{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5I7HJNQYCFXEP7KLFQMDOBMUUQ","short_pith_number":"pith:5I7HJNQY","canonical_record":{"source":{"id":"1007.4225","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-23T22:23:28Z","cross_cats_sorted":["math.AC","math.CO"],"title_canon_sha256":"b937d444ca5e09435bace5c25ed7632e9feda15e976b96eacaf3c939efc6735b","abstract_canon_sha256":"327ee4cd2586a4543c371010493f31f226dacf22fe0b1decb51411a268a461de"},"schema_version":"1.0"},"canonical_sha256":"ea3e74b618116e47fd4b2c18370594a42c89af81de90b7deadf170a52ed43a59","source":{"kind":"arxiv","id":"1007.4225","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4225","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4225v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4225","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"5I7HJNQYCFXE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5I7HJNQYCFXEP7KL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5I7HJNQY","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5I7HJNQYCFXEP7KLFQMDOBMUUQ","target":"record","payload":{"canonical_record":{"source":{"id":"1007.4225","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-23T22:23:28Z","cross_cats_sorted":["math.AC","math.CO"],"title_canon_sha256":"b937d444ca5e09435bace5c25ed7632e9feda15e976b96eacaf3c939efc6735b","abstract_canon_sha256":"327ee4cd2586a4543c371010493f31f226dacf22fe0b1decb51411a268a461de"},"schema_version":"1.0"},"canonical_sha256":"ea3e74b618116e47fd4b2c18370594a42c89af81de90b7deadf170a52ed43a59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:25.335192Z","signature_b64":"rR0buzn5ddVjFeIKc/c0GcL0KqgHGw8RVunKXIob+rmDAz4W1IFsz9vMd8m+Ao1U+DdXidhB7LmHh2HZkjEtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea3e74b618116e47fd4b2c18370594a42c89af81de90b7deadf170a52ed43a59","last_reissued_at":"2026-05-18T04:02:25.334733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:25.334733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.4225","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1r/MpaOQJuIkgOFLg9PorTsgYboJ2q6GYQh/lcqaOQ2UT1/bBoDPit9pJqpZjtvQq+491nwS/Nw2p1flwlZqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:32:18.498517Z"},"content_sha256":"0beb0680fa9e01e535c40b92c9b2749f883a43032dc59da7177324890a4ce465","schema_version":"1.0","event_id":"sha256:0beb0680fa9e01e535c40b92c9b2749f883a43032dc59da7177324890a4ce465"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5I7HJNQYCFXEP7KLFQMDOBMUUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nilsson solutions for irregular A-hypergeometric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Alicia Dickenstein, Federico Nicol\\'as Mart\\'inez, Laura Felicia Matusevich","submitted_at":"2010-07-23T22:23:28Z","abstract_excerpt":"We study the solutions of irregular A-hypergeometric systems that are constructed from Gr\\\"obner degenerations with respect to generic positive weight vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1,...,1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of complex n-space. Our results are more explicit when the parameters are generic or when the solutions studied a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4225","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s27Yb2F97i6EIsmZz0TiRbOWIQRZjz9O9CSvpO/Wh6Uyv/8v92puGfSoYbToUllVISfpPdhmu14tRmwUeKL6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:32:18.499161Z"},"content_sha256":"ad9146b553183df33173b97e0920d1208588127a0189cf5e9054163fef64d8cc","schema_version":"1.0","event_id":"sha256:ad9146b553183df33173b97e0920d1208588127a0189cf5e9054163fef64d8cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ/bundle.json","state_url":"https://pith.science/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ/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":"2026-05-23T03:32:18Z","links":{"resolver":"https://pith.science/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ","bundle":"https://pith.science/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ/bundle.json","state":"https://pith.science/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5I7HJNQYCFXEP7KLFQMDOBMUUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5I7HJNQYCFXEP7KLFQMDOBMUUQ","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":"327ee4cd2586a4543c371010493f31f226dacf22fe0b1decb51411a268a461de","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-23T22:23:28Z","title_canon_sha256":"b937d444ca5e09435bace5c25ed7632e9feda15e976b96eacaf3c939efc6735b"},"schema_version":"1.0","source":{"id":"1007.4225","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4225","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4225v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4225","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"5I7HJNQYCFXE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5I7HJNQYCFXEP7KL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5I7HJNQY","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ad9146b553183df33173b97e0920d1208588127a0189cf5e9054163fef64d8cc","target":"graph","created_at":"2026-05-18T04:02:25Z","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 study the solutions of irregular A-hypergeometric systems that are constructed from Gr\\\"obner degenerations with respect to generic positive weight vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1,...,1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of complex n-space. Our results are more explicit when the parameters are generic or when the solutions studied a","authors_text":"Alicia Dickenstein, Federico Nicol\\'as Mart\\'inez, Laura Felicia Matusevich","cross_cats":["math.AC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-23T22:23:28Z","title":"Nilsson solutions for irregular A-hypergeometric systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4225","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":"sha256:0beb0680fa9e01e535c40b92c9b2749f883a43032dc59da7177324890a4ce465","target":"record","created_at":"2026-05-18T04:02:25Z","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":"327ee4cd2586a4543c371010493f31f226dacf22fe0b1decb51411a268a461de","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-23T22:23:28Z","title_canon_sha256":"b937d444ca5e09435bace5c25ed7632e9feda15e976b96eacaf3c939efc6735b"},"schema_version":"1.0","source":{"id":"1007.4225","kind":"arxiv","version":2}},"canonical_sha256":"ea3e74b618116e47fd4b2c18370594a42c89af81de90b7deadf170a52ed43a59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea3e74b618116e47fd4b2c18370594a42c89af81de90b7deadf170a52ed43a59","first_computed_at":"2026-05-18T04:02:25.334733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:25.334733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rR0buzn5ddVjFeIKc/c0GcL0KqgHGw8RVunKXIob+rmDAz4W1IFsz9vMd8m+Ao1U+DdXidhB7LmHh2HZkjEtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:25.335192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4225","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0beb0680fa9e01e535c40b92c9b2749f883a43032dc59da7177324890a4ce465","sha256:ad9146b553183df33173b97e0920d1208588127a0189cf5e9054163fef64d8cc"],"state_sha256":"7a9c3c8ac60c924148e6bcecee89c9241acbfe2b6babe8f0fe6bb4e3536a537e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjckuJV8gC7Ygq0pUUdikm/QzIU+VHefvDv0PLyQ8wKuFuKiVh2hlSLAHxfXtLjRDalojkHDMPnlYAM/JJX9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:32:18.503165Z","bundle_sha256":"da6b1668b33f8efa925508c347f7ad1ce33e1e4759d906b58208906f4660f199"}}