{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MGJAS5BLZU2NOXD2WDGTYOJNMK","short_pith_number":"pith:MGJAS5BL","canonical_record":{"source":{"id":"1902.08664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-22T20:41:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6989be4c42ebb9ecbc2e0338462144c4089584de68401a5c7e7de8ebd706c7b9","abstract_canon_sha256":"2f9c2d09e0e754ebe630b5dc8ecde324352d22343fb178d70f3a74c891b9d8cf"},"schema_version":"1.0"},"canonical_sha256":"619209742bcd34d75c7ab0cd3c392d628286c27ddf6d3c288e4a7340df827f28","source":{"kind":"arxiv","id":"1902.08664","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08664","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08664v2","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08664","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"MGJAS5BLZU2N","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MGJAS5BLZU2NOXD2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MGJAS5BL","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MGJAS5BLZU2NOXD2WDGTYOJNMK","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-22T20:41:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6989be4c42ebb9ecbc2e0338462144c4089584de68401a5c7e7de8ebd706c7b9","abstract_canon_sha256":"2f9c2d09e0e754ebe630b5dc8ecde324352d22343fb178d70f3a74c891b9d8cf"},"schema_version":"1.0"},"canonical_sha256":"619209742bcd34d75c7ab0cd3c392d628286c27ddf6d3c288e4a7340df827f28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:53.325421Z","signature_b64":"LuSml608o6Zi37+MVcbnHFaHgCOZvY622s7HB5nlomkCfQI27xCLwioz2fTf82BJz3m/eG9F350UfNTNuZYLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"619209742bcd34d75c7ab0cd3c392d628286c27ddf6d3c288e4a7340df827f28","last_reissued_at":"2026-05-17T23:42:53.324733Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:53.324733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08664","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":"2026-05-17T23:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/d2+j0y3YIwR6xBtSXdHqqPm68MHEvSBdi199nPpIZoIfhcMNYMC6+g0DGt86DaEs5BZar0jpRPJbyddhHWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:21:50.059713Z"},"content_sha256":"5c6fa78793d79c227e0ef212698629e51ee91e7be5ddf4a34123474fa9915ed1","schema_version":"1.0","event_id":"sha256:5c6fa78793d79c227e0ef212698629e51ee91e7be5ddf4a34123474fa9915ed1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MGJAS5BLZU2NOXD2WDGTYOJNMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum structures from association schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Radhakrishnan Balu","submitted_at":"2019-02-22T20:41:53Z","abstract_excerpt":"Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and interacting Fock spaces (IFS) using the quantum probabilistic approach. Our constructions are based on the intersection numbers and their duals Krien parameters of the schemes with examples focused on regular (distance-regular and distance-transitive) graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08664","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":"2026-05-17T23:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVFXfmbXnFNGcalbivFwWSRi+B4RMET/Q3TMOQLjNcKksA9/SaPH3jj1RHyEtbBHgIXwj5LtvYMmxj/EAI1FCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:21:50.060408Z"},"content_sha256":"022ce402e9bbb7e6441b4f660cd8a4c5eb70a95dea088fc9ba87a21377a42e02","schema_version":"1.0","event_id":"sha256:022ce402e9bbb7e6441b4f660cd8a4c5eb70a95dea088fc9ba87a21377a42e02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK/bundle.json","state_url":"https://pith.science/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK/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":"2026-05-27T23:21:50Z","links":{"resolver":"https://pith.science/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK","bundle":"https://pith.science/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK/bundle.json","state":"https://pith.science/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGJAS5BLZU2NOXD2WDGTYOJNMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MGJAS5BLZU2NOXD2WDGTYOJNMK","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":"2f9c2d09e0e754ebe630b5dc8ecde324352d22343fb178d70f3a74c891b9d8cf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-22T20:41:53Z","title_canon_sha256":"6989be4c42ebb9ecbc2e0338462144c4089584de68401a5c7e7de8ebd706c7b9"},"schema_version":"1.0","source":{"id":"1902.08664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08664","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08664v2","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08664","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"MGJAS5BLZU2N","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MGJAS5BLZU2NOXD2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MGJAS5BL","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:022ce402e9bbb7e6441b4f660cd8a4c5eb70a95dea088fc9ba87a21377a42e02","target":"graph","created_at":"2026-05-17T23:42:53Z","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":"Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and interacting Fock spaces (IFS) using the quantum probabilistic approach. Our constructions are based on the intersection numbers and their duals Krien parameters of the schemes with examples focused on regular (distance-regular and distance-transitive) graphs.","authors_text":"Radhakrishnan Balu","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-22T20:41:53Z","title":"Quantum structures from association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08664","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":"sha256:5c6fa78793d79c227e0ef212698629e51ee91e7be5ddf4a34123474fa9915ed1","target":"record","created_at":"2026-05-17T23:42:53Z","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":"2f9c2d09e0e754ebe630b5dc8ecde324352d22343fb178d70f3a74c891b9d8cf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-22T20:41:53Z","title_canon_sha256":"6989be4c42ebb9ecbc2e0338462144c4089584de68401a5c7e7de8ebd706c7b9"},"schema_version":"1.0","source":{"id":"1902.08664","kind":"arxiv","version":2}},"canonical_sha256":"619209742bcd34d75c7ab0cd3c392d628286c27ddf6d3c288e4a7340df827f28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"619209742bcd34d75c7ab0cd3c392d628286c27ddf6d3c288e4a7340df827f28","first_computed_at":"2026-05-17T23:42:53.324733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:53.324733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LuSml608o6Zi37+MVcbnHFaHgCOZvY622s7HB5nlomkCfQI27xCLwioz2fTf82BJz3m/eG9F350UfNTNuZYLBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:53.325421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c6fa78793d79c227e0ef212698629e51ee91e7be5ddf4a34123474fa9915ed1","sha256:022ce402e9bbb7e6441b4f660cd8a4c5eb70a95dea088fc9ba87a21377a42e02"],"state_sha256":"23dabd3159a69197f82007bd057d623c20c75b39bd7ba00c1e4542b87965e419"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oM5gDMqZwaB3znPrc+w2AkF7yDwyWaBV7qJdNvXm3vPwh7oxZlcSNVu6mNZv7TsE7F6b7yA+jIzyj8Ei9HrxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:21:50.063995Z","bundle_sha256":"88637fcb166d82f9615e5db1d48c6b8302b4c1dfedd16313d1a44729489b73ba"}}