{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q3JCYWWDFNDGVXSDUFOKS7WOCQ","short_pith_number":"pith:Q3JCYWWD","canonical_record":{"source":{"id":"1109.4888","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-22T16:49:15Z","cross_cats_sorted":[],"title_canon_sha256":"bac67291ef84cefdf84080527850b66d4d2272842d343b7eba9910e6257e6bb4","abstract_canon_sha256":"a00e95eb700fa49f776c38ee86de2356662e5a8e254877b16736f691acdbcf73"},"schema_version":"1.0"},"canonical_sha256":"86d22c5ac32b466ade43a15ca97ece1439c6b8b4340ad396d3f5d90631e99e6e","source":{"kind":"arxiv","id":"1109.4888","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4888","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4888v3","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4888","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q3JCYWWDFNDG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3JCYWWDFNDGVXSD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3JCYWWD","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q3JCYWWDFNDGVXSDUFOKS7WOCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4888","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-22T16:49:15Z","cross_cats_sorted":[],"title_canon_sha256":"bac67291ef84cefdf84080527850b66d4d2272842d343b7eba9910e6257e6bb4","abstract_canon_sha256":"a00e95eb700fa49f776c38ee86de2356662e5a8e254877b16736f691acdbcf73"},"schema_version":"1.0"},"canonical_sha256":"86d22c5ac32b466ade43a15ca97ece1439c6b8b4340ad396d3f5d90631e99e6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:30.968289Z","signature_b64":"fbA+zLia54xpdrd663Ll5BhRQvqnGGg/LpBSwnHJVAYK5HsRBj0m0sVM/PHD9X+fAAyHKTaagrH6a0kMWd7SDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86d22c5ac32b466ade43a15ca97ece1439c6b8b4340ad396d3f5d90631e99e6e","last_reissued_at":"2026-05-18T03:31:30.967848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:30.967848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4888","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fXCcfywVZKHbPq5W4bihE7TQnvdrTk31pJR7UexTXDr+HjLWTQvYu7nHSqo0gzVL3i3MFeCWrw7J/fM6vgj7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:47:49.435945Z"},"content_sha256":"cafb08463af41c2c4f9a5944861aa8b4b563fab2f4760595e108c6bc99a10f99","schema_version":"1.0","event_id":"sha256:cafb08463af41c2c4f9a5944861aa8b4b563fab2f4760595e108c6bc99a10f99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q3JCYWWDFNDGVXSDUFOKS7WOCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum permutations, Hadamard matrices, and the search for matrix models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Teodor Banica","submitted_at":"2011-09-22T16:49:15Z","abstract_excerpt":"This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4888","kind":"arxiv","version":3},"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":"2026-05-18T03:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWtCBfaohKFP+4UnteOht/u3gQGOPS4PNhPQnGWH7zbx8+a+PMUQRcC5yESLwBwIPd4sqawhnTwRYK1zNQD7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:47:49.436286Z"},"content_sha256":"6ab856d375e73a0f1ce5d54ceb09a15d4dea3b11d43f8a7b5789d843ffd8cfbe","schema_version":"1.0","event_id":"sha256:6ab856d375e73a0f1ce5d54ceb09a15d4dea3b11d43f8a7b5789d843ffd8cfbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ/bundle.json","state_url":"https://pith.science/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ/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":"2026-05-31T20:47:49Z","links":{"resolver":"https://pith.science/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ","bundle":"https://pith.science/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ/bundle.json","state":"https://pith.science/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3JCYWWDFNDGVXSDUFOKS7WOCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q3JCYWWDFNDGVXSDUFOKS7WOCQ","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":"a00e95eb700fa49f776c38ee86de2356662e5a8e254877b16736f691acdbcf73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-22T16:49:15Z","title_canon_sha256":"bac67291ef84cefdf84080527850b66d4d2272842d343b7eba9910e6257e6bb4"},"schema_version":"1.0","source":{"id":"1109.4888","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4888","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4888v3","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4888","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q3JCYWWDFNDG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3JCYWWDFNDGVXSD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3JCYWWD","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:6ab856d375e73a0f1ce5d54ceb09a15d4dea3b11d43f8a7b5789d843ffd8cfbe","target":"graph","created_at":"2026-05-18T03:31:30Z","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":"This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.","authors_text":"Teodor Banica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-22T16:49:15Z","title":"Quantum permutations, Hadamard matrices, and the search for matrix models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4888","kind":"arxiv","version":3},"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:cafb08463af41c2c4f9a5944861aa8b4b563fab2f4760595e108c6bc99a10f99","target":"record","created_at":"2026-05-18T03:31:30Z","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":"a00e95eb700fa49f776c38ee86de2356662e5a8e254877b16736f691acdbcf73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-22T16:49:15Z","title_canon_sha256":"bac67291ef84cefdf84080527850b66d4d2272842d343b7eba9910e6257e6bb4"},"schema_version":"1.0","source":{"id":"1109.4888","kind":"arxiv","version":3}},"canonical_sha256":"86d22c5ac32b466ade43a15ca97ece1439c6b8b4340ad396d3f5d90631e99e6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86d22c5ac32b466ade43a15ca97ece1439c6b8b4340ad396d3f5d90631e99e6e","first_computed_at":"2026-05-18T03:31:30.967848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:30.967848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fbA+zLia54xpdrd663Ll5BhRQvqnGGg/LpBSwnHJVAYK5HsRBj0m0sVM/PHD9X+fAAyHKTaagrH6a0kMWd7SDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:30.968289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4888","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cafb08463af41c2c4f9a5944861aa8b4b563fab2f4760595e108c6bc99a10f99","sha256:6ab856d375e73a0f1ce5d54ceb09a15d4dea3b11d43f8a7b5789d843ffd8cfbe"],"state_sha256":"5a95f730fa5d2192e83979107d2be413c611c459227da3d646df83e9ce7b2afd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UjZkB7hnzrr7zWCqz5/o0ZcyKtJDThaDMt7CuvjMvP1fVjFzPPM7f1SMtfXMAW5bqALf8gy2GSYPT9MuQqkNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:47:49.438692Z","bundle_sha256":"434ed37d196b14c61bd3f9a88b4ee944cc6b4d17317c1987e08082eee6930fad"}}