{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7F56HOSGFVNPM4XLW3FAF4ZXWQ","short_pith_number":"pith:7F56HOSG","canonical_record":{"source":{"id":"1302.2554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-11T18:01:25Z","cross_cats_sorted":["math.MP","nlin.CD"],"title_canon_sha256":"99a47b8a48903014cf79a8a93546f0769104a06154cca537172f05e6a6ae8f59","abstract_canon_sha256":"41388f3d7f4a9beafd22bcb77f823980277058df43685a4a24a169f092f9ce3b"},"schema_version":"1.0"},"canonical_sha256":"f97be3ba462d5af672ebb6ca02f337b42aba630e4e2248acb8f4b6cfe0d921f6","source":{"kind":"arxiv","id":"1302.2554","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2554","created_at":"2026-05-18T01:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2554v1","created_at":"2026-05-18T01:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2554","created_at":"2026-05-18T01:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"7F56HOSGFVNP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7F56HOSGFVNPM4XL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7F56HOSG","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7F56HOSGFVNPM4XLW3FAF4ZXWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-11T18:01:25Z","cross_cats_sorted":["math.MP","nlin.CD"],"title_canon_sha256":"99a47b8a48903014cf79a8a93546f0769104a06154cca537172f05e6a6ae8f59","abstract_canon_sha256":"41388f3d7f4a9beafd22bcb77f823980277058df43685a4a24a169f092f9ce3b"},"schema_version":"1.0"},"canonical_sha256":"f97be3ba462d5af672ebb6ca02f337b42aba630e4e2248acb8f4b6cfe0d921f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:42.637700Z","signature_b64":"djwO3+ZTomM/eVzFu0UrjLDScLuGCRruYnXeVUbOp2r20HT/sEXT6NQjnTymVIfpJ4iHDj/xgFkd14jkQrTQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f97be3ba462d5af672ebb6ca02f337b42aba630e4e2248acb8f4b6cfe0d921f6","last_reissued_at":"2026-05-18T01:51:42.637172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:42.637172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2554","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":"2026-05-18T01:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Zt8a54HkRnrS1upKbcYPi8St016zGQB6hIVZK8H2i+1C2Oh8yD3u+GRxCcTUQXLmPPLNiE5b2iyqUwTtKdwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T01:22:09.552997Z"},"content_sha256":"91e1c672b7291540f12d72f1a8ac694163f2da8facd55de19e64ce47d716b9fc","schema_version":"1.0","event_id":"sha256:91e1c672b7291540f12d72f1a8ac694163f2da8facd55de19e64ce47d716b9fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7F56HOSGFVNPM4XLW3FAF4ZXWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"GSE statistics without spin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.CD"],"primary_cat":"math-ph","authors_text":"Christopher H. Joyner, Martin Sieber, Sebastian M\\\"uller","submitted_at":"2013-02-11T18:01:25Z","abstract_excerpt":"Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying feature: the combination of half-integer spin and time-reversal invariance. Here we provide an alternative mechanism for obtaining GSE statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. As an example, we construct a quantum graph with a particular discrete symmetry given by the quaternion group"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2554","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":"2026-05-18T01:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlskGW48RGpoFo7sCx+c0bqZnwZEpbApgsKmNagwwA0kcnDyU3fK0BLLJV+EwcZEcqxOHdWk8/FmAskbEFr0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T01:22:09.553715Z"},"content_sha256":"31f672fdfd318fbb23fb00e78955d47fa6835fb3b819c50d846d1341db23c1ae","schema_version":"1.0","event_id":"sha256:31f672fdfd318fbb23fb00e78955d47fa6835fb3b819c50d846d1341db23c1ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ/bundle.json","state_url":"https://pith.science/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ/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":"2026-05-24T01:22:09Z","links":{"resolver":"https://pith.science/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ","bundle":"https://pith.science/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ/bundle.json","state":"https://pith.science/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7F56HOSGFVNPM4XLW3FAF4ZXWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7F56HOSGFVNPM4XLW3FAF4ZXWQ","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":"41388f3d7f4a9beafd22bcb77f823980277058df43685a4a24a169f092f9ce3b","cross_cats_sorted":["math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-11T18:01:25Z","title_canon_sha256":"99a47b8a48903014cf79a8a93546f0769104a06154cca537172f05e6a6ae8f59"},"schema_version":"1.0","source":{"id":"1302.2554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2554","created_at":"2026-05-18T01:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2554v1","created_at":"2026-05-18T01:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2554","created_at":"2026-05-18T01:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"7F56HOSGFVNP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7F56HOSGFVNPM4XL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7F56HOSG","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:31f672fdfd318fbb23fb00e78955d47fa6835fb3b819c50d846d1341db23c1ae","target":"graph","created_at":"2026-05-18T01:51:42Z","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":"Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying feature: the combination of half-integer spin and time-reversal invariance. Here we provide an alternative mechanism for obtaining GSE statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. As an example, we construct a quantum graph with a particular discrete symmetry given by the quaternion group","authors_text":"Christopher H. Joyner, Martin Sieber, Sebastian M\\\"uller","cross_cats":["math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-11T18:01:25Z","title":"GSE statistics without spin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2554","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":"sha256:91e1c672b7291540f12d72f1a8ac694163f2da8facd55de19e64ce47d716b9fc","target":"record","created_at":"2026-05-18T01:51:42Z","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":"41388f3d7f4a9beafd22bcb77f823980277058df43685a4a24a169f092f9ce3b","cross_cats_sorted":["math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-11T18:01:25Z","title_canon_sha256":"99a47b8a48903014cf79a8a93546f0769104a06154cca537172f05e6a6ae8f59"},"schema_version":"1.0","source":{"id":"1302.2554","kind":"arxiv","version":1}},"canonical_sha256":"f97be3ba462d5af672ebb6ca02f337b42aba630e4e2248acb8f4b6cfe0d921f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f97be3ba462d5af672ebb6ca02f337b42aba630e4e2248acb8f4b6cfe0d921f6","first_computed_at":"2026-05-18T01:51:42.637172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:42.637172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djwO3+ZTomM/eVzFu0UrjLDScLuGCRruYnXeVUbOp2r20HT/sEXT6NQjnTymVIfpJ4iHDj/xgFkd14jkQrTQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:42.637700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91e1c672b7291540f12d72f1a8ac694163f2da8facd55de19e64ce47d716b9fc","sha256:31f672fdfd318fbb23fb00e78955d47fa6835fb3b819c50d846d1341db23c1ae"],"state_sha256":"8150b72764944ff2a2d0238f21d314617365e8442b3a3405e160de8ef58aee05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Xa77JSZij8gj/F6xCubP1O/646bzCU+iSavlkMmNrcTpm1avuZtldBP/fhoCzHwwJj2y54PqsH7ITZb9WbsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T01:22:09.557759Z","bundle_sha256":"dd6bd64617b4dca6e296146e50cf58ca924553f18d5e84f3e6031fb7c19f6a1b"}}