{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LVDIHE7UUGYHNU2PI3BC654A6K","short_pith_number":"pith:LVDIHE7U","canonical_record":{"source":{"id":"1705.09553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-26T12:40:55Z","cross_cats_sorted":[],"title_canon_sha256":"3309b2f671f0563a4ae603766fd2640abd0877e1c5a0a70d5adb78f050769cf3","abstract_canon_sha256":"88fba35c32903394a9c48e1538f6ddd7b3cd2828a6c1ab320724f8c172f82774"},"schema_version":"1.0"},"canonical_sha256":"5d468393f4a1b076d34f46c22f7780f2b02462a82dee114775ddbd3e9a7f6842","source":{"kind":"arxiv","id":"1705.09553","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09553","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09553v2","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09553","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"LVDIHE7UUGYH","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LVDIHE7UUGYHNU2P","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LVDIHE7U","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LVDIHE7UUGYHNU2PI3BC654A6K","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-26T12:40:55Z","cross_cats_sorted":[],"title_canon_sha256":"3309b2f671f0563a4ae603766fd2640abd0877e1c5a0a70d5adb78f050769cf3","abstract_canon_sha256":"88fba35c32903394a9c48e1538f6ddd7b3cd2828a6c1ab320724f8c172f82774"},"schema_version":"1.0"},"canonical_sha256":"5d468393f4a1b076d34f46c22f7780f2b02462a82dee114775ddbd3e9a7f6842","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:16.191836Z","signature_b64":"vYDq8aSzS4UWk6BQFQjco5tt5hmsHlFHj3UKf2kUuGRdWazhzt57Ovgd6/l6x+5r0xjGODrTutq+8hcuYkYtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d468393f4a1b076d34f46c22f7780f2b02462a82dee114775ddbd3e9a7f6842","last_reissued_at":"2026-05-18T00:22:16.191175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:16.191175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09553","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":"2026-05-18T00:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qcUz3RZfdG5boWrjEyD6wAMi4j3gpOB6soSohAur4iOWJ2hVuMIH4MrWWxy80Z2ltfArlbe1lb6GooYeXqqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:00:34.427675Z"},"content_sha256":"80daa10411b01b0e24f3c995bfb19784ea15da8247c6943bc84953756c9ced1c","schema_version":"1.0","event_id":"sha256:80daa10411b01b0e24f3c995bfb19784ea15da8247c6943bc84953756c9ced1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LVDIHE7UUGYHNU2PI3BC654A6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kato-Milne Cohomology and Polynomial Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Adam Chapman, Kelly McKinnie","submitted_at":"2017-05-26T12:40:55Z","abstract_excerpt":"Given a prime number $p$, a field $F$ with $\\operatorname{char}(F)=p$ and a positive integer $n$, we study the class-preserving modifications of Kato-Milne classes of decomposable differential forms. These modifications demonstrate a natural connection between differential forms and $p$-regular forms. A $p$-regular form is defined to be a homogeneous polynomial form of degree $p$ for which there is no nonzero point where all the order $p-1$ partial derivatives vanish simultaneously. We define a $\\widetilde C_{p,m}$ field to be a field over which every $p$-regular form of dimension greater than"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09553","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":"2026-05-18T00:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vpilAhP2ueb1cnXYTOLcYeWFWy5iL4Fxrg0Pcl/ggAeBrd4awSc/zLcQbzqllxnQotpdvB7oWQOv+z13QuYHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:00:34.428015Z"},"content_sha256":"87780189b8797713761e732342cd073359d40e3262b2b3e652d9a34f552e2574","schema_version":"1.0","event_id":"sha256:87780189b8797713761e732342cd073359d40e3262b2b3e652d9a34f552e2574"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVDIHE7UUGYHNU2PI3BC654A6K/bundle.json","state_url":"https://pith.science/pith/LVDIHE7UUGYHNU2PI3BC654A6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVDIHE7UUGYHNU2PI3BC654A6K/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":"2026-06-03T21:00:34Z","links":{"resolver":"https://pith.science/pith/LVDIHE7UUGYHNU2PI3BC654A6K","bundle":"https://pith.science/pith/LVDIHE7UUGYHNU2PI3BC654A6K/bundle.json","state":"https://pith.science/pith/LVDIHE7UUGYHNU2PI3BC654A6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVDIHE7UUGYHNU2PI3BC654A6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LVDIHE7UUGYHNU2PI3BC654A6K","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":"88fba35c32903394a9c48e1538f6ddd7b3cd2828a6c1ab320724f8c172f82774","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-26T12:40:55Z","title_canon_sha256":"3309b2f671f0563a4ae603766fd2640abd0877e1c5a0a70d5adb78f050769cf3"},"schema_version":"1.0","source":{"id":"1705.09553","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09553","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09553v2","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09553","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"LVDIHE7UUGYH","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LVDIHE7UUGYHNU2P","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LVDIHE7U","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:87780189b8797713761e732342cd073359d40e3262b2b3e652d9a34f552e2574","target":"graph","created_at":"2026-05-18T00:22:16Z","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":"Given a prime number $p$, a field $F$ with $\\operatorname{char}(F)=p$ and a positive integer $n$, we study the class-preserving modifications of Kato-Milne classes of decomposable differential forms. These modifications demonstrate a natural connection between differential forms and $p$-regular forms. A $p$-regular form is defined to be a homogeneous polynomial form of degree $p$ for which there is no nonzero point where all the order $p-1$ partial derivatives vanish simultaneously. We define a $\\widetilde C_{p,m}$ field to be a field over which every $p$-regular form of dimension greater than","authors_text":"Adam Chapman, Kelly McKinnie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-26T12:40:55Z","title":"Kato-Milne Cohomology and Polynomial Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09553","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":"sha256:80daa10411b01b0e24f3c995bfb19784ea15da8247c6943bc84953756c9ced1c","target":"record","created_at":"2026-05-18T00:22:16Z","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":"88fba35c32903394a9c48e1538f6ddd7b3cd2828a6c1ab320724f8c172f82774","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-26T12:40:55Z","title_canon_sha256":"3309b2f671f0563a4ae603766fd2640abd0877e1c5a0a70d5adb78f050769cf3"},"schema_version":"1.0","source":{"id":"1705.09553","kind":"arxiv","version":2}},"canonical_sha256":"5d468393f4a1b076d34f46c22f7780f2b02462a82dee114775ddbd3e9a7f6842","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d468393f4a1b076d34f46c22f7780f2b02462a82dee114775ddbd3e9a7f6842","first_computed_at":"2026-05-18T00:22:16.191175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:16.191175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vYDq8aSzS4UWk6BQFQjco5tt5hmsHlFHj3UKf2kUuGRdWazhzt57Ovgd6/l6x+5r0xjGODrTutq+8hcuYkYtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:16.191836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09553","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80daa10411b01b0e24f3c995bfb19784ea15da8247c6943bc84953756c9ced1c","sha256:87780189b8797713761e732342cd073359d40e3262b2b3e652d9a34f552e2574"],"state_sha256":"4659f76ed5e58d1cc6725100da9817b72e86f93b8bcca4fd0d06668a2ec6facf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"riQ9uk8+G0iv3sOBMtFd937zqjWp/FWNKTvh+7vT3avthx+ewgwOxkqnutY8im/yaCdm8NzajwZTYgu1NEFoAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:00:34.429831Z","bundle_sha256":"953e94761d470abc1416ff06013427cb53d3e94cfb2d3ee9d0730198bcac4e18"}}