{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IN6IP444HGZPX63PGAA555RT6R","short_pith_number":"pith:IN6IP444","canonical_record":{"source":{"id":"2605.18983","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-18T18:04:42Z","cross_cats_sorted":[],"title_canon_sha256":"32c8807984826243b9735f25153e66193f33075ee7c402a1beb8124195032bc7","abstract_canon_sha256":"d5222c425aa7d8a833d7ae984580aa86cd7be5158399248b7aecfba0f99461ef"},"schema_version":"1.0"},"canonical_sha256":"437c87f39c39b2fbfb6f3001def633f47aa9be7ae70485cb18ed15dd7ecf35da","source":{"kind":"arxiv","id":"2605.18983","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18983","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18983v1","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18983","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"pith_short_12","alias_value":"IN6IP444HGZP","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"pith_short_16","alias_value":"IN6IP444HGZPX63P","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"pith_short_8","alias_value":"IN6IP444","created_at":"2026-05-20T00:06:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IN6IP444HGZPX63PGAA555RT6R","target":"record","payload":{"canonical_record":{"source":{"id":"2605.18983","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-18T18:04:42Z","cross_cats_sorted":[],"title_canon_sha256":"32c8807984826243b9735f25153e66193f33075ee7c402a1beb8124195032bc7","abstract_canon_sha256":"d5222c425aa7d8a833d7ae984580aa86cd7be5158399248b7aecfba0f99461ef"},"schema_version":"1.0"},"canonical_sha256":"437c87f39c39b2fbfb6f3001def633f47aa9be7ae70485cb18ed15dd7ecf35da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:40.988102Z","signature_b64":"4Fyt+vyO0zL1eMe7ZK3jWHVRuJvpGGMwSbVV1V2sNS6om8Uyj2Fdxi00AkAj2E1g0ipov8QxSCFIFWaREr0xDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"437c87f39c39b2fbfb6f3001def633f47aa9be7ae70485cb18ed15dd7ecf35da","last_reissued_at":"2026-05-20T00:06:40.987266Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:40.987266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.18983","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":"2026-05-20T00:06:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aqIJGxYh/uBi3JdBnnYoZqZZAt1YCFE2z2Szfw7aE+6cbdAeFRaES2NTnapgnGE0NI5ADuXE8N1YTguPsglOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:02:11.587711Z"},"content_sha256":"8c1961bd3b4d2d08b23a161518c7eba488c99fb01f7d6033c548bbd75d483d21","schema_version":"1.0","event_id":"sha256:8c1961bd3b4d2d08b23a161518c7eba488c99fb01f7d6033c548bbd75d483d21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IN6IP444HGZPX63PGAA555RT6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Outer Type Severi-Brauer Schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cameron Ruether","submitted_at":"2026-05-18T18:04:42Z","abstract_excerpt":"We introduce the notion of a lowered flag of $\\mathcal{O}$--modules in order to define a sheaf of flags of ideals isomorphic to the sheaf of parabolic subgroups for the general linear group $\\mathbf{GL}_{1,\\mathcal{A}}$ of an Azumaya algebra over a general scheme $S$. This notion is extended to the outer type $A_n$ case and we define a suitable sheaf of flags of ideals isomorphic to the sheaf of parabolic subgroups for a unitary group over $S$. When the group is suitably split these are related to flags of submodules in a vector bundle or in a vector bundle with hermitian form, respectively. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18983","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/2605.18983/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":"2026-05-20T00:06:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVhUKyTUhJwXQs925aB6953GwTIxBLLXeW4FEi7Pta/zPMSFf+aFOW1tiTHntzZSaTcvAsxju0Oc8hjrij0JDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:02:11.588092Z"},"content_sha256":"c0516d71bd19d382d94a1f18753d0573d2d58a0ed2e6bd54a4799bf58507de16","schema_version":"1.0","event_id":"sha256:c0516d71bd19d382d94a1f18753d0573d2d58a0ed2e6bd54a4799bf58507de16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IN6IP444HGZPX63PGAA555RT6R/bundle.json","state_url":"https://pith.science/pith/IN6IP444HGZPX63PGAA555RT6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IN6IP444HGZPX63PGAA555RT6R/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":"2026-06-04T15:02:11Z","links":{"resolver":"https://pith.science/pith/IN6IP444HGZPX63PGAA555RT6R","bundle":"https://pith.science/pith/IN6IP444HGZPX63PGAA555RT6R/bundle.json","state":"https://pith.science/pith/IN6IP444HGZPX63PGAA555RT6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IN6IP444HGZPX63PGAA555RT6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IN6IP444HGZPX63PGAA555RT6R","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":"d5222c425aa7d8a833d7ae984580aa86cd7be5158399248b7aecfba0f99461ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-18T18:04:42Z","title_canon_sha256":"32c8807984826243b9735f25153e66193f33075ee7c402a1beb8124195032bc7"},"schema_version":"1.0","source":{"id":"2605.18983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18983","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18983v1","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18983","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"pith_short_12","alias_value":"IN6IP444HGZP","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"pith_short_16","alias_value":"IN6IP444HGZPX63P","created_at":"2026-05-20T00:06:40Z"},{"alias_kind":"pith_short_8","alias_value":"IN6IP444","created_at":"2026-05-20T00:06:40Z"}],"graph_snapshots":[{"event_id":"sha256:c0516d71bd19d382d94a1f18753d0573d2d58a0ed2e6bd54a4799bf58507de16","target":"graph","created_at":"2026-05-20T00:06:40Z","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/2605.18983/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the notion of a lowered flag of $\\mathcal{O}$--modules in order to define a sheaf of flags of ideals isomorphic to the sheaf of parabolic subgroups for the general linear group $\\mathbf{GL}_{1,\\mathcal{A}}$ of an Azumaya algebra over a general scheme $S$. This notion is extended to the outer type $A_n$ case and we define a suitable sheaf of flags of ideals isomorphic to the sheaf of parabolic subgroups for a unitary group over $S$. When the group is suitably split these are related to flags of submodules in a vector bundle or in a vector bundle with hermitian form, respectively. W","authors_text":"Cameron Ruether","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-18T18:04:42Z","title":"Outer Type Severi-Brauer Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18983","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":"sha256:8c1961bd3b4d2d08b23a161518c7eba488c99fb01f7d6033c548bbd75d483d21","target":"record","created_at":"2026-05-20T00:06:40Z","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":"d5222c425aa7d8a833d7ae984580aa86cd7be5158399248b7aecfba0f99461ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-18T18:04:42Z","title_canon_sha256":"32c8807984826243b9735f25153e66193f33075ee7c402a1beb8124195032bc7"},"schema_version":"1.0","source":{"id":"2605.18983","kind":"arxiv","version":1}},"canonical_sha256":"437c87f39c39b2fbfb6f3001def633f47aa9be7ae70485cb18ed15dd7ecf35da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"437c87f39c39b2fbfb6f3001def633f47aa9be7ae70485cb18ed15dd7ecf35da","first_computed_at":"2026-05-20T00:06:40.987266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:06:40.987266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Fyt+vyO0zL1eMe7ZK3jWHVRuJvpGGMwSbVV1V2sNS6om8Uyj2Fdxi00AkAj2E1g0ipov8QxSCFIFWaREr0xDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:06:40.988102Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c1961bd3b4d2d08b23a161518c7eba488c99fb01f7d6033c548bbd75d483d21","sha256:c0516d71bd19d382d94a1f18753d0573d2d58a0ed2e6bd54a4799bf58507de16"],"state_sha256":"5606c52823353c91b527671a2b5505bebd926435d1dce224d4f9547ad6472855"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jK1dln6/uIJItydhl8ThEPmCibAeMPiebGFZLuOL3n/O5OY/OCzPmkqzuh7I3oraVt0nxO7c2fgt7cinX2Q8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:02:11.590159Z","bundle_sha256":"2a90270768c4ee2712a6f89b9a56e640ff8ed71ab1cb7a0def6011fadc3cf0a9"}}