{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2KDW63QEZEYVK4RMPD4AYPEU3V","short_pith_number":"pith:2KDW63QE","canonical_record":{"source":{"id":"1011.5939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-26T23:37:27Z","cross_cats_sorted":["math.AP","math.CO","math.MG","math.NT"],"title_canon_sha256":"c9f49bac35ec2f13f96e989b76e0cc3aaa4e63ecbdd9b2c41ad6c8967a395750","abstract_canon_sha256":"a709bbd23dbd9b073ca1fa5212caff568dc50d9c1d1194760fac18ea3c272d91"},"schema_version":"1.0"},"canonical_sha256":"d2876f6e04c93155722c78f80c3c94dd6871af023b624739aa586cdeeb0ef5ab","source":{"kind":"arxiv","id":"1011.5939","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5939","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5939v2","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5939","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"2KDW63QEZEYV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2KDW63QEZEYVK4RM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2KDW63QE","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2KDW63QEZEYVK4RMPD4AYPEU3V","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-26T23:37:27Z","cross_cats_sorted":["math.AP","math.CO","math.MG","math.NT"],"title_canon_sha256":"c9f49bac35ec2f13f96e989b76e0cc3aaa4e63ecbdd9b2c41ad6c8967a395750","abstract_canon_sha256":"a709bbd23dbd9b073ca1fa5212caff568dc50d9c1d1194760fac18ea3c272d91"},"schema_version":"1.0"},"canonical_sha256":"d2876f6e04c93155722c78f80c3c94dd6871af023b624739aa586cdeeb0ef5ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:35.050510Z","signature_b64":"H27Z/yGEBJICkEHqPIknzCdMiV4LnKKe0lk+2jNGdJBFzvxuATnwza4GEYIuWv+lBZKNoUF7NPXV+lDXf80zDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2876f6e04c93155722c78f80c3c94dd6871af023b624739aa586cdeeb0ef5ab","last_reissued_at":"2026-05-18T04:23:35.049858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:35.049858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5939","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":"2026-05-18T04:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aVsTfydAcvShtgEPUshSnL/kWUH/lF79fId4W151y0Sga3WPuMd0HbDRbR6g+IX1l624FWNap+5wWjiF75gQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:55:40.272713Z"},"content_sha256":"3cccd9d6c1c1f45660e0509cbc3761257dc0d3746ddd76c14ea6e8b195338b0f","schema_version":"1.0","event_id":"sha256:3cccd9d6c1c1f45660e0509cbc3761257dc0d3746ddd76c14ea6e8b195338b0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2KDW63QEZEYVK4RMPD4AYPEU3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier integral operators, fractal sets and the regular value theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CO","math.MG","math.NT"],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Krystal Taylor, Suresh Eswarathasan","submitted_at":"2010-11-26T23:37:27Z","abstract_excerpt":"We prove that if ${\\mathcal E} \\subset {\\Bbb R}^{2d}$, $d \\ge 2$, is an Ahlfors-David regular product set of sufficiently large Hausdorff dimension, denoted by $dim_{{\\mathcal H}}({\\mathcal E})$, and $\\phi$ is a sufficiently regular function, then the upper Minkowski dimension of the set $$ \\{w \\in {\\mathcal E}: \\phi_l(w)=t_l; 1 \\leq l \\leq m \\}$$ does not exceed $dim_{{\\mathcal H}}({\\mathcal E})-m$, in line with the regular value theorem from the elementary differential geometry. Our arguments are based on the mapping properties of the underlying Fourier Integral Operators and are intimately "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5939","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":"2026-05-18T04:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BIi08XwWyJiXiQ5LVppnlKDSsXr4XFmiVJhlOlav1wUOGsZ5dcARr85ytlPn8f2UR3AFr/mZJ4xuBVFfifPZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:55:40.273071Z"},"content_sha256":"75ffc853188f0aba7711825334c061236b46f1be5cd6985f98dfe41d809e9d40","schema_version":"1.0","event_id":"sha256:75ffc853188f0aba7711825334c061236b46f1be5cd6985f98dfe41d809e9d40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KDW63QEZEYVK4RMPD4AYPEU3V/bundle.json","state_url":"https://pith.science/pith/2KDW63QEZEYVK4RMPD4AYPEU3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KDW63QEZEYVK4RMPD4AYPEU3V/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":"2026-06-04T02:55:40Z","links":{"resolver":"https://pith.science/pith/2KDW63QEZEYVK4RMPD4AYPEU3V","bundle":"https://pith.science/pith/2KDW63QEZEYVK4RMPD4AYPEU3V/bundle.json","state":"https://pith.science/pith/2KDW63QEZEYVK4RMPD4AYPEU3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KDW63QEZEYVK4RMPD4AYPEU3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2KDW63QEZEYVK4RMPD4AYPEU3V","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":"a709bbd23dbd9b073ca1fa5212caff568dc50d9c1d1194760fac18ea3c272d91","cross_cats_sorted":["math.AP","math.CO","math.MG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-26T23:37:27Z","title_canon_sha256":"c9f49bac35ec2f13f96e989b76e0cc3aaa4e63ecbdd9b2c41ad6c8967a395750"},"schema_version":"1.0","source":{"id":"1011.5939","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5939","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5939v2","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5939","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"2KDW63QEZEYV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2KDW63QEZEYVK4RM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2KDW63QE","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:75ffc853188f0aba7711825334c061236b46f1be5cd6985f98dfe41d809e9d40","target":"graph","created_at":"2026-05-18T04:23:35Z","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 prove that if ${\\mathcal E} \\subset {\\Bbb R}^{2d}$, $d \\ge 2$, is an Ahlfors-David regular product set of sufficiently large Hausdorff dimension, denoted by $dim_{{\\mathcal H}}({\\mathcal E})$, and $\\phi$ is a sufficiently regular function, then the upper Minkowski dimension of the set $$ \\{w \\in {\\mathcal E}: \\phi_l(w)=t_l; 1 \\leq l \\leq m \\}$$ does not exceed $dim_{{\\mathcal H}}({\\mathcal E})-m$, in line with the regular value theorem from the elementary differential geometry. Our arguments are based on the mapping properties of the underlying Fourier Integral Operators and are intimately ","authors_text":"Alex Iosevich, Krystal Taylor, Suresh Eswarathasan","cross_cats":["math.AP","math.CO","math.MG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-26T23:37:27Z","title":"Fourier integral operators, fractal sets and the regular value theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5939","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":"sha256:3cccd9d6c1c1f45660e0509cbc3761257dc0d3746ddd76c14ea6e8b195338b0f","target":"record","created_at":"2026-05-18T04:23:35Z","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":"a709bbd23dbd9b073ca1fa5212caff568dc50d9c1d1194760fac18ea3c272d91","cross_cats_sorted":["math.AP","math.CO","math.MG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-26T23:37:27Z","title_canon_sha256":"c9f49bac35ec2f13f96e989b76e0cc3aaa4e63ecbdd9b2c41ad6c8967a395750"},"schema_version":"1.0","source":{"id":"1011.5939","kind":"arxiv","version":2}},"canonical_sha256":"d2876f6e04c93155722c78f80c3c94dd6871af023b624739aa586cdeeb0ef5ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2876f6e04c93155722c78f80c3c94dd6871af023b624739aa586cdeeb0ef5ab","first_computed_at":"2026-05-18T04:23:35.049858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:35.049858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H27Z/yGEBJICkEHqPIknzCdMiV4LnKKe0lk+2jNGdJBFzvxuATnwza4GEYIuWv+lBZKNoUF7NPXV+lDXf80zDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:35.050510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5939","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cccd9d6c1c1f45660e0509cbc3761257dc0d3746ddd76c14ea6e8b195338b0f","sha256:75ffc853188f0aba7711825334c061236b46f1be5cd6985f98dfe41d809e9d40"],"state_sha256":"d05b2e731318337f22af2d18ff15eb1b21ceaeecd1537903d65fec0885f3f010"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2I1zCshPxnSF3nEHpT91lNjPfvNlw/xlyv5L1B8HsZSo3fStnfxY/onLm7qsSrqyB0DiQ4dfurcZVdm7Gk0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:55:40.275075Z","bundle_sha256":"2dc55ac5bc45af97fe429b32246fa508a951ddfa5455d9d94c96a5a906f1c885"}}