{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OZSRTC3QIXRJTEUPRCLW6GMX4K","short_pith_number":"pith:OZSRTC3Q","canonical_record":{"source":{"id":"1805.01714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-04T11:10:26Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6cc88847d22b41457400a09b2e7c26eef861d7f052dd439b361729208d3b793f","abstract_canon_sha256":"b82dbe6f039d5806b05f2856edca69759113c508d7fe3a70f549c02684dfbce3"},"schema_version":"1.0"},"canonical_sha256":"7665198b7045e299928f88976f1997e2a0c85dc7dad446c4cf6f1bf79d3f0c22","source":{"kind":"arxiv","id":"1805.01714","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01714","created_at":"2026-05-18T00:16:46Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01714v1","created_at":"2026-05-18T00:16:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01714","created_at":"2026-05-18T00:16:46Z"},{"alias_kind":"pith_short_12","alias_value":"OZSRTC3QIXRJ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OZSRTC3QIXRJTEUP","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OZSRTC3Q","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OZSRTC3QIXRJTEUPRCLW6GMX4K","target":"record","payload":{"canonical_record":{"source":{"id":"1805.01714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-04T11:10:26Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6cc88847d22b41457400a09b2e7c26eef861d7f052dd439b361729208d3b793f","abstract_canon_sha256":"b82dbe6f039d5806b05f2856edca69759113c508d7fe3a70f549c02684dfbce3"},"schema_version":"1.0"},"canonical_sha256":"7665198b7045e299928f88976f1997e2a0c85dc7dad446c4cf6f1bf79d3f0c22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:46.938862Z","signature_b64":"Id763z8rddNpLmW2Q4/G7vutotK/BlrPA2oR+ryTvGO/BCNjq9SdZ44UxlnXDcKie44JB1Xq48L9HDtZlr3xBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7665198b7045e299928f88976f1997e2a0c85dc7dad446c4cf6f1bf79d3f0c22","last_reissued_at":"2026-05-18T00:16:46.938208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:46.938208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.01714","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":"2026-05-18T00:16:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bUf3dzrJTuDFLoZRukC2tKR6aS1ZWEeLiZjFD7PrXy7N55l0GEyJqlHUw9PjARLk1ZtdBeP1bKwcZXgWKgmGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:00:37.024768Z"},"content_sha256":"67702fd8b7904c3d9258fde3f89385fad119ea8a7abf7f53eee9f0075184230a","schema_version":"1.0","event_id":"sha256:67702fd8b7904c3d9258fde3f89385fad119ea8a7abf7f53eee9f0075184230a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OZSRTC3QIXRJTEUPRCLW6GMX4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intersection numbers of twisted cycles and cocycles for degenerate arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AG","authors_text":"Yoshiaki Goto","submitted_at":"2018-05-04T11:10:26Z","abstract_excerpt":"We study the intersection numbers defined on twisted homology or cohomology groups that are associated with hypergeometric integrals corresponding to degenerate hyperplane arrangements in the projective $k$-space. We present formulas to evaluate the intersection numbers in the case when exactly one $(k+1)$-tuple of the hyperplanes intersects at a point. As an application, we discuss the contiguity relations of hypergeometric functions in terms of the intersection numbers on twisted cohomology groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01714","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":"2026-05-18T00:16:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UvSabUfO5JJQELHbpeEedKRLo1sCHYnwhyzPSuydNhmYfWpS5zwQXW8tw22K0oB1nIXVnY+jkyI8DEnELi3/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:00:37.025109Z"},"content_sha256":"78a3727d068efab502e6df87f245b4bd92d96be302374f8dcd18fa1077d8ac44","schema_version":"1.0","event_id":"sha256:78a3727d068efab502e6df87f245b4bd92d96be302374f8dcd18fa1077d8ac44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K/bundle.json","state_url":"https://pith.science/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K/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":"2026-06-23T13:00:37Z","links":{"resolver":"https://pith.science/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K","bundle":"https://pith.science/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K/bundle.json","state":"https://pith.science/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZSRTC3QIXRJTEUPRCLW6GMX4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OZSRTC3QIXRJTEUPRCLW6GMX4K","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":"b82dbe6f039d5806b05f2856edca69759113c508d7fe3a70f549c02684dfbce3","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-04T11:10:26Z","title_canon_sha256":"6cc88847d22b41457400a09b2e7c26eef861d7f052dd439b361729208d3b793f"},"schema_version":"1.0","source":{"id":"1805.01714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01714","created_at":"2026-05-18T00:16:46Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01714v1","created_at":"2026-05-18T00:16:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01714","created_at":"2026-05-18T00:16:46Z"},{"alias_kind":"pith_short_12","alias_value":"OZSRTC3QIXRJ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OZSRTC3QIXRJTEUP","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OZSRTC3Q","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:78a3727d068efab502e6df87f245b4bd92d96be302374f8dcd18fa1077d8ac44","target":"graph","created_at":"2026-05-18T00:16:46Z","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":"We study the intersection numbers defined on twisted homology or cohomology groups that are associated with hypergeometric integrals corresponding to degenerate hyperplane arrangements in the projective $k$-space. We present formulas to evaluate the intersection numbers in the case when exactly one $(k+1)$-tuple of the hyperplanes intersects at a point. As an application, we discuss the contiguity relations of hypergeometric functions in terms of the intersection numbers on twisted cohomology groups.","authors_text":"Yoshiaki Goto","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-04T11:10:26Z","title":"Intersection numbers of twisted cycles and cocycles for degenerate arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01714","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":"sha256:67702fd8b7904c3d9258fde3f89385fad119ea8a7abf7f53eee9f0075184230a","target":"record","created_at":"2026-05-18T00:16:46Z","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":"b82dbe6f039d5806b05f2856edca69759113c508d7fe3a70f549c02684dfbce3","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-04T11:10:26Z","title_canon_sha256":"6cc88847d22b41457400a09b2e7c26eef861d7f052dd439b361729208d3b793f"},"schema_version":"1.0","source":{"id":"1805.01714","kind":"arxiv","version":1}},"canonical_sha256":"7665198b7045e299928f88976f1997e2a0c85dc7dad446c4cf6f1bf79d3f0c22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7665198b7045e299928f88976f1997e2a0c85dc7dad446c4cf6f1bf79d3f0c22","first_computed_at":"2026-05-18T00:16:46.938208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:46.938208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Id763z8rddNpLmW2Q4/G7vutotK/BlrPA2oR+ryTvGO/BCNjq9SdZ44UxlnXDcKie44JB1Xq48L9HDtZlr3xBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:46.938862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67702fd8b7904c3d9258fde3f89385fad119ea8a7abf7f53eee9f0075184230a","sha256:78a3727d068efab502e6df87f245b4bd92d96be302374f8dcd18fa1077d8ac44"],"state_sha256":"ee93f51d092edbc757974f37c97a81e8e46106c7cc0d40129bad7ea603a1f964"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BdvLsw4K17ob8BzawSkRAGrpPTR/I4s/Ot8wqYavzQ4qJAkkG/X8EQoelOElt7MdPvdJ85MYsYj4HiiNmKKtDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:00:37.027580Z","bundle_sha256":"bad818adc09022f520949f0404ef178435ded38d744f0b326a0d98b605ca09e5"}}