd49fceb88502a8baf0aa3d60229dd266a16da3e6992cfbe"},"schema_version":"1.0","source":{"id":"1104.5213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5213","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5213v2","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5213","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZFHTDDBDTYE4","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZFHTDDBDTYE46NE2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZFHTDDBD","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:610ccbe0f9d2702add2da6d63f193d6b99b5e5fc68ba20e7f2bd83eb1e926467","target":"graph","created_at":"2026-05-18T00:20:49Z","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":"The problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favour of the square root voting system, where the voting weights of member states are proportional to the square root of their population are discussed and a link between this solution and the random walk in the one-dimensional lattice is established. It is known that the voting power of every member state is approximately equal to its voting weight, if the threshold q for the qualified majority","authors_text":"Karol Zyczkowski, Wojciech Slomczynski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-04-27T18:51:41Z","title":"Square root voting system, optimal threshold and \\pi"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5213","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":"sha256:6ca063b9f8f408de939c9dd1b8976effe494062a4794243c1bce1dc533755fba","target":"record","created_at":"2026-05-18T00:20:49Z","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":"7e8a29b97d9bda70a1d2ebc4782d4cb898f446b92172a6fd78bcf7b9697f11bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-04-27T18:51:41Z","title_canon_sha256":"517bcde20a7b01adcd49fceb88502a8baf0aa3d60229dd266a16da3e6992cfbe"},"schema_version":"1.0","source":{"id":"1104.5213","kind":"arxiv","version":2}},"canonical_sha256":"c94f318c239e09cf349aedad4e8447d08f0dbdfe59916802dab3972216bce98e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c94f318c239e09cf349aedad4e8447d08f0dbdfe59916802dab3972216bce98e","first_computed_at":"2026-05-18T00:20:49.630529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:49.630529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/A0pN8gBusA9sK+AzEhj5fy6u+AhTXNAwASauqaQpN0vu0iMSyAH3K2j8amky/sttXMIsb9ozZmtW3jjrhNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:49.631166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ca063b9f8f408de939c9dd1b8976effe494062a4794243c1bce1dc533755fba","sha256:610ccbe0f9d2702add2da6d63f193d6b99b5e5fc68ba20e7f2bd83eb1e926467"],"state_sha256":"522d254deb8bc6463b8b57baee0c5f1be7837a9a040cd9ead7d57bec77286dc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HyrwsVmlO1SCX/vb3wHvLPom7kTU79Eb76b6Jkj6JCXIMpxCso0+QDvQGTKbzQ4R/dqvxFmOY5KJaCxSgp1aCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T23:27:27.514533Z","bundle_sha256":"91c854cc67533b1357c48ad1864f54e0e936e7aa2e0e7857b9cf6b5b5a35038b"}}