{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3ADL2FZ2FNGWXQ4RQAQ5S7OFT7","short_pith_number":"pith:3ADL2FZ2","canonical_record":{"source":{"id":"2505.23218","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-05-29T08:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"14fdbc2d9aa50fba7cbbb2217c35177dccc994eb563d61aadbef3d83c9194d3f","abstract_canon_sha256":"f3befd84deda443060379ac37e0a9dfa258a42133b7e0d65a181085296d118c1"},"schema_version":"1.0"},"canonical_sha256":"d806bd173a2b4d6bc3918021d97dc59fca2099df87bec4a7ae12846f65b7cb13","source":{"kind":"arxiv","id":"2505.23218","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23218","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23218v1","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23218","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"3ADL2FZ2FNGW","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"3ADL2FZ2FNGWXQ4R","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"3ADL2FZ2","created_at":"2026-07-05T11:11:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3ADL2FZ2FNGWXQ4RQAQ5S7OFT7","target":"record","payload":{"canonical_record":{"source":{"id":"2505.23218","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-05-29T08:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"14fdbc2d9aa50fba7cbbb2217c35177dccc994eb563d61aadbef3d83c9194d3f","abstract_canon_sha256":"f3befd84deda443060379ac37e0a9dfa258a42133b7e0d65a181085296d118c1"},"schema_version":"1.0"},"canonical_sha256":"d806bd173a2b4d6bc3918021d97dc59fca2099df87bec4a7ae12846f65b7cb13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:57.675490Z","signature_b64":"3rDACoDQeJQWe8MA72qb4Wp7N+bV/7HitjmoCPPHPZSCmifbjkGBNX+79DQFzhHru2HhkXPPJ1XSYcAKerzXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d806bd173a2b4d6bc3918021d97dc59fca2099df87bec4a7ae12846f65b7cb13","last_reissued_at":"2026-07-05T11:11:57.674923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:57.674923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.23218","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":"2026-07-05T11:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yh1gCAuzk24oNfB6uZDI8Lc4ByT+EExBGqQxKfsEGz6r9kl3tBCWjVquvbWPqapzur1xvVyX52P8h4MLz2NvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:39:44.062704Z"},"content_sha256":"9dc6658f26630ae7c334a938002e5e48cf19a66cd78137e6a8a598f600676c4c","schema_version":"1.0","event_id":"sha256:9dc6658f26630ae7c334a938002e5e48cf19a66cd78137e6a8a598f600676c4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3ADL2FZ2FNGWXQ4RQAQ5S7OFT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An application of the hit problem to the algebraic transfer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nguyen Sum","submitted_at":"2025-05-29T08:02:44Z","abstract_excerpt":"Let $P_k$ be the polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$ over the field $\\mathbb F_2$ with two elements, in $k$ variables $x_1, x_2, \\ldots , x_k$, each variable of degree 1. Denote by $GL_k$ the general linear group over $\\mathbb F_2$ which regularly acts on $P_k$. The algebra $P_k$ is a module over the mod-2 Steenrod algebra $\\mathcal A$. In 1989, Singer [22] defined the $k$-th homological algebraic transfer, which is a homomorphism $$\\varphi_k=(\\varphi_k)_m :{\\rm Tor}^{\\mathcal A}_{k,k+m} (\\mathbb F_2,\\mathbb F_2) \\to (\\mathbb F_2\\otimes_{\\mathcal A}P_k)_m^{GL_k}$$ from the ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23218","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/2505.23218/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":"2026-07-05T11:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OVlGojlu7o1VuyJwx2e36yAgbBUW7IE8P6OB/4mkmT/PeGeJGUgNO0Xu2SXPKqnYr/t5qnh1E5gVje7BjWJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:39:44.063196Z"},"content_sha256":"23dacdf3e96776e494cfa4e3cafaa9ce971e4dddbc1206b19dd1612de71b069d","schema_version":"1.0","event_id":"sha256:23dacdf3e96776e494cfa4e3cafaa9ce971e4dddbc1206b19dd1612de71b069d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7/bundle.json","state_url":"https://pith.science/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7/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":"2026-08-09T02:39:44Z","links":{"resolver":"https://pith.science/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7","bundle":"https://pith.science/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7/bundle.json","state":"https://pith.science/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ADL2FZ2FNGWXQ4RQAQ5S7OFT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3ADL2FZ2FNGWXQ4RQAQ5S7OFT7","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":"f3befd84deda443060379ac37e0a9dfa258a42133b7e0d65a181085296d118c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-05-29T08:02:44Z","title_canon_sha256":"14fdbc2d9aa50fba7cbbb2217c35177dccc994eb563d61aadbef3d83c9194d3f"},"schema_version":"1.0","source":{"id":"2505.23218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23218","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23218v1","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23218","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"3ADL2FZ2FNGW","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"3ADL2FZ2FNGWXQ4R","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"3ADL2FZ2","created_at":"2026-07-05T11:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:23dacdf3e96776e494cfa4e3cafaa9ce971e4dddbc1206b19dd1612de71b069d","target":"graph","created_at":"2026-07-05T11:11:57Z","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/2505.23218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $P_k$ be the polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$ over the field $\\mathbb F_2$ with two elements, in $k$ variables $x_1, x_2, \\ldots , x_k$, each variable of degree 1. Denote by $GL_k$ the general linear group over $\\mathbb F_2$ which regularly acts on $P_k$. The algebra $P_k$ is a module over the mod-2 Steenrod algebra $\\mathcal A$. In 1989, Singer [22] defined the $k$-th homological algebraic transfer, which is a homomorphism $$\\varphi_k=(\\varphi_k)_m :{\\rm Tor}^{\\mathcal A}_{k,k+m} (\\mathbb F_2,\\mathbb F_2) \\to (\\mathbb F_2\\otimes_{\\mathcal A}P_k)_m^{GL_k}$$ from the ho","authors_text":"Nguyen Sum","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-05-29T08:02:44Z","title":"An application of the hit problem to the algebraic transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23218","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":"sha256:9dc6658f26630ae7c334a938002e5e48cf19a66cd78137e6a8a598f600676c4c","target":"record","created_at":"2026-07-05T11:11:57Z","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":"f3befd84deda443060379ac37e0a9dfa258a42133b7e0d65a181085296d118c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-05-29T08:02:44Z","title_canon_sha256":"14fdbc2d9aa50fba7cbbb2217c35177dccc994eb563d61aadbef3d83c9194d3f"},"schema_version":"1.0","source":{"id":"2505.23218","kind":"arxiv","version":1}},"canonical_sha256":"d806bd173a2b4d6bc3918021d97dc59fca2099df87bec4a7ae12846f65b7cb13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d806bd173a2b4d6bc3918021d97dc59fca2099df87bec4a7ae12846f65b7cb13","first_computed_at":"2026-07-05T11:11:57.674923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:57.674923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rDACoDQeJQWe8MA72qb4Wp7N+bV/7HitjmoCPPHPZSCmifbjkGBNX+79DQFzhHru2HhkXPPJ1XSYcAKerzXBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:57.675490Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.23218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dc6658f26630ae7c334a938002e5e48cf19a66cd78137e6a8a598f600676c4c","sha256:23dacdf3e96776e494cfa4e3cafaa9ce971e4dddbc1206b19dd1612de71b069d"],"state_sha256":"3ac5c172f73fabd7974ddba8b9a9da3f09c3df4e06e5c78e05f075562d0ea644"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ro1Z3gwRWaRXYEwMCTduCEY28wz9wyJHLzvUzV5mF2O3wh3qIl6baonnOU3Sv96Xk9g/TUOtK2PVr1E8ZtiZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:39:44.067481Z","bundle_sha256":"02d7a811f0ffb9c93d17b623fcb45a01b0a67effbd8fd0570f173b973de86f06"}}