{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LOQ3ZZWGF2NHIXJIAWQBKEIKZN","short_pith_number":"pith:LOQ3ZZWG","canonical_record":{"source":{"id":"2403.08472","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-03-13T12:38:09Z","cross_cats_sorted":[],"title_canon_sha256":"6c66bcc834547b6f904057cea18bbe25ef1569032358778c0339c3d1754f46c0","abstract_canon_sha256":"df74098d60ae73d828d5dec3af3ef536882605d0a9871e4de4b1b9029e0741a9"},"schema_version":"1.0"},"canonical_sha256":"5ba1bce6c62e9a745d2805a015110acb5b7026ff59da4c603660f26ab72cc843","source":{"kind":"arxiv","id":"2403.08472","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.08472","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"2403.08472v3","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.08472","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"LOQ3ZZWGF2NH","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"pith_short_16","alias_value":"LOQ3ZZWGF2NHIXJI","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"pith_short_8","alias_value":"LOQ3ZZWG","created_at":"2026-07-05T11:43:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LOQ3ZZWGF2NHIXJIAWQBKEIKZN","target":"record","payload":{"canonical_record":{"source":{"id":"2403.08472","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-03-13T12:38:09Z","cross_cats_sorted":[],"title_canon_sha256":"6c66bcc834547b6f904057cea18bbe25ef1569032358778c0339c3d1754f46c0","abstract_canon_sha256":"df74098d60ae73d828d5dec3af3ef536882605d0a9871e4de4b1b9029e0741a9"},"schema_version":"1.0"},"canonical_sha256":"5ba1bce6c62e9a745d2805a015110acb5b7026ff59da4c603660f26ab72cc843","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:54.755424Z","signature_b64":"pR+QWdMXAAWNwd/XHZ4k4b+3cv0Rm5uIxdUox+maIJfbMcbAyY8TeWc+yNsqItnoTW/0Ygw8VSs9nhdzobQfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ba1bce6c62e9a745d2805a015110acb5b7026ff59da4c603660f26ab72cc843","last_reissued_at":"2026-07-05T11:43:54.754968Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:54.754968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.08472","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NS7jDqPrNMkDAQMBfW2a8+p3tx/jjyJuprWlZxbGLJgqZ7Lvhj5iM8zAk4JvRjKpzatuQZhgrF/MRtlMVRHUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:58:32.042289Z"},"content_sha256":"b246fa867f28c4356f3cb057e72f39d1e3934610c970a0c3704873caf45b43cb","schema_version":"1.0","event_id":"sha256:b246fa867f28c4356f3cb057e72f39d1e3934610c970a0c3704873caf45b43cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LOQ3ZZWGF2NHIXJIAWQBKEIKZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beilinson-Parshin adeles via solid algebraic geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christopher Brav, Grigorii Konovalov","submitted_at":"2024-03-13T12:38:09Z","abstract_excerpt":"In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson-Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for soli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.08472","kind":"arxiv","version":3},"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/2403.08472/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":"2026-07-05T11:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7f8VW4fnNdGYbRyLRrk7dFoa6yV7ipKYjejYnb+v7Y73/5EmcXIzKW558MG+WbcUYu6nvPJWKsEm/Nfp49lIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:58:32.042784Z"},"content_sha256":"ad92a8226b08a3e973e1a7926e01be8b313e5df8a4c8f896a12237aa9c5ed1ce","schema_version":"1.0","event_id":"sha256:ad92a8226b08a3e973e1a7926e01be8b313e5df8a4c8f896a12237aa9c5ed1ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN/bundle.json","state_url":"https://pith.science/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN/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":"2026-08-05T23:58:32Z","links":{"resolver":"https://pith.science/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN","bundle":"https://pith.science/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN/bundle.json","state":"https://pith.science/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOQ3ZZWGF2NHIXJIAWQBKEIKZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LOQ3ZZWGF2NHIXJIAWQBKEIKZN","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":"df74098d60ae73d828d5dec3af3ef536882605d0a9871e4de4b1b9029e0741a9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-03-13T12:38:09Z","title_canon_sha256":"6c66bcc834547b6f904057cea18bbe25ef1569032358778c0339c3d1754f46c0"},"schema_version":"1.0","source":{"id":"2403.08472","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.08472","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"2403.08472v3","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.08472","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"LOQ3ZZWGF2NH","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"pith_short_16","alias_value":"LOQ3ZZWGF2NHIXJI","created_at":"2026-07-05T11:43:54Z"},{"alias_kind":"pith_short_8","alias_value":"LOQ3ZZWG","created_at":"2026-07-05T11:43:54Z"}],"graph_snapshots":[{"event_id":"sha256:ad92a8226b08a3e973e1a7926e01be8b313e5df8a4c8f896a12237aa9c5ed1ce","target":"graph","created_at":"2026-07-05T11:43:54Z","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/2403.08472/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson-Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for soli","authors_text":"Christopher Brav, Grigorii Konovalov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-03-13T12:38:09Z","title":"Beilinson-Parshin adeles via solid algebraic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.08472","kind":"arxiv","version":3},"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:b246fa867f28c4356f3cb057e72f39d1e3934610c970a0c3704873caf45b43cb","target":"record","created_at":"2026-07-05T11:43:54Z","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":"df74098d60ae73d828d5dec3af3ef536882605d0a9871e4de4b1b9029e0741a9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-03-13T12:38:09Z","title_canon_sha256":"6c66bcc834547b6f904057cea18bbe25ef1569032358778c0339c3d1754f46c0"},"schema_version":"1.0","source":{"id":"2403.08472","kind":"arxiv","version":3}},"canonical_sha256":"5ba1bce6c62e9a745d2805a015110acb5b7026ff59da4c603660f26ab72cc843","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ba1bce6c62e9a745d2805a015110acb5b7026ff59da4c603660f26ab72cc843","first_computed_at":"2026-07-05T11:43:54.754968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:54.754968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pR+QWdMXAAWNwd/XHZ4k4b+3cv0Rm5uIxdUox+maIJfbMcbAyY8TeWc+yNsqItnoTW/0Ygw8VSs9nhdzobQfAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:54.755424Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.08472","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b246fa867f28c4356f3cb057e72f39d1e3934610c970a0c3704873caf45b43cb","sha256:ad92a8226b08a3e973e1a7926e01be8b313e5df8a4c8f896a12237aa9c5ed1ce"],"state_sha256":"098e31bbe3a96b064c3f3b4cbc7f452fafb448669a3063643ea4657b7ad197d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qiqyROViSI7fUIECwmhlMH5u17zLOe7i4uyG0sjBfLYIWJyfR2l6J/dFmcOQU4sM4vGmWbUFMf1XQFXSGkVsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T23:58:32.046532Z","bundle_sha256":"20a7e435f34f366bb1c182e46ab971cd8fc3fbcdebfd7bce3a97b0c66b9b87a2"}}