{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QWPS3VWFUCVMMP6IYCUPCBCYHY","short_pith_number":"pith:QWPS3VWF","canonical_record":{"source":{"id":"1501.06004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-24T04:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"75ae8b320228bf89ac0fb91daab201c438fe24212ba2915eaf4a8c9a73f0754a","abstract_canon_sha256":"a92d85347de8699bb30194c53c459e4cb5c36234d69ef15f3a29f3ada563a969"},"schema_version":"1.0"},"canonical_sha256":"859f2dd6c5a0aac63fc8c0a8f104583e0242d89794b7371f99a6881e928c511b","source":{"kind":"arxiv","id":"1501.06004","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06004","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06004v2","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06004","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"QWPS3VWFUCVM","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWPS3VWFUCVMMP6I","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWPS3VWF","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QWPS3VWFUCVMMP6IYCUPCBCYHY","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-24T04:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"75ae8b320228bf89ac0fb91daab201c438fe24212ba2915eaf4a8c9a73f0754a","abstract_canon_sha256":"a92d85347de8699bb30194c53c459e4cb5c36234d69ef15f3a29f3ada563a969"},"schema_version":"1.0"},"canonical_sha256":"859f2dd6c5a0aac63fc8c0a8f104583e0242d89794b7371f99a6881e928c511b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:27.880082Z","signature_b64":"FLT12gEkAkabDeuEWWyMOUVKqGDnRhgC3DhDus43JMuYW7NEgJf5/WsR9SIT3c6KyhqQFdiQPd77nChTjdrsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"859f2dd6c5a0aac63fc8c0a8f104583e0242d89794b7371f99a6881e928c511b","last_reissued_at":"2026-05-18T00:20:27.879621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:27.879621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06004","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":"2026-05-18T00:20:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJ05cxzwq07sy3Gtl5eP7UBaYmli4kwXR83PNq1N8uqnkDtumKOPZEvFlq/Jx0ZJAHwRGHlePKz8F+3AbRLAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:53:22.819418Z"},"content_sha256":"1e11cc78b7cda8e68bafa457ad5c338a294d2734a861f2b21025f1fc9dc13aa8","schema_version":"1.0","event_id":"sha256:1e11cc78b7cda8e68bafa457ad5c338a294d2734a861f2b21025f1fc9dc13aa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QWPS3VWFUCVMMP6IYCUPCBCYHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separability Criterion for Multi-Mode Gaussian States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"K. V. S. Shiv Chaitanya, Sibasish Ghosh, V. Srinivasan","submitted_at":"2015-01-24T04:54:30Z","abstract_excerpt":"In this paper, we give Separability criterion for the multi-mode Gaussian states using the Marchenko-Pastur theorem. We show that the Marchenko-Pastur theorem from random matrix theory as necessary and sufficient condition for separability of multimode Gaussian states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06004","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":"2026-05-18T00:20:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvkWAUpPH3w/+YYoymDJZ+kg0EYNmeUmU0rxjJ/XRAwH62q/Dj1ZQhkQTBXAMBvVOfISY0qIrLbCGIY/8nbMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:53:22.820086Z"},"content_sha256":"43048dc89f14ea38e967d935bdcfa8cb5c06b66e83534b05999be03197800a26","schema_version":"1.0","event_id":"sha256:43048dc89f14ea38e967d935bdcfa8cb5c06b66e83534b05999be03197800a26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY/bundle.json","state_url":"https://pith.science/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY/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":"2026-05-22T23:53:22Z","links":{"resolver":"https://pith.science/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY","bundle":"https://pith.science/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY/bundle.json","state":"https://pith.science/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWPS3VWFUCVMMP6IYCUPCBCYHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QWPS3VWFUCVMMP6IYCUPCBCYHY","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":"a92d85347de8699bb30194c53c459e4cb5c36234d69ef15f3a29f3ada563a969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-24T04:54:30Z","title_canon_sha256":"75ae8b320228bf89ac0fb91daab201c438fe24212ba2915eaf4a8c9a73f0754a"},"schema_version":"1.0","source":{"id":"1501.06004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06004","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06004v2","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06004","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"QWPS3VWFUCVM","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWPS3VWFUCVMMP6I","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWPS3VWF","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:43048dc89f14ea38e967d935bdcfa8cb5c06b66e83534b05999be03197800a26","target":"graph","created_at":"2026-05-18T00:20:27Z","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 this paper, we give Separability criterion for the multi-mode Gaussian states using the Marchenko-Pastur theorem. We show that the Marchenko-Pastur theorem from random matrix theory as necessary and sufficient condition for separability of multimode Gaussian states.","authors_text":"K. V. S. Shiv Chaitanya, Sibasish Ghosh, V. Srinivasan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-24T04:54:30Z","title":"Separability Criterion for Multi-Mode Gaussian States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06004","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":"sha256:1e11cc78b7cda8e68bafa457ad5c338a294d2734a861f2b21025f1fc9dc13aa8","target":"record","created_at":"2026-05-18T00:20:27Z","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":"a92d85347de8699bb30194c53c459e4cb5c36234d69ef15f3a29f3ada563a969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-24T04:54:30Z","title_canon_sha256":"75ae8b320228bf89ac0fb91daab201c438fe24212ba2915eaf4a8c9a73f0754a"},"schema_version":"1.0","source":{"id":"1501.06004","kind":"arxiv","version":2}},"canonical_sha256":"859f2dd6c5a0aac63fc8c0a8f104583e0242d89794b7371f99a6881e928c511b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"859f2dd6c5a0aac63fc8c0a8f104583e0242d89794b7371f99a6881e928c511b","first_computed_at":"2026-05-18T00:20:27.879621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:27.879621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FLT12gEkAkabDeuEWWyMOUVKqGDnRhgC3DhDus43JMuYW7NEgJf5/WsR9SIT3c6KyhqQFdiQPd77nChTjdrsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:27.880082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e11cc78b7cda8e68bafa457ad5c338a294d2734a861f2b21025f1fc9dc13aa8","sha256:43048dc89f14ea38e967d935bdcfa8cb5c06b66e83534b05999be03197800a26"],"state_sha256":"afb71c1e4086208b86946ff696b50d37c59c7cea14dddff9326e378f16442687"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pEt3WgOgd9QQRRfBoJTu1f2EWCA9QYZ2ZuHMQZncsNETR7Zu8g8vzvHsHRZoqOUtP1no4bArsvH/+rU80scVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:53:22.823513Z","bundle_sha256":"1eef2048f4655e296414f222fcf951333ba99f259e380f0c410d82a61015b5b2"}}