{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3A2PHZ4E4RTI4QTWXQST2LQZKL","short_pith_number":"pith:3A2PHZ4E","canonical_record":{"source":{"id":"1110.0162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-02T09:15:25Z","cross_cats_sorted":[],"title_canon_sha256":"ef65612c40c982ae1f9b3c69d8871d04b52ebf8cd57388df680fe2a58f667d14","abstract_canon_sha256":"f4a244f1822ec61a2b7326f3ec267e187fcdef536647c42c4f6217016c0b4f5b"},"schema_version":"1.0"},"canonical_sha256":"d834f3e784e4668e4276bc253d2e1952f09ad981c2e6d71b18763b0bf8d416d0","source":{"kind":"arxiv","id":"1110.0162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0162","created_at":"2026-05-18T03:36:46Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0162v1","created_at":"2026-05-18T03:36:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0162","created_at":"2026-05-18T03:36:46Z"},{"alias_kind":"pith_short_12","alias_value":"3A2PHZ4E4RTI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3A2PHZ4E4RTI4QTW","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3A2PHZ4E","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3A2PHZ4E4RTI4QTWXQST2LQZKL","target":"record","payload":{"canonical_record":{"source":{"id":"1110.0162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-02T09:15:25Z","cross_cats_sorted":[],"title_canon_sha256":"ef65612c40c982ae1f9b3c69d8871d04b52ebf8cd57388df680fe2a58f667d14","abstract_canon_sha256":"f4a244f1822ec61a2b7326f3ec267e187fcdef536647c42c4f6217016c0b4f5b"},"schema_version":"1.0"},"canonical_sha256":"d834f3e784e4668e4276bc253d2e1952f09ad981c2e6d71b18763b0bf8d416d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:46.661990Z","signature_b64":"FuD23LnWeYEJLDvut07rB0fy25HwL1SslodLYy5owb4Mwtun797vKFiRP8GbJIT2TVFJng46M9osMpeaa/t7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d834f3e784e4668e4276bc253d2e1952f09ad981c2e6d71b18763b0bf8d416d0","last_reissued_at":"2026-05-18T03:36:46.661333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:46.661333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.0162","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":"2026-05-18T03:36:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rWvnlQCkGXcs3v+ViARUntszAURm1WJVoSBiDcAVJm6TjT81j8bCf6csZSvjMSs/V8T5mq++YXklwHzMrogkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:04:35.106661Z"},"content_sha256":"7898d976b9ba099dedc7131e11aa6d17126ea72bc4b0ec00aeaee7eaaa2e0406","schema_version":"1.0","event_id":"sha256:7898d976b9ba099dedc7131e11aa6d17126ea72bc4b0ec00aeaee7eaaa2e0406"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3A2PHZ4E4RTI4QTWXQST2LQZKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On computation of the characteristic polynomials of the discriminantal arrangements and the arrangements generated by generic points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akimichi Takemura, Yasuhide Numata","submitted_at":"2011-10-02T09:15:25Z","abstract_excerpt":"In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the discriminantal arrangement with the parameter (n,k) is isomorphic to the intersection lattice of the hyperplane arrangement generated by n generic points in the d-dimensional vector space where d=n-k-1. The combinatorics of the discriminantal arrangements is very hard, except for the special cases of the Boolean arrangements (k=0) and the braid arrangements (k=1). We re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0162","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":""},"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":"2026-05-18T03:36:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mJ0SyOXIp51WFo+r5al3JVpq5iU9AelBZorhxEKvfI1yh3hT8owR7xAzvy1EfJ5mDff3Dl0o1zhwGqyMO5DrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:04:35.107371Z"},"content_sha256":"76547e1036318f518b2ecb84a13ecd360985d9b7e46b6dba919ae7ea3fc7f3aa","schema_version":"1.0","event_id":"sha256:76547e1036318f518b2ecb84a13ecd360985d9b7e46b6dba919ae7ea3fc7f3aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL/bundle.json","state_url":"https://pith.science/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL/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":"2026-05-27T13:04:35Z","links":{"resolver":"https://pith.science/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL","bundle":"https://pith.science/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL/bundle.json","state":"https://pith.science/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3A2PHZ4E4RTI4QTWXQST2LQZKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3A2PHZ4E4RTI4QTWXQST2LQZKL","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":"f4a244f1822ec61a2b7326f3ec267e187fcdef536647c42c4f6217016c0b4f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-02T09:15:25Z","title_canon_sha256":"ef65612c40c982ae1f9b3c69d8871d04b52ebf8cd57388df680fe2a58f667d14"},"schema_version":"1.0","source":{"id":"1110.0162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0162","created_at":"2026-05-18T03:36:46Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0162v1","created_at":"2026-05-18T03:36:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0162","created_at":"2026-05-18T03:36:46Z"},{"alias_kind":"pith_short_12","alias_value":"3A2PHZ4E4RTI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3A2PHZ4E4RTI4QTW","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3A2PHZ4E","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:76547e1036318f518b2ecb84a13ecd360985d9b7e46b6dba919ae7ea3fc7f3aa","target":"graph","created_at":"2026-05-18T03:36:46Z","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":"In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the discriminantal arrangement with the parameter (n,k) is isomorphic to the intersection lattice of the hyperplane arrangement generated by n generic points in the d-dimensional vector space where d=n-k-1. The combinatorics of the discriminantal arrangements is very hard, except for the special cases of the Boolean arrangements (k=0) and the braid arrangements (k=1). We re","authors_text":"Akimichi Takemura, Yasuhide Numata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-02T09:15:25Z","title":"On computation of the characteristic polynomials of the discriminantal arrangements and the arrangements generated by generic points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0162","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":"sha256:7898d976b9ba099dedc7131e11aa6d17126ea72bc4b0ec00aeaee7eaaa2e0406","target":"record","created_at":"2026-05-18T03:36:46Z","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":"f4a244f1822ec61a2b7326f3ec267e187fcdef536647c42c4f6217016c0b4f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-02T09:15:25Z","title_canon_sha256":"ef65612c40c982ae1f9b3c69d8871d04b52ebf8cd57388df680fe2a58f667d14"},"schema_version":"1.0","source":{"id":"1110.0162","kind":"arxiv","version":1}},"canonical_sha256":"d834f3e784e4668e4276bc253d2e1952f09ad981c2e6d71b18763b0bf8d416d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d834f3e784e4668e4276bc253d2e1952f09ad981c2e6d71b18763b0bf8d416d0","first_computed_at":"2026-05-18T03:36:46.661333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:46.661333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuD23LnWeYEJLDvut07rB0fy25HwL1SslodLYy5owb4Mwtun797vKFiRP8GbJIT2TVFJng46M9osMpeaa/t7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:46.661990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7898d976b9ba099dedc7131e11aa6d17126ea72bc4b0ec00aeaee7eaaa2e0406","sha256:76547e1036318f518b2ecb84a13ecd360985d9b7e46b6dba919ae7ea3fc7f3aa"],"state_sha256":"1a90aa5b4fb9171ac8f84494da1a3b932525f55e42bc2b8302fb29b3cc543ff0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Uu0mLBL0gDRHYzV550dg8I9gIV/A933QeU4FO8tUCS52EDUEtzoLhSoQEZDZwgFGEMxFJOTy7rkCFIRauL/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:04:35.111211Z","bundle_sha256":"90f6e86f23cbf7c437ca42de5303f6f39d0496ebb962b2f8b3cc201a1a2e7365"}}