{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YNEOQZSGD5SPKEZUOHYI43ZIAC","short_pith_number":"pith:YNEOQZSG","canonical_record":{"source":{"id":"1903.07327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-18T09:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"dfec1d06be8926071780709cb18fc6a52f94897df2935d586162d87c88dfbb9e","abstract_canon_sha256":"8ee578473a8a946e084b6b2a0ec3c8312b66ca5002b03ac57b8686196d5b11ec"},"schema_version":"1.0"},"canonical_sha256":"c348e866461f64f5133471f08e6f28009e461c00ca13be41e353463b925322f0","source":{"kind":"arxiv","id":"1903.07327","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07327","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07327v1","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07327","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"pith_short_12","alias_value":"YNEOQZSGD5SP","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YNEOQZSGD5SPKEZU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YNEOQZSG","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YNEOQZSGD5SPKEZUOHYI43ZIAC","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-18T09:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"dfec1d06be8926071780709cb18fc6a52f94897df2935d586162d87c88dfbb9e","abstract_canon_sha256":"8ee578473a8a946e084b6b2a0ec3c8312b66ca5002b03ac57b8686196d5b11ec"},"schema_version":"1.0"},"canonical_sha256":"c348e866461f64f5133471f08e6f28009e461c00ca13be41e353463b925322f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:01.696201Z","signature_b64":"r2+1GOJBC5eWZxmhf/dLIQ12Y5/RGvnUO31t6ZYaM9hjTZVt3rbz6kekoPYmEoRSghCLkIB574YqIxdnelFgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c348e866461f64f5133471f08e6f28009e461c00ca13be41e353463b925322f0","last_reissued_at":"2026-05-17T23:51:01.695647Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:01.695647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07327","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":"2026-05-17T23:51:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbPKfdRsv/PUyxK57ApVcuo2W+xVI3BPkmLlWPxqcOCA0y10BnTVYgeiSfHiDey8DibnNsq1pit+zu4JWwiACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:54:14.174234Z"},"content_sha256":"62b583fde367fac06aaf043b559199b2f8350dc2aded5ba0ccb0504089e1a5a7","schema_version":"1.0","event_id":"sha256:62b583fde367fac06aaf043b559199b2f8350dc2aded5ba0ccb0504089e1a5a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YNEOQZSGD5SPKEZUOHYI43ZIAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Space regularity for evolution operators modeled on H\\\"ormander vector fields with time dependent measurable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marco Bramanti","submitted_at":"2019-03-18T09:35:50Z","abstract_excerpt":"We consider a heat-type operator L structured on the left invariant 1-homogeneous vector fields which are generators of a Carnot group, multiplied by a uniformly positive matrix of bounded measurable coefficients depending only on time. We prove that if Lu is smooth with respect to the space variables, the same is true for u, with quantitative regularity estimates in the scale of Sobolev spaces defined by right invariant vector fields. Moreover, the solution and its space derivatives satisfy a 1/2-H\\\"older continuity estimate with respect to time. The result is proved both for weak solutions a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07327","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":"2026-05-17T23:51:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gVxYJwMbZv1nYXspifqv8RW/SWYWbTb0qpUxObj00OaCr8zz8gF+HsuZV64JnVt8BPvZV+XRgR693rXhzo9+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:54:14.174595Z"},"content_sha256":"0b88a04ba6dc0e5fa1583e14eb30f406a1cfbadaeaf7c1d6cca15d5f52ecec97","schema_version":"1.0","event_id":"sha256:0b88a04ba6dc0e5fa1583e14eb30f406a1cfbadaeaf7c1d6cca15d5f52ecec97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC/bundle.json","state_url":"https://pith.science/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC/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":"2026-06-25T16:54:14Z","links":{"resolver":"https://pith.science/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC","bundle":"https://pith.science/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC/bundle.json","state":"https://pith.science/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNEOQZSGD5SPKEZUOHYI43ZIAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YNEOQZSGD5SPKEZUOHYI43ZIAC","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":"8ee578473a8a946e084b6b2a0ec3c8312b66ca5002b03ac57b8686196d5b11ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-18T09:35:50Z","title_canon_sha256":"dfec1d06be8926071780709cb18fc6a52f94897df2935d586162d87c88dfbb9e"},"schema_version":"1.0","source":{"id":"1903.07327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07327","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07327v1","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07327","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"pith_short_12","alias_value":"YNEOQZSGD5SP","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YNEOQZSGD5SPKEZU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YNEOQZSG","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:0b88a04ba6dc0e5fa1583e14eb30f406a1cfbadaeaf7c1d6cca15d5f52ecec97","target":"graph","created_at":"2026-05-17T23:51:01Z","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 consider a heat-type operator L structured on the left invariant 1-homogeneous vector fields which are generators of a Carnot group, multiplied by a uniformly positive matrix of bounded measurable coefficients depending only on time. We prove that if Lu is smooth with respect to the space variables, the same is true for u, with quantitative regularity estimates in the scale of Sobolev spaces defined by right invariant vector fields. Moreover, the solution and its space derivatives satisfy a 1/2-H\\\"older continuity estimate with respect to time. The result is proved both for weak solutions a","authors_text":"Marco Bramanti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-18T09:35:50Z","title":"Space regularity for evolution operators modeled on H\\\"ormander vector fields with time dependent measurable coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07327","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":"sha256:62b583fde367fac06aaf043b559199b2f8350dc2aded5ba0ccb0504089e1a5a7","target":"record","created_at":"2026-05-17T23:51:01Z","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":"8ee578473a8a946e084b6b2a0ec3c8312b66ca5002b03ac57b8686196d5b11ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-18T09:35:50Z","title_canon_sha256":"dfec1d06be8926071780709cb18fc6a52f94897df2935d586162d87c88dfbb9e"},"schema_version":"1.0","source":{"id":"1903.07327","kind":"arxiv","version":1}},"canonical_sha256":"c348e866461f64f5133471f08e6f28009e461c00ca13be41e353463b925322f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c348e866461f64f5133471f08e6f28009e461c00ca13be41e353463b925322f0","first_computed_at":"2026-05-17T23:51:01.695647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:01.695647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2+1GOJBC5eWZxmhf/dLIQ12Y5/RGvnUO31t6ZYaM9hjTZVt3rbz6kekoPYmEoRSghCLkIB574YqIxdnelFgCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:01.696201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62b583fde367fac06aaf043b559199b2f8350dc2aded5ba0ccb0504089e1a5a7","sha256:0b88a04ba6dc0e5fa1583e14eb30f406a1cfbadaeaf7c1d6cca15d5f52ecec97"],"state_sha256":"8595d29384113d85502cb6256e008af22620bfe49dc2a2bcad22e8c7397f159b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FAV5DywjSglbaWTojOIVyVjpn9My6Sgt9wsLmN3MES12P8AYnRlHCV7jAGQraF96uSTFuYOlIAhNk3VCnDBSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T16:54:14.176725Z","bundle_sha256":"34e92c26cbcd6e687e40d78841879941df3e127de3dbbd07c69f195c97213c9f"}}