{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6TKYOGWFFBBIYR6BVK6O5SWWRB","short_pith_number":"pith:6TKYOGWF","canonical_record":{"source":{"id":"1308.5901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-27T15:38:40Z","cross_cats_sorted":["math.AC","math.CA"],"title_canon_sha256":"43d1478dbbf407d290f13eebed802af6aa8b2a52c0938253e9d4afdb5e3262a3","abstract_canon_sha256":"b64c89ac531c2c2957ce8f1869bb5e9c26294ad31cfe11facbe8285656c71baa"},"schema_version":"1.0"},"canonical_sha256":"f4d5871ac528428c47c1aabceecad6887ebcb988982765e2c8494b20cd3f6f69","source":{"kind":"arxiv","id":"1308.5901","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5901","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5901v2","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5901","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"6TKYOGWFFBBI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6TKYOGWFFBBIYR6B","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6TKYOGWF","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6TKYOGWFFBBIYR6BVK6O5SWWRB","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-27T15:38:40Z","cross_cats_sorted":["math.AC","math.CA"],"title_canon_sha256":"43d1478dbbf407d290f13eebed802af6aa8b2a52c0938253e9d4afdb5e3262a3","abstract_canon_sha256":"b64c89ac531c2c2957ce8f1869bb5e9c26294ad31cfe11facbe8285656c71baa"},"schema_version":"1.0"},"canonical_sha256":"f4d5871ac528428c47c1aabceecad6887ebcb988982765e2c8494b20cd3f6f69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.372132Z","signature_b64":"sFGrvSRbm0ySQ64gsJmczwVRpRmW/2cbjyqgdZ7uMPynv6287KDywAW0gzc2YG8hKhpgCFx0SPI4IpfliKMhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4d5871ac528428c47c1aabceecad6887ebcb988982765e2c8494b20cd3f6f69","last_reissued_at":"2026-05-18T00:13:38.371600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.371600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5901","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":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LX3NL6rsn4w0onb61v1Dg3zIHxvQtD5vq92gEwtpeWrdHMod7181ikIMVgbmwPCH21OoMAoG6DQ6Rv1WIJjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:40:01.687133Z"},"content_sha256":"efc9d741b3bc875c6a1ddfaadecffd5911a7219c5fc628d1290f53349d902f58","schema_version":"1.0","event_id":"sha256:efc9d741b3bc875c6a1ddfaadecffd5911a7219c5fc628d1290f53349d902f58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6TKYOGWFFBBIYR6BVK6O5SWWRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Torus equivariant D-modules and hypergeometric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CA"],"primary_cat":"math.AG","authors_text":"Christine Berkesch, Laura Felicia Matusevich, Uli Walther","submitted_at":"2013-08-27T15:38:40Z","abstract_excerpt":"We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant D-modules and show that it preserves key properties, such as holonomicity, regularity, and reducibility of monodromy representation. We also examine its effect on solutions, characteristic varieties, and singular loci. When applied to certain binomial D-modules, our functor produces saturations of the classical hypergeometric differential equations, a fact that s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5901","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":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0xAMdPsZAcakQ/RV6O5ARlr8saQWavNLg/nZLwh8IguhONB7uqYPDtvc0434gqgmH8LpyIVQk3xlkHhAT9h6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:40:01.687506Z"},"content_sha256":"23a2f5b4bef5c84e71c227927474dd5594b103b1dad53a9f7bb386455193827a","schema_version":"1.0","event_id":"sha256:23a2f5b4bef5c84e71c227927474dd5594b103b1dad53a9f7bb386455193827a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB/bundle.json","state_url":"https://pith.science/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB/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":"2026-05-22T20:40:01Z","links":{"resolver":"https://pith.science/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB","bundle":"https://pith.science/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB/bundle.json","state":"https://pith.science/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TKYOGWFFBBIYR6BVK6O5SWWRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6TKYOGWFFBBIYR6BVK6O5SWWRB","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":"b64c89ac531c2c2957ce8f1869bb5e9c26294ad31cfe11facbe8285656c71baa","cross_cats_sorted":["math.AC","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-27T15:38:40Z","title_canon_sha256":"43d1478dbbf407d290f13eebed802af6aa8b2a52c0938253e9d4afdb5e3262a3"},"schema_version":"1.0","source":{"id":"1308.5901","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5901","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5901v2","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5901","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"6TKYOGWFFBBI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6TKYOGWFFBBIYR6B","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6TKYOGWF","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:23a2f5b4bef5c84e71c227927474dd5594b103b1dad53a9f7bb386455193827a","target":"graph","created_at":"2026-05-18T00:13:38Z","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 formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant D-modules and show that it preserves key properties, such as holonomicity, regularity, and reducibility of monodromy representation. We also examine its effect on solutions, characteristic varieties, and singular loci. When applied to certain binomial D-modules, our functor produces saturations of the classical hypergeometric differential equations, a fact that s","authors_text":"Christine Berkesch, Laura Felicia Matusevich, Uli Walther","cross_cats":["math.AC","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-27T15:38:40Z","title":"Torus equivariant D-modules and hypergeometric systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5901","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:efc9d741b3bc875c6a1ddfaadecffd5911a7219c5fc628d1290f53349d902f58","target":"record","created_at":"2026-05-18T00:13:38Z","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":"b64c89ac531c2c2957ce8f1869bb5e9c26294ad31cfe11facbe8285656c71baa","cross_cats_sorted":["math.AC","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-27T15:38:40Z","title_canon_sha256":"43d1478dbbf407d290f13eebed802af6aa8b2a52c0938253e9d4afdb5e3262a3"},"schema_version":"1.0","source":{"id":"1308.5901","kind":"arxiv","version":2}},"canonical_sha256":"f4d5871ac528428c47c1aabceecad6887ebcb988982765e2c8494b20cd3f6f69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4d5871ac528428c47c1aabceecad6887ebcb988982765e2c8494b20cd3f6f69","first_computed_at":"2026-05-18T00:13:38.371600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:38.371600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sFGrvSRbm0ySQ64gsJmczwVRpRmW/2cbjyqgdZ7uMPynv6287KDywAW0gzc2YG8hKhpgCFx0SPI4IpfliKMhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:38.372132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5901","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efc9d741b3bc875c6a1ddfaadecffd5911a7219c5fc628d1290f53349d902f58","sha256:23a2f5b4bef5c84e71c227927474dd5594b103b1dad53a9f7bb386455193827a"],"state_sha256":"a0bcd404cda1d2d25d28c76fbd56c00a043f96bee6d3be3be9b87efed984a65c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5l+kxIGL3kkBgMp9ZRLC9mk5wwmxZLfuW/88WUqx+Q3yBp4csFYoI5Lw+Wv2i5Jc7CTENiASGJnbwP8iRvsoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T20:40:01.689621Z","bundle_sha256":"f6ee986c156fb260905a1f16193a60c6eac0b10f7c9d7eedd160f64242f83f3c"}}