{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GTJELFTQNQCW7DC2BU5OJKTWL6","short_pith_number":"pith:GTJELFTQ","canonical_record":{"source":{"id":"1505.03970","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-15T07:07:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"bdfbd2097c770c4e4b7f646b784c7c1bfa5569671c21100afdf0a27967f42df2","abstract_canon_sha256":"f6da13f42730446e299f172162aee093841ffaf8059c4ac2174ee304aebc5cbd"},"schema_version":"1.0"},"canonical_sha256":"34d24596706c056f8c5a0d3ae4aa765fa241056678f05a6dd7c72e61c1e04655","source":{"kind":"arxiv","id":"1505.03970","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03970","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03970v2","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03970","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"GTJELFTQNQCW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GTJELFTQNQCW7DC2","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GTJELFTQ","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GTJELFTQNQCW7DC2BU5OJKTWL6","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03970","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-15T07:07:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"bdfbd2097c770c4e4b7f646b784c7c1bfa5569671c21100afdf0a27967f42df2","abstract_canon_sha256":"f6da13f42730446e299f172162aee093841ffaf8059c4ac2174ee304aebc5cbd"},"schema_version":"1.0"},"canonical_sha256":"34d24596706c056f8c5a0d3ae4aa765fa241056678f05a6dd7c72e61c1e04655","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:36.742754Z","signature_b64":"q0m+orSxc7ArYFoEvwoXav6FzSpAp6XhnojLvVFXibeofltRrezHKb+8rUaqofWg3BvHyhK7OaLV3DCIg+f6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34d24596706c056f8c5a0d3ae4aa765fa241056678f05a6dd7c72e61c1e04655","last_reissued_at":"2026-05-18T00:38:36.742329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:36.742329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03970","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":"2026-05-18T00:38:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7l0p+XUpVpxhWe1zDXNQkr4pOpCKcPgzOMOx9KdOEAgdfhnGZVCtttZ/6ZaMv+waELfB7r3B7iN+kj9+7iyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:37:08.268448Z"},"content_sha256":"f545fbbde80d317e0b5e2061a3b89f0d2a7801113c1c82b8f2b68304c35fcc73","schema_version":"1.0","event_id":"sha256:f545fbbde80d317e0b5e2061a3b89f0d2a7801113c1c82b8f2b68304c35fcc73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GTJELFTQNQCW7DC2BU5OJKTWL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$C^1$-triangulations of semialgebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Masahiro Shiota, Toru Ohmoto","submitted_at":"2015-05-15T07:07:32Z","abstract_excerpt":"We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is $C^1$ differentiable. As an application, we give a straightforward definition of the integration $\\int_X \\omega$ over a compact semialgebraic subset $X$ of a differential form $\\omega$ on an ambient algebraic manifold, that provides a significant simplification of the theory of semialgebraic singular chains and integrations. Our results hold over every (possibly non-archimedian) real closed field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03970","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":"2026-05-18T00:38:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7VUEbhf8qHKuLXx6fq/qQSRAr+H0Ifj2LyZwhQKLHzAIAYaDOoAxCXeGkZCOdb4JbyZsF9xCIW64UUsAXQ57Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:37:08.268801Z"},"content_sha256":"abc8aa5c47e8cde37bc55d1674ee79d1f60f17be7bb1caeefb7c78fcae5c26f7","schema_version":"1.0","event_id":"sha256:abc8aa5c47e8cde37bc55d1674ee79d1f60f17be7bb1caeefb7c78fcae5c26f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTJELFTQNQCW7DC2BU5OJKTWL6/bundle.json","state_url":"https://pith.science/pith/GTJELFTQNQCW7DC2BU5OJKTWL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTJELFTQNQCW7DC2BU5OJKTWL6/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":"2026-06-04T23:37:08Z","links":{"resolver":"https://pith.science/pith/GTJELFTQNQCW7DC2BU5OJKTWL6","bundle":"https://pith.science/pith/GTJELFTQNQCW7DC2BU5OJKTWL6/bundle.json","state":"https://pith.science/pith/GTJELFTQNQCW7DC2BU5OJKTWL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTJELFTQNQCW7DC2BU5OJKTWL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GTJELFTQNQCW7DC2BU5OJKTWL6","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":"f6da13f42730446e299f172162aee093841ffaf8059c4ac2174ee304aebc5cbd","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-15T07:07:32Z","title_canon_sha256":"bdfbd2097c770c4e4b7f646b784c7c1bfa5569671c21100afdf0a27967f42df2"},"schema_version":"1.0","source":{"id":"1505.03970","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03970","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03970v2","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03970","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"GTJELFTQNQCW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GTJELFTQNQCW7DC2","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GTJELFTQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:abc8aa5c47e8cde37bc55d1674ee79d1f60f17be7bb1caeefb7c78fcae5c26f7","target":"graph","created_at":"2026-05-18T00:38:36Z","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 show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is $C^1$ differentiable. As an application, we give a straightforward definition of the integration $\\int_X \\omega$ over a compact semialgebraic subset $X$ of a differential form $\\omega$ on an ambient algebraic manifold, that provides a significant simplification of the theory of semialgebraic singular chains and integrations. Our results hold over every (possibly non-archimedian) real closed field.","authors_text":"Masahiro Shiota, Toru Ohmoto","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-15T07:07:32Z","title":"$C^1$-triangulations of semialgebraic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03970","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:f545fbbde80d317e0b5e2061a3b89f0d2a7801113c1c82b8f2b68304c35fcc73","target":"record","created_at":"2026-05-18T00:38:36Z","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":"f6da13f42730446e299f172162aee093841ffaf8059c4ac2174ee304aebc5cbd","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-15T07:07:32Z","title_canon_sha256":"bdfbd2097c770c4e4b7f646b784c7c1bfa5569671c21100afdf0a27967f42df2"},"schema_version":"1.0","source":{"id":"1505.03970","kind":"arxiv","version":2}},"canonical_sha256":"34d24596706c056f8c5a0d3ae4aa765fa241056678f05a6dd7c72e61c1e04655","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34d24596706c056f8c5a0d3ae4aa765fa241056678f05a6dd7c72e61c1e04655","first_computed_at":"2026-05-18T00:38:36.742329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:36.742329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q0m+orSxc7ArYFoEvwoXav6FzSpAp6XhnojLvVFXibeofltRrezHKb+8rUaqofWg3BvHyhK7OaLV3DCIg+f6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:36.742754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03970","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f545fbbde80d317e0b5e2061a3b89f0d2a7801113c1c82b8f2b68304c35fcc73","sha256:abc8aa5c47e8cde37bc55d1674ee79d1f60f17be7bb1caeefb7c78fcae5c26f7"],"state_sha256":"b8efb05eacb9858b0752e0ea9dd0af7a8c61519993fb70edb1e8978a020982b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+j2i+uPGS6PX1sDbvp6HIQ4GiG/7N6cVJJ7/Ij6h8rrwERvmBu/qsXJ5mpItSoU4fdGcN5laXmudYq4RLhLlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:37:08.271784Z","bundle_sha256":"58b267e81fca4ec579a539bcdf66af78585f4a87fa64f3afe90e0ba756255eef"}}