{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GUOUBWRRB6KUBVCQFQE3THGEFC","short_pith_number":"pith:GUOUBWRR","canonical_record":{"source":{"id":"1012.0618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-03T01:21:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"4d86a9341353c17dc9406de8d2be743d449fd8aae450e39f28126121971abb1b","abstract_canon_sha256":"396e632babe194726dc9b532fb1a17b56f22de25532c7a67f1f9118cf585780a"},"schema_version":"1.0"},"canonical_sha256":"351d40da310f9540d4502c09b99cc428a138db430e7847651ab9c719a427ab6d","source":{"kind":"arxiv","id":"1012.0618","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0618","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0618v2","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0618","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"GUOUBWRRB6KU","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GUOUBWRRB6KUBVCQ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GUOUBWRR","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GUOUBWRRB6KUBVCQFQE3THGEFC","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-03T01:21:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"4d86a9341353c17dc9406de8d2be743d449fd8aae450e39f28126121971abb1b","abstract_canon_sha256":"396e632babe194726dc9b532fb1a17b56f22de25532c7a67f1f9118cf585780a"},"schema_version":"1.0"},"canonical_sha256":"351d40da310f9540d4502c09b99cc428a138db430e7847651ab9c719a427ab6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:22.731940Z","signature_b64":"aKHjGrn85j8ZCZZ3rCGG2webxfY2Co0XoYM2zwSt7N0fAdATm12cstLc962AVKsN9H+AuRU25eE9pAcXWZi8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"351d40da310f9540d4502c09b99cc428a138db430e7847651ab9c719a427ab6d","last_reissued_at":"2026-05-18T03:19:22.731194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:22.731194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0618","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":"2026-05-18T03:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YdGrsw2qDJVfS6jW4CQNiNC8CnMusZRSKRels44Y7NDuMy8ML7hH6UgiIUDSqN4tbj/jbXVxCgaak7owU6P2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:29:29.978685Z"},"content_sha256":"12b48f20ec66f5f04313930e194c9ffae524d7a424e7c395a92aab912dc76fc7","schema_version":"1.0","event_id":"sha256:12b48f20ec66f5f04313930e194c9ffae524d7a424e7c395a92aab912dc76fc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GUOUBWRRB6KUBVCQFQE3THGEFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Irregular Binomial $D$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Francisco-Jes\\'us Castro-Jim\\'enez, Mar\\'ia-Cruz Fern\\'andez-Fern\\'andez","submitted_at":"2010-12-03T01:21:28Z","abstract_excerpt":"We prove that a holonomic binomial $D$--module $M_A (I,\\beta)$ is regular if and only if certain associated primes of $I$ determined by the parameter vector $\\beta\\in \\CC^d$ are homogeneous. We further describe the slopes of $M_A(I,\\beta)$ along a coordinate subspace in terms of the known slopes of some related hypergeometric $D$--modules that also depend on $\\beta$. When the parameter $\\beta$ is generic, we also compute the dimension of the generic stalk of the irregularity of $M_A(I,\\beta)$ along a coordinate hyperplane and provide some remarks about the construction of its Gevrey solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0618","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":"2026-05-18T03:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v+Vk3BRLDYcrdGLCaSACDP+xDJP2QbCuVbMso+SOCZuOzasrjKAxS4EjleLyhxeLf25SFqra5QT1XQNCTvM2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:29:29.979038Z"},"content_sha256":"fe601f5b7a2b2d670df8e5ca08f17041660221742914d616252dd4e8e6b71806","schema_version":"1.0","event_id":"sha256:fe601f5b7a2b2d670df8e5ca08f17041660221742914d616252dd4e8e6b71806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUOUBWRRB6KUBVCQFQE3THGEFC/bundle.json","state_url":"https://pith.science/pith/GUOUBWRRB6KUBVCQFQE3THGEFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUOUBWRRB6KUBVCQFQE3THGEFC/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":"2026-06-24T17:29:29Z","links":{"resolver":"https://pith.science/pith/GUOUBWRRB6KUBVCQFQE3THGEFC","bundle":"https://pith.science/pith/GUOUBWRRB6KUBVCQFQE3THGEFC/bundle.json","state":"https://pith.science/pith/GUOUBWRRB6KUBVCQFQE3THGEFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUOUBWRRB6KUBVCQFQE3THGEFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GUOUBWRRB6KUBVCQFQE3THGEFC","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":"396e632babe194726dc9b532fb1a17b56f22de25532c7a67f1f9118cf585780a","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-03T01:21:28Z","title_canon_sha256":"4d86a9341353c17dc9406de8d2be743d449fd8aae450e39f28126121971abb1b"},"schema_version":"1.0","source":{"id":"1012.0618","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0618","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0618v2","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0618","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"GUOUBWRRB6KU","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GUOUBWRRB6KUBVCQ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GUOUBWRR","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:fe601f5b7a2b2d670df8e5ca08f17041660221742914d616252dd4e8e6b71806","target":"graph","created_at":"2026-05-18T03:19:22Z","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":"We prove that a holonomic binomial $D$--module $M_A (I,\\beta)$ is regular if and only if certain associated primes of $I$ determined by the parameter vector $\\beta\\in \\CC^d$ are homogeneous. We further describe the slopes of $M_A(I,\\beta)$ along a coordinate subspace in terms of the known slopes of some related hypergeometric $D$--modules that also depend on $\\beta$. When the parameter $\\beta$ is generic, we also compute the dimension of the generic stalk of the irregularity of $M_A(I,\\beta)$ along a coordinate hyperplane and provide some remarks about the construction of its Gevrey solutions.","authors_text":"Francisco-Jes\\'us Castro-Jim\\'enez, Mar\\'ia-Cruz Fern\\'andez-Fern\\'andez","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-03T01:21:28Z","title":"On Irregular Binomial $D$-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0618","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":"sha256:12b48f20ec66f5f04313930e194c9ffae524d7a424e7c395a92aab912dc76fc7","target":"record","created_at":"2026-05-18T03:19:22Z","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":"396e632babe194726dc9b532fb1a17b56f22de25532c7a67f1f9118cf585780a","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-03T01:21:28Z","title_canon_sha256":"4d86a9341353c17dc9406de8d2be743d449fd8aae450e39f28126121971abb1b"},"schema_version":"1.0","source":{"id":"1012.0618","kind":"arxiv","version":2}},"canonical_sha256":"351d40da310f9540d4502c09b99cc428a138db430e7847651ab9c719a427ab6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"351d40da310f9540d4502c09b99cc428a138db430e7847651ab9c719a427ab6d","first_computed_at":"2026-05-18T03:19:22.731194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:22.731194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKHjGrn85j8ZCZZ3rCGG2webxfY2Co0XoYM2zwSt7N0fAdATm12cstLc962AVKsN9H+AuRU25eE9pAcXWZi8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:22.731940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0618","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12b48f20ec66f5f04313930e194c9ffae524d7a424e7c395a92aab912dc76fc7","sha256:fe601f5b7a2b2d670df8e5ca08f17041660221742914d616252dd4e8e6b71806"],"state_sha256":"bef06a9c73cada1a6cf9dacc5a7eb2efdae720f511e17c4f44cabaa0d137f930"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/z9PjT3qfuSKGLF0gzAzAJInLYAvy8nA9N0BAof9q/goYrXNAhzuZ+lwcKLbV0k4rs0kuGaY0nkeGl8fr5RTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:29:29.981004Z","bundle_sha256":"88b3c5db357674fc4d5ecd52a37bf6b154d13449db625d4a3c48595257008bc8"}}