{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AHYBFCUYIRYHSTEHTPOVBKTENG","short_pith_number":"pith:AHYBFCUY","canonical_record":{"source":{"id":"1509.06950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-23T12:55:46Z","cross_cats_sorted":["math.CV","math.KT","math.NT"],"title_canon_sha256":"948d7f24e85d74c1b6f1681e5e6738e298b758e4fa5943a1d319d9f6016f8dc4","abstract_canon_sha256":"bc51ff7f23a3e3a75f15b1b66d3b5a1c7ecf3e939b117f12e790faa1937ba33c"},"schema_version":"1.0"},"canonical_sha256":"01f0128a984470794c879bdd50aa64699fb0b08de0f1d697d52aab3790b88647","source":{"kind":"arxiv","id":"1509.06950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06950","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06950v1","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06950","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"AHYBFCUYIRYH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AHYBFCUYIRYHSTEH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AHYBFCUY","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AHYBFCUYIRYHSTEHTPOVBKTENG","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-23T12:55:46Z","cross_cats_sorted":["math.CV","math.KT","math.NT"],"title_canon_sha256":"948d7f24e85d74c1b6f1681e5e6738e298b758e4fa5943a1d319d9f6016f8dc4","abstract_canon_sha256":"bc51ff7f23a3e3a75f15b1b66d3b5a1c7ecf3e939b117f12e790faa1937ba33c"},"schema_version":"1.0"},"canonical_sha256":"01f0128a984470794c879bdd50aa64699fb0b08de0f1d697d52aab3790b88647","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:17.420660Z","signature_b64":"0TJ+/Hv/QyGv8F10L3fV1gF6OyMaOZz1DdJzE1Z15UKYuMYRlsq7BGOyav9QKBWY/wV/713BzPGoltg83q2tAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01f0128a984470794c879bdd50aa64699fb0b08de0f1d697d52aab3790b88647","last_reissued_at":"2026-05-18T01:32:17.419947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:17.419947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06950","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":"2026-05-18T01:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Vdqn8Ahq8qeAtR3JD+a72Qyqh1c5MoxCfjygZECgusHJa1bU3IrrLeT1U36m9y8k2kw4CLVDqOyXh4cDitICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:37:19.187969Z"},"content_sha256":"a07cf701d9846f045890782ee0e190c1c5eb719ee0cc79e80a0a24df2125d460","schema_version":"1.0","event_id":"sha256:a07cf701d9846f045890782ee0e190c1c5eb719ee0cc79e80a0a24df2125d460"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AHYBFCUYIRYHSTEHTPOVBKTENG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula, Part I: convergence theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.KT","math.NT"],"primary_cat":"math.AG","authors_text":"Kenichiro Kimura, Masaki Hanamura, Tomohide Terasoma","submitted_at":"2015-09-23T12:55:46Z","abstract_excerpt":"In this paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies allowability (or admissibility), a condition on the dimension of the intersection of the set and the pole divisor of the differential form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06950","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":"2026-05-18T01:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NcFu6qdSvqSTf4WsCC+AZc1JvCsaGaIx7ciarWUde4/VPFb4OEAHxj8uY6ao3OdvU0oI6hepr2mPITyUTNK7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:37:19.188326Z"},"content_sha256":"66998a7bb8632da49b58e74fcf0c4fc398d454e5a68a380b1e704940f5bb3735","schema_version":"1.0","event_id":"sha256:66998a7bb8632da49b58e74fcf0c4fc398d454e5a68a380b1e704940f5bb3735"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHYBFCUYIRYHSTEHTPOVBKTENG/bundle.json","state_url":"https://pith.science/pith/AHYBFCUYIRYHSTEHTPOVBKTENG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHYBFCUYIRYHSTEHTPOVBKTENG/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":"2026-06-01T18:37:19Z","links":{"resolver":"https://pith.science/pith/AHYBFCUYIRYHSTEHTPOVBKTENG","bundle":"https://pith.science/pith/AHYBFCUYIRYHSTEHTPOVBKTENG/bundle.json","state":"https://pith.science/pith/AHYBFCUYIRYHSTEHTPOVBKTENG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHYBFCUYIRYHSTEHTPOVBKTENG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AHYBFCUYIRYHSTEHTPOVBKTENG","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":"bc51ff7f23a3e3a75f15b1b66d3b5a1c7ecf3e939b117f12e790faa1937ba33c","cross_cats_sorted":["math.CV","math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-23T12:55:46Z","title_canon_sha256":"948d7f24e85d74c1b6f1681e5e6738e298b758e4fa5943a1d319d9f6016f8dc4"},"schema_version":"1.0","source":{"id":"1509.06950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06950","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06950v1","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06950","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"AHYBFCUYIRYH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AHYBFCUYIRYHSTEH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AHYBFCUY","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:66998a7bb8632da49b58e74fcf0c4fc398d454e5a68a380b1e704940f5bb3735","target":"graph","created_at":"2026-05-18T01:32:17Z","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 paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies allowability (or admissibility), a condition on the dimension of the intersection of the set and the pole divisor of the differential form.","authors_text":"Kenichiro Kimura, Masaki Hanamura, Tomohide Terasoma","cross_cats":["math.CV","math.KT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-23T12:55:46Z","title":"Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula, Part I: convergence theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06950","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:a07cf701d9846f045890782ee0e190c1c5eb719ee0cc79e80a0a24df2125d460","target":"record","created_at":"2026-05-18T01:32:17Z","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":"bc51ff7f23a3e3a75f15b1b66d3b5a1c7ecf3e939b117f12e790faa1937ba33c","cross_cats_sorted":["math.CV","math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-23T12:55:46Z","title_canon_sha256":"948d7f24e85d74c1b6f1681e5e6738e298b758e4fa5943a1d319d9f6016f8dc4"},"schema_version":"1.0","source":{"id":"1509.06950","kind":"arxiv","version":1}},"canonical_sha256":"01f0128a984470794c879bdd50aa64699fb0b08de0f1d697d52aab3790b88647","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01f0128a984470794c879bdd50aa64699fb0b08de0f1d697d52aab3790b88647","first_computed_at":"2026-05-18T01:32:17.419947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:17.419947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0TJ+/Hv/QyGv8F10L3fV1gF6OyMaOZz1DdJzE1Z15UKYuMYRlsq7BGOyav9QKBWY/wV/713BzPGoltg83q2tAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:17.420660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a07cf701d9846f045890782ee0e190c1c5eb719ee0cc79e80a0a24df2125d460","sha256:66998a7bb8632da49b58e74fcf0c4fc398d454e5a68a380b1e704940f5bb3735"],"state_sha256":"7b40bbba4c64f318f44a37e0f1fc2c4b2d423fab8b7670e3124e52815240f8d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kg4tmhyVUaVkuS05Akl8xPVCWuNprkL8Cttge1RnVAxsLwWB37POY069hsVJmi9FjgO7dIoOOHuhcyZgsQAQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:37:19.190390Z","bundle_sha256":"b245ac584365ce8130b0a08dc887a994c6cc4fa0aeb373f3b5ed62dd763aabe6"}}