{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2QLUVGDPQONRDRNWLD7RCC2T5K","short_pith_number":"pith:2QLUVGDP","canonical_record":{"source":{"id":"1811.11302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-27T23:02:19Z","cross_cats_sorted":[],"title_canon_sha256":"186fe7316fe6629856aa209c97b631982a645c294547467b3868974cc0a2b4ae","abstract_canon_sha256":"79aa61524f35dc732881080990ef2fe5af37bf218b149eaae4faf40b7fc46ed8"},"schema_version":"1.0"},"canonical_sha256":"d4174a986f839b11c5b658ff110b53eaa45f9f15c2109fd1615327c56de31100","source":{"kind":"arxiv","id":"1811.11302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11302","created_at":"2026-05-17T23:59:44Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11302v1","created_at":"2026-05-17T23:59:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11302","created_at":"2026-05-17T23:59:44Z"},{"alias_kind":"pith_short_12","alias_value":"2QLUVGDPQONR","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QLUVGDPQONRDRNW","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QLUVGDP","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2QLUVGDPQONRDRNWLD7RCC2T5K","target":"record","payload":{"canonical_record":{"source":{"id":"1811.11302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-27T23:02:19Z","cross_cats_sorted":[],"title_canon_sha256":"186fe7316fe6629856aa209c97b631982a645c294547467b3868974cc0a2b4ae","abstract_canon_sha256":"79aa61524f35dc732881080990ef2fe5af37bf218b149eaae4faf40b7fc46ed8"},"schema_version":"1.0"},"canonical_sha256":"d4174a986f839b11c5b658ff110b53eaa45f9f15c2109fd1615327c56de31100","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:44.239889Z","signature_b64":"MJfsJurSF7M5jJJMgD7UG9CTlJ+PZM4ajYhRYoBuSae3ufsbWzpLYzhGJQDhlokuAf3aPbhHoE68UaEI1LEdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4174a986f839b11c5b658ff110b53eaa45f9f15c2109fd1615327c56de31100","last_reissued_at":"2026-05-17T23:59:44.239314Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:44.239314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.11302","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":"2026-05-17T23:59:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Iplt5aqoPASdvSOpiXPFESYD/hp/ah41QZb5ocklJpJ59LRY0Yskg463dZzH0frurVeuPKBledQeShewDJVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:12:29.968810Z"},"content_sha256":"d756c8b0c0aea3e49a1b584d8d77e46ad101d96be0d6d57626e48f2cf1fecbcd","schema_version":"1.0","event_id":"sha256:d756c8b0c0aea3e49a1b584d8d77e46ad101d96be0d6d57626e48f2cf1fecbcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2QLUVGDPQONRDRNWLD7RCC2T5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A QR Decomposition Approach to Factor Modelling: A Thesis Report","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Immanuel Manohar","submitted_at":"2018-11-27T23:02:19Z","abstract_excerpt":"An observed $K$-dimensional series $\\left\\{ y_{n}\\right\\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\\varepsilon_{n}$ is taken to relate the factors with the observation. The goal is to determine the dimension of the factors, $p$, the factor loading matrix, $Q$, and the factors $f_{n}$. Here, it is assumed that the noise co-variance is positive definite and allowed to be correlated with the factors. An augmented matrix, \\[ \\tilde{M}\\triangleq\\left[\\begin{array}{cccc} \\tilde{\\S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11302","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":"2026-05-17T23:59:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hJY9Ee2MxbFeeEzBUxFd7ETTlvxvxsHAwhHPJTrrxeMFkhVbSZebAub2gJ3CH1SclMS0YUJZhO5RmzIhauXlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:12:29.969312Z"},"content_sha256":"2e601b29f4a4b4e85c26c9e04c0de2243c4edd41e1b0eb164f4b5729d4a57e0e","schema_version":"1.0","event_id":"sha256:2e601b29f4a4b4e85c26c9e04c0de2243c4edd41e1b0eb164f4b5729d4a57e0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QLUVGDPQONRDRNWLD7RCC2T5K/bundle.json","state_url":"https://pith.science/pith/2QLUVGDPQONRDRNWLD7RCC2T5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QLUVGDPQONRDRNWLD7RCC2T5K/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":"2026-05-30T16:12:29Z","links":{"resolver":"https://pith.science/pith/2QLUVGDPQONRDRNWLD7RCC2T5K","bundle":"https://pith.science/pith/2QLUVGDPQONRDRNWLD7RCC2T5K/bundle.json","state":"https://pith.science/pith/2QLUVGDPQONRDRNWLD7RCC2T5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QLUVGDPQONRDRNWLD7RCC2T5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2QLUVGDPQONRDRNWLD7RCC2T5K","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":"79aa61524f35dc732881080990ef2fe5af37bf218b149eaae4faf40b7fc46ed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-27T23:02:19Z","title_canon_sha256":"186fe7316fe6629856aa209c97b631982a645c294547467b3868974cc0a2b4ae"},"schema_version":"1.0","source":{"id":"1811.11302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11302","created_at":"2026-05-17T23:59:44Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11302v1","created_at":"2026-05-17T23:59:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11302","created_at":"2026-05-17T23:59:44Z"},{"alias_kind":"pith_short_12","alias_value":"2QLUVGDPQONR","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QLUVGDPQONRDRNW","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QLUVGDP","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:2e601b29f4a4b4e85c26c9e04c0de2243c4edd41e1b0eb164f4b5729d4a57e0e","target":"graph","created_at":"2026-05-17T23:59:44Z","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"},"paper":{"abstract_excerpt":"An observed $K$-dimensional series $\\left\\{ y_{n}\\right\\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\\varepsilon_{n}$ is taken to relate the factors with the observation. The goal is to determine the dimension of the factors, $p$, the factor loading matrix, $Q$, and the factors $f_{n}$. Here, it is assumed that the noise co-variance is positive definite and allowed to be correlated with the factors. An augmented matrix, \\[ \\tilde{M}\\triangleq\\left[\\begin{array}{cccc} \\tilde{\\S","authors_text":"Immanuel Manohar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-27T23:02:19Z","title":"A QR Decomposition Approach to Factor Modelling: A Thesis Report"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11302","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:d756c8b0c0aea3e49a1b584d8d77e46ad101d96be0d6d57626e48f2cf1fecbcd","target":"record","created_at":"2026-05-17T23:59:44Z","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":"79aa61524f35dc732881080990ef2fe5af37bf218b149eaae4faf40b7fc46ed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-27T23:02:19Z","title_canon_sha256":"186fe7316fe6629856aa209c97b631982a645c294547467b3868974cc0a2b4ae"},"schema_version":"1.0","source":{"id":"1811.11302","kind":"arxiv","version":1}},"canonical_sha256":"d4174a986f839b11c5b658ff110b53eaa45f9f15c2109fd1615327c56de31100","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4174a986f839b11c5b658ff110b53eaa45f9f15c2109fd1615327c56de31100","first_computed_at":"2026-05-17T23:59:44.239314Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:44.239314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MJfsJurSF7M5jJJMgD7UG9CTlJ+PZM4ajYhRYoBuSae3ufsbWzpLYzhGJQDhlokuAf3aPbhHoE68UaEI1LEdAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:44.239889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d756c8b0c0aea3e49a1b584d8d77e46ad101d96be0d6d57626e48f2cf1fecbcd","sha256:2e601b29f4a4b4e85c26c9e04c0de2243c4edd41e1b0eb164f4b5729d4a57e0e"],"state_sha256":"b45d0f91282e1bf52d048940630bd7be806299ed60e7408ef5e51039bd50bdb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UvbD32z80SM2jciTvp9p/OIByzMu5w+Fo23+jvDqaU0CMBawpbw5DObTI6AN0pAe8/w0h76n3i05K0c4m40tBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:12:29.971521Z","bundle_sha256":"ccbba37507024dd119f8865700c7661db28c2d0c4f35887593a54a0409bbafa6"}}