{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RTKA3TUTUDKFSBMXMNEMIY3SAD","short_pith_number":"pith:RTKA3TUT","canonical_record":{"source":{"id":"1010.1133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-06T12:09:29Z","cross_cats_sorted":[],"title_canon_sha256":"b016bfbd672bf1bfba67cccf6834486be555a717fcbe17bd82e361aff4f78a6c","abstract_canon_sha256":"93878c91ba1096fb76d2528bca1cc35922f2c7d98fd49be2b16689d03fc7ee61"},"schema_version":"1.0"},"canonical_sha256":"8cd40dce93a0d45905976348c4637200dc7b01020f30575764a295e7410c4a80","source":{"kind":"arxiv","id":"1010.1133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1133","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1133v1","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1133","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"RTKA3TUTUDKF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RTKA3TUTUDKFSBMX","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RTKA3TUT","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RTKA3TUTUDKFSBMXMNEMIY3SAD","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-06T12:09:29Z","cross_cats_sorted":[],"title_canon_sha256":"b016bfbd672bf1bfba67cccf6834486be555a717fcbe17bd82e361aff4f78a6c","abstract_canon_sha256":"93878c91ba1096fb76d2528bca1cc35922f2c7d98fd49be2b16689d03fc7ee61"},"schema_version":"1.0"},"canonical_sha256":"8cd40dce93a0d45905976348c4637200dc7b01020f30575764a295e7410c4a80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:49.752102Z","signature_b64":"NXV/eYU4ym8GLR2aYiieB43uiR1aNgXOcqpG+CkuKIsYUvbU/RqFSdrDvJav8fbju2AQYUelke08zn7sVVxNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cd40dce93a0d45905976348c4637200dc7b01020f30575764a295e7410c4a80","last_reissued_at":"2026-05-18T04:39:49.751632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:49.751632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1133","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":"2026-05-18T04:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hT04//RI9joOJ8CoQvVAgTJjzqsWyD7bx8AqCMzdXrFDmv3mStqMsR4EnkYuLZBxOImdDaiH9fdbvvnKuxA0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:42:07.382648Z"},"content_sha256":"6d4e15ce69fa77fbbfde326da47793f096174ebd7af93f57e197e90b5e246346","schema_version":"1.0","event_id":"sha256:6d4e15ce69fa77fbbfde326da47793f096174ebd7af93f57e197e90b5e246346"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RTKA3TUTUDKFSBMXMNEMIY3SAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isodiametric sets in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Davide Vittone, Gian Paolo Leonardi, Severine Rigot","submitted_at":"2010-10-06T12:09:29Z","abstract_excerpt":"In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an isodiametric set, and up to negligible sets, we prove that its boundary is given by the graphs of two locally Lipschitz functions. Moreover, in the restricted class of rotationally invariant sets, we give a quite complete characterization of any compact (rotationally invariant) isodiametric set. More specifically, its Steiner symmetrization with respect to the Cn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1133","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":"2026-05-18T04:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MeVyNUaeLtwiP1ffUkqV7QbA5r/DldnBY2Yu1QnRTZBoJ3kjQDf+yojhnoOGFgzivqycBJ6FMB6oRAhSr+mfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:42:07.383185Z"},"content_sha256":"478fc267fb326c381360267d7eb973816b914ed19f43d9d44bd328f9170316e8","schema_version":"1.0","event_id":"sha256:478fc267fb326c381360267d7eb973816b914ed19f43d9d44bd328f9170316e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD/bundle.json","state_url":"https://pith.science/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD/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":"2026-06-04T17:42:07Z","links":{"resolver":"https://pith.science/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD","bundle":"https://pith.science/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD/bundle.json","state":"https://pith.science/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTKA3TUTUDKFSBMXMNEMIY3SAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RTKA3TUTUDKFSBMXMNEMIY3SAD","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":"93878c91ba1096fb76d2528bca1cc35922f2c7d98fd49be2b16689d03fc7ee61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-06T12:09:29Z","title_canon_sha256":"b016bfbd672bf1bfba67cccf6834486be555a717fcbe17bd82e361aff4f78a6c"},"schema_version":"1.0","source":{"id":"1010.1133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1133","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1133v1","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1133","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"RTKA3TUTUDKF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RTKA3TUTUDKFSBMX","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RTKA3TUT","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:478fc267fb326c381360267d7eb973816b914ed19f43d9d44bd328f9170316e8","target":"graph","created_at":"2026-05-18T04:39:49Z","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 the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an isodiametric set, and up to negligible sets, we prove that its boundary is given by the graphs of two locally Lipschitz functions. Moreover, in the restricted class of rotationally invariant sets, we give a quite complete characterization of any compact (rotationally invariant) isodiametric set. More specifically, its Steiner symmetrization with respect to the Cn","authors_text":"Davide Vittone, Gian Paolo Leonardi, Severine Rigot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-06T12:09:29Z","title":"Isodiametric sets in the Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1133","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":"sha256:6d4e15ce69fa77fbbfde326da47793f096174ebd7af93f57e197e90b5e246346","target":"record","created_at":"2026-05-18T04:39:49Z","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":"93878c91ba1096fb76d2528bca1cc35922f2c7d98fd49be2b16689d03fc7ee61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-06T12:09:29Z","title_canon_sha256":"b016bfbd672bf1bfba67cccf6834486be555a717fcbe17bd82e361aff4f78a6c"},"schema_version":"1.0","source":{"id":"1010.1133","kind":"arxiv","version":1}},"canonical_sha256":"8cd40dce93a0d45905976348c4637200dc7b01020f30575764a295e7410c4a80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cd40dce93a0d45905976348c4637200dc7b01020f30575764a295e7410c4a80","first_computed_at":"2026-05-18T04:39:49.751632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:49.751632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NXV/eYU4ym8GLR2aYiieB43uiR1aNgXOcqpG+CkuKIsYUvbU/RqFSdrDvJav8fbju2AQYUelke08zn7sVVxNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:49.752102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d4e15ce69fa77fbbfde326da47793f096174ebd7af93f57e197e90b5e246346","sha256:478fc267fb326c381360267d7eb973816b914ed19f43d9d44bd328f9170316e8"],"state_sha256":"4c31af124657e890c49cddc0a035a24c15155b09bb5b838fa4157c9317ea5bcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"atlsaU8+SIuBbYdP1Lj7yt4ORiktt2tR+MXu8yvUGms1R3r7bIrGj/9erCrNi3zHwI97Qtpka9Q1ewfdNjJfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:42:07.385832Z","bundle_sha256":"ee520f3b0436e84c3d454c10abb85d5105eab31dce9043de434cb23b7ef72c1d"}}