{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PJG7I5Z3OC7S5MDEWX7MDOT7YP","short_pith_number":"pith:PJG7I5Z3","canonical_record":{"source":{"id":"2607.04875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-06T09:50:20Z","cross_cats_sorted":["cs.IR","math.CO","stat.ML"],"title_canon_sha256":"725e6824583f616cbfb277198583d9b8e0be5055639e7db56ab93bdb9697a94c","abstract_canon_sha256":"86a98b6026cebcb08f57649d8bcd1cace2bbd8af48fdc70dc60bd282ad466af2"},"schema_version":"1.0"},"canonical_sha256":"7a4df4773b70bf2eb064b5fec1ba7fc3ef825c6b015a3441b1676f79149f0965","source":{"kind":"arxiv","id":"2607.04875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04875","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04875v1","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04875","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"pith_short_12","alias_value":"PJG7I5Z3OC7S","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"pith_short_16","alias_value":"PJG7I5Z3OC7S5MDE","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"pith_short_8","alias_value":"PJG7I5Z3","created_at":"2026-07-07T02:20:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PJG7I5Z3OC7S5MDEWX7MDOT7YP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.04875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-06T09:50:20Z","cross_cats_sorted":["cs.IR","math.CO","stat.ML"],"title_canon_sha256":"725e6824583f616cbfb277198583d9b8e0be5055639e7db56ab93bdb9697a94c","abstract_canon_sha256":"86a98b6026cebcb08f57649d8bcd1cace2bbd8af48fdc70dc60bd282ad466af2"},"schema_version":"1.0"},"canonical_sha256":"7a4df4773b70bf2eb064b5fec1ba7fc3ef825c6b015a3441b1676f79149f0965","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:20:08.753623Z","signature_b64":"I2xd7rc5SbdUtLO4lLilCnlKJ31ffbsFDYb/NOeHQnuWep/5JjlGJ8BkXv1u0PBdjGtPw38yMmD2uVcmOxHFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4df4773b70bf2eb064b5fec1ba7fc3ef825c6b015a3441b1676f79149f0965","last_reissued_at":"2026-07-07T02:20:08.752813Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:20:08.752813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.04875","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":"2026-07-07T02:20:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJnwhLt4u8MQrwm3t2hv02o14uv5m9mgalURCVlnMFZCaYSvNl1L5YilJ0+AeFyuoeXMredDgYwqyOQYGY2CDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:12:54.972978Z"},"content_sha256":"dbda72961df2540286d1ec53db2f9a8582818c4137c0e18666cb3034f45d099d","schema_version":"1.0","event_id":"sha256:dbda72961df2540286d1ec53db2f9a8582818c4137c0e18666cb3034f45d099d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PJG7I5Z3OC7S5MDEWX7MDOT7YP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Entrywise Power Matrix Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IR","math.CO","stat.ML"],"primary_cat":"cs.CC","authors_text":"Arnaud Vandaele, Nicolas Gillis, Stefano Sicilia, Subhayan Saha","submitted_at":"2026-07-06T09:50:20Z","abstract_excerpt":"Given a nonnegative matrix $X$, a factorization rank $r$ and a real parameter $p$, entrywise power matrix factorization (EPMF) looks for a low-rank matrix $X_r$ such that $X = |X_r|^{\\circ p}$ (exact case) or $X \\approx |X_r|^{\\circ p}$ (approximate case), where $(\\cdot)^{\\circ p}$ denotes the component-wise exponent. EPMF includes the modulus model ($p=1$) and component-wise square factorization ($p=2$) as special cases, the latter being closely related to the square root rank. We analyze the computational complexity of the exact decision problem and the Frobenius-norm approximation problem, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04875","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/2607.04875/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":"2026-07-07T02:20:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZX/8+2QsBPtthb/jjF4idoVc/XIa8W1e/LzS3B6PPNPQZtGCrdnjG0G3UfvG+7kwDqm+/9MK+wBI3WPSU0HCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:12:54.973524Z"},"content_sha256":"5048088ace4543227e211c1b7c169b194a08101d812bf257d61660d763b0632b","schema_version":"1.0","event_id":"sha256:5048088ace4543227e211c1b7c169b194a08101d812bf257d61660d763b0632b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP/bundle.json","state_url":"https://pith.science/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP/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":"2026-08-09T09:12:54Z","links":{"resolver":"https://pith.science/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP","bundle":"https://pith.science/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP/bundle.json","state":"https://pith.science/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJG7I5Z3OC7S5MDEWX7MDOT7YP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PJG7I5Z3OC7S5MDEWX7MDOT7YP","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":"86a98b6026cebcb08f57649d8bcd1cace2bbd8af48fdc70dc60bd282ad466af2","cross_cats_sorted":["cs.IR","math.CO","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-06T09:50:20Z","title_canon_sha256":"725e6824583f616cbfb277198583d9b8e0be5055639e7db56ab93bdb9697a94c"},"schema_version":"1.0","source":{"id":"2607.04875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04875","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04875v1","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04875","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"pith_short_12","alias_value":"PJG7I5Z3OC7S","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"pith_short_16","alias_value":"PJG7I5Z3OC7S5MDE","created_at":"2026-07-07T02:20:08Z"},{"alias_kind":"pith_short_8","alias_value":"PJG7I5Z3","created_at":"2026-07-07T02:20:08Z"}],"graph_snapshots":[{"event_id":"sha256:5048088ace4543227e211c1b7c169b194a08101d812bf257d61660d763b0632b","target":"graph","created_at":"2026-07-07T02:20:08Z","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/2607.04875/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a nonnegative matrix $X$, a factorization rank $r$ and a real parameter $p$, entrywise power matrix factorization (EPMF) looks for a low-rank matrix $X_r$ such that $X = |X_r|^{\\circ p}$ (exact case) or $X \\approx |X_r|^{\\circ p}$ (approximate case), where $(\\cdot)^{\\circ p}$ denotes the component-wise exponent. EPMF includes the modulus model ($p=1$) and component-wise square factorization ($p=2$) as special cases, the latter being closely related to the square root rank. We analyze the computational complexity of the exact decision problem and the Frobenius-norm approximation problem, ","authors_text":"Arnaud Vandaele, Nicolas Gillis, Stefano Sicilia, Subhayan Saha","cross_cats":["cs.IR","math.CO","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-06T09:50:20Z","title":"On the Complexity of Entrywise Power Matrix Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04875","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:dbda72961df2540286d1ec53db2f9a8582818c4137c0e18666cb3034f45d099d","target":"record","created_at":"2026-07-07T02:20:08Z","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":"86a98b6026cebcb08f57649d8bcd1cace2bbd8af48fdc70dc60bd282ad466af2","cross_cats_sorted":["cs.IR","math.CO","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-07-06T09:50:20Z","title_canon_sha256":"725e6824583f616cbfb277198583d9b8e0be5055639e7db56ab93bdb9697a94c"},"schema_version":"1.0","source":{"id":"2607.04875","kind":"arxiv","version":1}},"canonical_sha256":"7a4df4773b70bf2eb064b5fec1ba7fc3ef825c6b015a3441b1676f79149f0965","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4df4773b70bf2eb064b5fec1ba7fc3ef825c6b015a3441b1676f79149f0965","first_computed_at":"2026-07-07T02:20:08.752813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:20:08.752813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2xd7rc5SbdUtLO4lLilCnlKJ31ffbsFDYb/NOeHQnuWep/5JjlGJ8BkXv1u0PBdjGtPw38yMmD2uVcmOxHFBA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:20:08.753623Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbda72961df2540286d1ec53db2f9a8582818c4137c0e18666cb3034f45d099d","sha256:5048088ace4543227e211c1b7c169b194a08101d812bf257d61660d763b0632b"],"state_sha256":"e7127258a99a45441875d0074029019c1718e30edfcbf6aa5289965d6ed5daef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JTqagdUj3hlqqQVyEVLOcsMyZ68GI4cZSQMvzRIWIVISlQjjes2rVS6axae9BNEeugn6OrVdPcDcILHxzTAQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:12:54.977234Z","bundle_sha256":"0b94dde2d8aa45e2957ed283d95ce71235acf1161521411b5f1c6a2922883115"}}