{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XO6UBUCZ5MLUMOTPFB2JAJMRTM","short_pith_number":"pith:XO6UBUCZ","canonical_record":{"source":{"id":"1501.04398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-19T06:15:21Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"c71c6e5c05cff938ebb99b1a405e711aa36a98e2c3f01a742dc6d8bf89a5d91b","abstract_canon_sha256":"ee19f7e27da2fbebf19bb113cc7db3ce0b74a4c3f8fd2f47dd76da8105a7da23"},"schema_version":"1.0"},"canonical_sha256":"bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a","source":{"kind":"arxiv","id":"1501.04398","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04398","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04398v1","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04398","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"XO6UBUCZ5MLU","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XO6UBUCZ5MLUMOTP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XO6UBUCZ","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XO6UBUCZ5MLUMOTPFB2JAJMRTM","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-19T06:15:21Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"c71c6e5c05cff938ebb99b1a405e711aa36a98e2c3f01a742dc6d8bf89a5d91b","abstract_canon_sha256":"ee19f7e27da2fbebf19bb113cc7db3ce0b74a4c3f8fd2f47dd76da8105a7da23"},"schema_version":"1.0"},"canonical_sha256":"bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:31.334827Z","signature_b64":"isofDHpdnwjpMF5n1a9BW/28vtDlsPj9srH+qVPD3yl2sqWzZn2uIV4m6oUw5JCxjQUfeYFv7cOD6AipypTaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a","last_reissued_at":"2026-05-18T00:15:31.334123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:31.334123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04398","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":"2026-05-18T00:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mb++onAswrgJmvDE6qJ1lI9iiHE644jOI25Z041Gt7n6UNkj0nr6YcclyxnxCLPc3aMlabwOvs5KvlxaW09uCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:25:26.942214Z"},"content_sha256":"2e16c63c57aeda13bb7c44f4c061508060becf8262393e1881c598829ba67440","schema_version":"1.0","event_id":"sha256:2e16c63c57aeda13bb7c44f4c061508060becf8262393e1881c598829ba67440"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XO6UBUCZ5MLUMOTPFB2JAJMRTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectrally extremal vertices, strong cospectrality and state transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"Gabriel Coutinho","submitted_at":"2015-01-19T06:15:21Z","abstract_excerpt":"In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a combinatorial property called strong cospectrality. Here we determine the structure of graphs containing pairs of vertices which are strongly cospectral and satisfy a certain extremal property related to the spectrum of the graph. If the graph satisfies this property globally and is regular, we also show that the existence of a partition of the vertex set into pairs of vertices at maximum distance admitting perfect state transfer fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04398","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":"2026-05-18T00:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C19ZVUQiFimF2ncF27fRFbURTTfcqP396tWzq0/VU1gps9IhLWqy/ipx2B8pSBkeDifXUbyqjWvV8fDqrTD1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:25:26.942956Z"},"content_sha256":"8c1431ce7a7e446af150eac20153cb6c3be896ef144ba68e6d8667fbbe9c4d6d","schema_version":"1.0","event_id":"sha256:8c1431ce7a7e446af150eac20153cb6c3be896ef144ba68e6d8667fbbe9c4d6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM/bundle.json","state_url":"https://pith.science/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM/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":"2026-05-31T19:25:26Z","links":{"resolver":"https://pith.science/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM","bundle":"https://pith.science/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM/bundle.json","state":"https://pith.science/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XO6UBUCZ5MLUMOTPFB2JAJMRTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XO6UBUCZ5MLUMOTPFB2JAJMRTM","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":"ee19f7e27da2fbebf19bb113cc7db3ce0b74a4c3f8fd2f47dd76da8105a7da23","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-19T06:15:21Z","title_canon_sha256":"c71c6e5c05cff938ebb99b1a405e711aa36a98e2c3f01a742dc6d8bf89a5d91b"},"schema_version":"1.0","source":{"id":"1501.04398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04398","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04398v1","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04398","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"XO6UBUCZ5MLU","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XO6UBUCZ5MLUMOTP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XO6UBUCZ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:8c1431ce7a7e446af150eac20153cb6c3be896ef144ba68e6d8667fbbe9c4d6d","target":"graph","created_at":"2026-05-18T00:15:31Z","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":"In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a combinatorial property called strong cospectrality. Here we determine the structure of graphs containing pairs of vertices which are strongly cospectral and satisfy a certain extremal property related to the spectrum of the graph. If the graph satisfies this property globally and is regular, we also show that the existence of a partition of the vertex set into pairs of vertices at maximum distance admitting perfect state transfer fo","authors_text":"Gabriel Coutinho","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-19T06:15:21Z","title":"Spectrally extremal vertices, strong cospectrality and state transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04398","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":"sha256:2e16c63c57aeda13bb7c44f4c061508060becf8262393e1881c598829ba67440","target":"record","created_at":"2026-05-18T00:15:31Z","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":"ee19f7e27da2fbebf19bb113cc7db3ce0b74a4c3f8fd2f47dd76da8105a7da23","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-19T06:15:21Z","title_canon_sha256":"c71c6e5c05cff938ebb99b1a405e711aa36a98e2c3f01a742dc6d8bf89a5d91b"},"schema_version":"1.0","source":{"id":"1501.04398","kind":"arxiv","version":1}},"canonical_sha256":"bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a","first_computed_at":"2026-05-18T00:15:31.334123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:31.334123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"isofDHpdnwjpMF5n1a9BW/28vtDlsPj9srH+qVPD3yl2sqWzZn2uIV4m6oUw5JCxjQUfeYFv7cOD6AipypTaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:31.334827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e16c63c57aeda13bb7c44f4c061508060becf8262393e1881c598829ba67440","sha256:8c1431ce7a7e446af150eac20153cb6c3be896ef144ba68e6d8667fbbe9c4d6d"],"state_sha256":"0bb511725b19461414d1f49ab0aa3831ca1c5a272f0ecfa53aad7fc32deaa8ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKJgxC3C9FMsH//pSi7AY+B7rQOxmOcXxGUddiE2IilKJm72kZrgPIAmz+b7KeYUfhdbzThBP8EMk7KWfxjtAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:25:26.946671Z","bundle_sha256":"ec0887287a2f83b8853dd8df038c12551ddfd0177f84c9ad9e81f45981572b38"}}