{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CWODUGPEZA5Z76RMYKDFG5N5RO","short_pith_number":"pith:CWODUGPE","canonical_record":{"source":{"id":"2502.20588","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-27T23:18:07Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"3f2a5ee5a302e5c934cdea059bbd79e4057670208bb200704cc6176eb6a8b186","abstract_canon_sha256":"8b2d0601c2c039fedaf23d2302866ac742870a5ab5f727a97dbb67d798252fb7"},"schema_version":"1.0"},"canonical_sha256":"159c3a19e4c83b9ffa2cc2865375bd8ba919e3d16d0e9baade159fa8bd863572","source":{"kind":"arxiv","id":"2502.20588","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.20588","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"2502.20588v1","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.20588","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"CWODUGPEZA5Z","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"pith_short_16","alias_value":"CWODUGPEZA5Z76RM","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"pith_short_8","alias_value":"CWODUGPE","created_at":"2026-06-02T02:04:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CWODUGPEZA5Z76RMYKDFG5N5RO","target":"record","payload":{"canonical_record":{"source":{"id":"2502.20588","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-27T23:18:07Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"3f2a5ee5a302e5c934cdea059bbd79e4057670208bb200704cc6176eb6a8b186","abstract_canon_sha256":"8b2d0601c2c039fedaf23d2302866ac742870a5ab5f727a97dbb67d798252fb7"},"schema_version":"1.0"},"canonical_sha256":"159c3a19e4c83b9ffa2cc2865375bd8ba919e3d16d0e9baade159fa8bd863572","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:05.186843Z","signature_b64":"e11+uhC0cdGE5tee60lsVv+HRLidKza6ERPuarFbZasGP/GrchBjG9aMGN6Kc1mYi+E+I1MwSGyCUN3i9KNCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"159c3a19e4c83b9ffa2cc2865375bd8ba919e3d16d0e9baade159fa8bd863572","last_reissued_at":"2026-06-02T02:04:05.186310Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:05.186310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.20588","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":"2026-06-02T02:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uUSh5au5EqiGLwRVPSwjFa4yrc0+7+YKai3SHsDmu9elzHcBqlv91tHNscGxgPAJw1G0lz7QWhnoN8UEuB4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:21:00.095526Z"},"content_sha256":"6b305bd28d7d5146ea0e5f1ef93a06c7a0924315924c8baedce6357a370e2b5e","schema_version":"1.0","event_id":"sha256:6b305bd28d7d5146ea0e5f1ef93a06c7a0924315924c8baedce6357a370e2b5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CWODUGPEZA5Z76RMYKDFG5N5RO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A finite sufficient set of conditions for catalytic majorization","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Aditya Nema, Ananda G. Maity, David Elkouss, Sergii Strelchuk","submitted_at":"2025-02-27T23:18:07Z","abstract_excerpt":"The majorization relation has found numerous applications in mathematics, quantum information and resource theory, and quantum thermodynamics, where it describes the allowable transitions between two physical states. In many cases, when state vector $x$ does not majorize state vector $y$, it is nevertheless possible to find a catalyst - another vector $z$ such that $x \\otimes z$ majorizes $y \\otimes z$. Determining the feasibility of such catalytic transformation typically involves checking an infinite set of inequalities. Here, we derive a finite sufficient set of inequalities that imply cata"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20588","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/2502.20588/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":"2026-06-02T02:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOm6pMRv7BPSfZwm9KPrXP9pjzSLVmHKFhk9yyK4YMjG9ltG3qNy0U0l8ta7dDqlDyFYSwamJrZQteMjWdPBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:21:00.095909Z"},"content_sha256":"42aaa57ad3cf6ac2cff5c371dc03ac707695e85cd6b5d15fa6075d82bb75c8e7","schema_version":"1.0","event_id":"sha256:42aaa57ad3cf6ac2cff5c371dc03ac707695e85cd6b5d15fa6075d82bb75c8e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWODUGPEZA5Z76RMYKDFG5N5RO/bundle.json","state_url":"https://pith.science/pith/CWODUGPEZA5Z76RMYKDFG5N5RO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWODUGPEZA5Z76RMYKDFG5N5RO/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":"2026-06-30T17:21:00Z","links":{"resolver":"https://pith.science/pith/CWODUGPEZA5Z76RMYKDFG5N5RO","bundle":"https://pith.science/pith/CWODUGPEZA5Z76RMYKDFG5N5RO/bundle.json","state":"https://pith.science/pith/CWODUGPEZA5Z76RMYKDFG5N5RO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWODUGPEZA5Z76RMYKDFG5N5RO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CWODUGPEZA5Z76RMYKDFG5N5RO","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":"8b2d0601c2c039fedaf23d2302866ac742870a5ab5f727a97dbb67d798252fb7","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-27T23:18:07Z","title_canon_sha256":"3f2a5ee5a302e5c934cdea059bbd79e4057670208bb200704cc6176eb6a8b186"},"schema_version":"1.0","source":{"id":"2502.20588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.20588","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"2502.20588v1","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.20588","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"CWODUGPEZA5Z","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"pith_short_16","alias_value":"CWODUGPEZA5Z76RM","created_at":"2026-06-02T02:04:05Z"},{"alias_kind":"pith_short_8","alias_value":"CWODUGPE","created_at":"2026-06-02T02:04:05Z"}],"graph_snapshots":[{"event_id":"sha256:42aaa57ad3cf6ac2cff5c371dc03ac707695e85cd6b5d15fa6075d82bb75c8e7","target":"graph","created_at":"2026-06-02T02:04:05Z","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/2502.20588/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The majorization relation has found numerous applications in mathematics, quantum information and resource theory, and quantum thermodynamics, where it describes the allowable transitions between two physical states. In many cases, when state vector $x$ does not majorize state vector $y$, it is nevertheless possible to find a catalyst - another vector $z$ such that $x \\otimes z$ majorizes $y \\otimes z$. Determining the feasibility of such catalytic transformation typically involves checking an infinite set of inequalities. Here, we derive a finite sufficient set of inequalities that imply cata","authors_text":"Aditya Nema, Ananda G. Maity, David Elkouss, Sergii Strelchuk","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-27T23:18:07Z","title":"A finite sufficient set of conditions for catalytic majorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20588","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":"sha256:6b305bd28d7d5146ea0e5f1ef93a06c7a0924315924c8baedce6357a370e2b5e","target":"record","created_at":"2026-06-02T02:04:05Z","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":"8b2d0601c2c039fedaf23d2302866ac742870a5ab5f727a97dbb67d798252fb7","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-27T23:18:07Z","title_canon_sha256":"3f2a5ee5a302e5c934cdea059bbd79e4057670208bb200704cc6176eb6a8b186"},"schema_version":"1.0","source":{"id":"2502.20588","kind":"arxiv","version":1}},"canonical_sha256":"159c3a19e4c83b9ffa2cc2865375bd8ba919e3d16d0e9baade159fa8bd863572","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"159c3a19e4c83b9ffa2cc2865375bd8ba919e3d16d0e9baade159fa8bd863572","first_computed_at":"2026-06-02T02:04:05.186310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:05.186310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e11+uhC0cdGE5tee60lsVv+HRLidKza6ERPuarFbZasGP/GrchBjG9aMGN6Kc1mYi+E+I1MwSGyCUN3i9KNCCg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:05.186843Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.20588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b305bd28d7d5146ea0e5f1ef93a06c7a0924315924c8baedce6357a370e2b5e","sha256:42aaa57ad3cf6ac2cff5c371dc03ac707695e85cd6b5d15fa6075d82bb75c8e7"],"state_sha256":"b64f9e872c56c935a5121d6de688a5c155bafffa936befc1dda9dd1e8be9395b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSQrbn//UgBtIAjUIRQKm9C0POiFI9LnxHux1lXYk4sVKcfRsKpR+5XFDbzxKNQZj5imBl0LlkdtWmr7TbfADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:21:00.098230Z","bundle_sha256":"c34b2c16dbe77415542ff72cb534d2fc36976dd35fc2e9d8cdac9d3b3b0b3efc"}}