{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZHHMCZABDF2IIHUDYWC3RJVO5A","short_pith_number":"pith:ZHHMCZAB","canonical_record":{"source":{"id":"1109.0060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-01T01:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"57a25a66b6f48c5dcd4cde11a45eff0e72e555f90f3c9e10259e622f113681cb","abstract_canon_sha256":"929382f37e3610c5a2f5bf3cbdcb4da5922385e363439679021ffd64a626d4d5"},"schema_version":"1.0"},"canonical_sha256":"c9cec164011974841e83c585b8a6aee834aba4ff5e3a84819c20d51797cd0124","source":{"kind":"arxiv","id":"1109.0060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0060","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0060v1","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0060","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZHHMCZABDF2I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZHHMCZABDF2IIHUD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZHHMCZAB","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZHHMCZABDF2IIHUDYWC3RJVO5A","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-01T01:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"57a25a66b6f48c5dcd4cde11a45eff0e72e555f90f3c9e10259e622f113681cb","abstract_canon_sha256":"929382f37e3610c5a2f5bf3cbdcb4da5922385e363439679021ffd64a626d4d5"},"schema_version":"1.0"},"canonical_sha256":"c9cec164011974841e83c585b8a6aee834aba4ff5e3a84819c20d51797cd0124","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:17.540863Z","signature_b64":"5Wlu2BsXLdIVto0ryL0eodepq3K2nxeEaefQnZHbUZhBgWK5d81zIrXIBR2TC5Ie7shRNQfsFbsqghw5Bi9oDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9cec164011974841e83c585b8a6aee834aba4ff5e3a84819c20d51797cd0124","last_reissued_at":"2026-05-18T04:14:17.539755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:17.539755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0060","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":"2026-05-18T04:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6WH8pYEeqCTY9BcG87gWSrk2XxuU4w7MFV8T5mn4nhQZG90BjsvHEoPVrfsTZ7bVU0CjzHyL/s+PeR3luSPqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:28:14.390889Z"},"content_sha256":"be9475dd6d42be9f4fc50b0da6318a51d4076f9e58ff44b255d253909f7058cd","schema_version":"1.0","event_id":"sha256:be9475dd6d42be9f4fc50b0da6318a51d4076f9e58ff44b255d253909f7058cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZHHMCZABDF2IIHUDYWC3RJVO5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mutually unbiased bases for quantum states defined over p-adic numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander Russell, Wim van Dam","submitted_at":"2011-09-01T01:02:49Z","abstract_excerpt":"We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known.\n  We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0060","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":"2026-05-18T04:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4jPKFlCff+m33xOmxYaod9wIgwry5lo6H6QPwWxHUdJNKNoRRazLSKXvwS4Xy+uK+t9r4NYj7iLKPrDi27nRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:28:14.391237Z"},"content_sha256":"ff3dcca913ea3b535b69e85d4067ce9ec065d70b34a17547e440ead0fad15731","schema_version":"1.0","event_id":"sha256:ff3dcca913ea3b535b69e85d4067ce9ec065d70b34a17547e440ead0fad15731"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A/bundle.json","state_url":"https://pith.science/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A/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":"2026-05-20T15:28:14Z","links":{"resolver":"https://pith.science/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A","bundle":"https://pith.science/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A/bundle.json","state":"https://pith.science/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHHMCZABDF2IIHUDYWC3RJVO5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZHHMCZABDF2IIHUDYWC3RJVO5A","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":"929382f37e3610c5a2f5bf3cbdcb4da5922385e363439679021ffd64a626d4d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-01T01:02:49Z","title_canon_sha256":"57a25a66b6f48c5dcd4cde11a45eff0e72e555f90f3c9e10259e622f113681cb"},"schema_version":"1.0","source":{"id":"1109.0060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0060","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0060v1","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0060","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZHHMCZABDF2I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZHHMCZABDF2IIHUD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZHHMCZAB","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:ff3dcca913ea3b535b69e85d4067ce9ec065d70b34a17547e440ead0fad15731","target":"graph","created_at":"2026-05-18T04:14:17Z","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":"We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known.\n  We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces.","authors_text":"Alexander Russell, Wim van Dam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-01T01:02:49Z","title":"Mutually unbiased bases for quantum states defined over p-adic numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0060","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:be9475dd6d42be9f4fc50b0da6318a51d4076f9e58ff44b255d253909f7058cd","target":"record","created_at":"2026-05-18T04:14:17Z","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":"929382f37e3610c5a2f5bf3cbdcb4da5922385e363439679021ffd64a626d4d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-01T01:02:49Z","title_canon_sha256":"57a25a66b6f48c5dcd4cde11a45eff0e72e555f90f3c9e10259e622f113681cb"},"schema_version":"1.0","source":{"id":"1109.0060","kind":"arxiv","version":1}},"canonical_sha256":"c9cec164011974841e83c585b8a6aee834aba4ff5e3a84819c20d51797cd0124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9cec164011974841e83c585b8a6aee834aba4ff5e3a84819c20d51797cd0124","first_computed_at":"2026-05-18T04:14:17.539755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:17.539755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Wlu2BsXLdIVto0ryL0eodepq3K2nxeEaefQnZHbUZhBgWK5d81zIrXIBR2TC5Ie7shRNQfsFbsqghw5Bi9oDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:17.540863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be9475dd6d42be9f4fc50b0da6318a51d4076f9e58ff44b255d253909f7058cd","sha256:ff3dcca913ea3b535b69e85d4067ce9ec065d70b34a17547e440ead0fad15731"],"state_sha256":"7604525d924f2ad3adead8a2e83813aba702cf474a809e52608d9f3c84e24ab9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1vgYA02GMTKgJXp0ec2r9K+seb+0p4BgC2keLUtbck5C3itMvFazzAPRPXMsl6hX+u24B2APAJmzo8v/AepAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T15:28:14.393198Z","bundle_sha256":"36ac641f00197c2091c303dde8a52f5d10c5b6750c0690608223c6d27a00dd36"}}