{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:643IKEGHXSG2RKBMARJU4JR6PZ","short_pith_number":"pith:643IKEGH","canonical_record":{"source":{"id":"2606.10872","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-09T13:49:08Z","cross_cats_sorted":[],"title_canon_sha256":"957ceae361ce95ba222d28f66e0afdfdef525aa7f58885e8949884d48f83d217","abstract_canon_sha256":"98f0d397f8638e56b243c83d9f8ed3c7ca71321a88f8b55d84110f1d1f28aa15"},"schema_version":"1.0"},"canonical_sha256":"f7368510c7bc8da8a82c04534e263e7e599626f9f49fed227e930ce0dc566422","source":{"kind":"arxiv","id":"2606.10872","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10872","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10872v1","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10872","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"pith_short_12","alias_value":"643IKEGHXSG2","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"pith_short_16","alias_value":"643IKEGHXSG2RKBM","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"pith_short_8","alias_value":"643IKEGH","created_at":"2026-06-10T01:10:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:643IKEGHXSG2RKBMARJU4JR6PZ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.10872","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-09T13:49:08Z","cross_cats_sorted":[],"title_canon_sha256":"957ceae361ce95ba222d28f66e0afdfdef525aa7f58885e8949884d48f83d217","abstract_canon_sha256":"98f0d397f8638e56b243c83d9f8ed3c7ca71321a88f8b55d84110f1d1f28aa15"},"schema_version":"1.0"},"canonical_sha256":"f7368510c7bc8da8a82c04534e263e7e599626f9f49fed227e930ce0dc566422","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:44.850866Z","signature_b64":"UBGf8eVLKLqv9H/8IVQ3wtQzVlANBwH1r15LE9D0lzB3X1NOwRq4R3GXBEelR0EBM/4pGzysU0ExikMsMJuqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7368510c7bc8da8a82c04534e263e7e599626f9f49fed227e930ce0dc566422","last_reissued_at":"2026-06-10T01:10:44.850063Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:44.850063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.10872","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":"2026-06-10T01:10:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOGck+ucwIwH4C4oulDZbX7lkUHYkZhKub/NGvzv5DMa2SDKLfuPtax9fDhPyRS4Ko6tDqlycn5SH/jyd7E5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:56:38.001597Z"},"content_sha256":"fc3af24b375bf017e7e6220c1364eb1b30d585a82e4e2824dc8ac3a8d51ba6b8","schema_version":"1.0","event_id":"sha256:fc3af24b375bf017e7e6220c1364eb1b30d585a82e4e2824dc8ac3a8d51ba6b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:643IKEGHXSG2RKBMARJU4JR6PZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Colorings of Spheres","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Olivier Lalonde","submitted_at":"2026-06-09T13:49:08Z","abstract_excerpt":"Cameron, Montanaro, Newman, Severini and Winter gave a construction which shows that, for $n \\in \\{2,4,8\\}$, any graph $G$ which admits a real $n$-dimensional orthogonal representation is quantumly $n$-colorable. This result can be recast as the statement that the real sphere $S^{n-1}$ is quantumly $n$-colorable for these values of $n$. We investigate possible extensions of their construction. We first show that their hypothesis that the orthogonal representation be real-valued is required by proving that there is no analogue of this for the complex spheres, which all have quantum chromatic nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10872/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-10T01:10:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jMcNLAVFmidw1pH8FP8tIunjLojDs8QE4KYuKavalqIIamaD9ZvwNajLeg/UzH8am5FWVZsN9t9bgVq0usjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:56:38.001970Z"},"content_sha256":"12317e5689784c5c635093562acbb2c99a071cbe59f0c54ddc858bbf75a3de15","schema_version":"1.0","event_id":"sha256:12317e5689784c5c635093562acbb2c99a071cbe59f0c54ddc858bbf75a3de15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/643IKEGHXSG2RKBMARJU4JR6PZ/bundle.json","state_url":"https://pith.science/pith/643IKEGHXSG2RKBMARJU4JR6PZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/643IKEGHXSG2RKBMARJU4JR6PZ/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":"2026-07-02T23:56:38Z","links":{"resolver":"https://pith.science/pith/643IKEGHXSG2RKBMARJU4JR6PZ","bundle":"https://pith.science/pith/643IKEGHXSG2RKBMARJU4JR6PZ/bundle.json","state":"https://pith.science/pith/643IKEGHXSG2RKBMARJU4JR6PZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/643IKEGHXSG2RKBMARJU4JR6PZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:643IKEGHXSG2RKBMARJU4JR6PZ","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":"98f0d397f8638e56b243c83d9f8ed3c7ca71321a88f8b55d84110f1d1f28aa15","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-09T13:49:08Z","title_canon_sha256":"957ceae361ce95ba222d28f66e0afdfdef525aa7f58885e8949884d48f83d217"},"schema_version":"1.0","source":{"id":"2606.10872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10872","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10872v1","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10872","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"pith_short_12","alias_value":"643IKEGHXSG2","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"pith_short_16","alias_value":"643IKEGHXSG2RKBM","created_at":"2026-06-10T01:10:44Z"},{"alias_kind":"pith_short_8","alias_value":"643IKEGH","created_at":"2026-06-10T01:10:44Z"}],"graph_snapshots":[{"event_id":"sha256:12317e5689784c5c635093562acbb2c99a071cbe59f0c54ddc858bbf75a3de15","target":"graph","created_at":"2026-06-10T01:10:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.10872/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Cameron, Montanaro, Newman, Severini and Winter gave a construction which shows that, for $n \\in \\{2,4,8\\}$, any graph $G$ which admits a real $n$-dimensional orthogonal representation is quantumly $n$-colorable. This result can be recast as the statement that the real sphere $S^{n-1}$ is quantumly $n$-colorable for these values of $n$. We investigate possible extensions of their construction. We first show that their hypothesis that the orthogonal representation be real-valued is required by proving that there is no analogue of this for the complex spheres, which all have quantum chromatic nu","authors_text":"Olivier Lalonde","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-09T13:49:08Z","title":"Quantum Colorings of Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10872","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:fc3af24b375bf017e7e6220c1364eb1b30d585a82e4e2824dc8ac3a8d51ba6b8","target":"record","created_at":"2026-06-10T01:10:44Z","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":"98f0d397f8638e56b243c83d9f8ed3c7ca71321a88f8b55d84110f1d1f28aa15","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-09T13:49:08Z","title_canon_sha256":"957ceae361ce95ba222d28f66e0afdfdef525aa7f58885e8949884d48f83d217"},"schema_version":"1.0","source":{"id":"2606.10872","kind":"arxiv","version":1}},"canonical_sha256":"f7368510c7bc8da8a82c04534e263e7e599626f9f49fed227e930ce0dc566422","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7368510c7bc8da8a82c04534e263e7e599626f9f49fed227e930ce0dc566422","first_computed_at":"2026-06-10T01:10:44.850063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:44.850063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UBGf8eVLKLqv9H/8IVQ3wtQzVlANBwH1r15LE9D0lzB3X1NOwRq4R3GXBEelR0EBM/4pGzysU0ExikMsMJuqDQ==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:44.850866Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc3af24b375bf017e7e6220c1364eb1b30d585a82e4e2824dc8ac3a8d51ba6b8","sha256:12317e5689784c5c635093562acbb2c99a071cbe59f0c54ddc858bbf75a3de15"],"state_sha256":"e6801b26aed3bf941df3128e9efe63eeb5fe84210bf27cd5a2fa891ce7b2a631"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C0EK1bIoX4diRtBhJe3sy/NIxye5ERpp0OrKa+FMobS1SBqz9ONg01Lfb1cPZmvjH7A1Tg38QJ54JjnD3Z6CDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T23:56:38.004039Z","bundle_sha256":"a01df2488a39798353bffebc574711ddbc1232a82b8ebf4a5798b382a17ee6e0"}}