{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CMTEOBIVIFKBYVGX2XWSIWLGRI","short_pith_number":"pith:CMTEOBIV","canonical_record":{"source":{"id":"1202.3083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T16:40:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"73fab3b65c6c87eae41fabfa25fdb0833a7c337ce617428a7c557b8af5bad8ef","abstract_canon_sha256":"a2d717a2100c4e8cb42497d5e94f022e01f35163d235b9b7419f574f09f78fa7"},"schema_version":"1.0"},"canonical_sha256":"132647051541541c54d7d5ed2459668a38ef786c05672efffdba22b4cae00ccc","source":{"kind":"arxiv","id":"1202.3083","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3083","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3083v2","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3083","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"CMTEOBIVIFKB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CMTEOBIVIFKBYVGX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CMTEOBIV","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CMTEOBIVIFKBYVGX2XWSIWLGRI","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T16:40:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"73fab3b65c6c87eae41fabfa25fdb0833a7c337ce617428a7c557b8af5bad8ef","abstract_canon_sha256":"a2d717a2100c4e8cb42497d5e94f022e01f35163d235b9b7419f574f09f78fa7"},"schema_version":"1.0"},"canonical_sha256":"132647051541541c54d7d5ed2459668a38ef786c05672efffdba22b4cae00ccc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:26.215118Z","signature_b64":"PIQfWOnu0hXao6Phd5KkpsXc3KCd4/9hNajQUaphogAnj796Yti+rEqF2ulQ2LCSGHQFLytW9FUT7pNGOEjxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"132647051541541c54d7d5ed2459668a38ef786c05672efffdba22b4cae00ccc","last_reissued_at":"2026-05-18T01:30:26.214294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:26.214294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3083","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":"2026-05-18T01:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w0zSvTRFCDZesFoLfKpy1U0v/4p3FrKptPY+uGfEsOyH7QieKDgtsM65ePVpvwWggvcXlXLHUn3m11sPoRRLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:20:12.535693Z"},"content_sha256":"8f5346ff9cfaf3515cdb0a6af4ca7fa291bbdbe66b28196b70c4ae72d4d05fd8","schema_version":"1.0","event_id":"sha256:8f5346ff9cfaf3515cdb0a6af4ca7fa291bbdbe66b28196b70c4ae72d4d05fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CMTEOBIVIFKBYVGX2XWSIWLGRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Francesco Bigolin, Francesco Serra Cassano, Laura Caravenna","submitted_at":"2012-02-14T16:40:37Z","abstract_excerpt":"In this paper we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation \\phi_y+ [\\phi^{2}/2]_t=w, where w is a bounded function depending on \\phi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3083","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":"2026-05-18T01:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GF8H0X5IxYuaoJk4F9VesXxrXupKADuwhW3YSqz+7Y0NUUmQT04mnxzSSspdfDgMgfIWyKU7URRvxuNrtrtUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:20:12.536029Z"},"content_sha256":"f81b55dddef1673449fd7f02dd7e81c6c9bae7255f2917d6e54b8e55b7bdd57f","schema_version":"1.0","event_id":"sha256:f81b55dddef1673449fd7f02dd7e81c6c9bae7255f2917d6e54b8e55b7bdd57f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI/bundle.json","state_url":"https://pith.science/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI/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":"2026-06-02T14:20:12Z","links":{"resolver":"https://pith.science/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI","bundle":"https://pith.science/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI/bundle.json","state":"https://pith.science/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CMTEOBIVIFKBYVGX2XWSIWLGRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CMTEOBIVIFKBYVGX2XWSIWLGRI","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":"a2d717a2100c4e8cb42497d5e94f022e01f35163d235b9b7419f574f09f78fa7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T16:40:37Z","title_canon_sha256":"73fab3b65c6c87eae41fabfa25fdb0833a7c337ce617428a7c557b8af5bad8ef"},"schema_version":"1.0","source":{"id":"1202.3083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3083","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3083v2","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3083","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"CMTEOBIVIFKB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CMTEOBIVIFKBYVGX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CMTEOBIV","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:f81b55dddef1673449fd7f02dd7e81c6c9bae7255f2917d6e54b8e55b7bdd57f","target":"graph","created_at":"2026-05-18T01:30:26Z","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 we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation \\phi_y+ [\\phi^{2}/2]_t=w, where w is a bounded function depending on \\phi.","authors_text":"Francesco Bigolin, Francesco Serra Cassano, Laura Caravenna","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T16:40:37Z","title":"Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3083","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":"sha256:8f5346ff9cfaf3515cdb0a6af4ca7fa291bbdbe66b28196b70c4ae72d4d05fd8","target":"record","created_at":"2026-05-18T01:30:26Z","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":"a2d717a2100c4e8cb42497d5e94f022e01f35163d235b9b7419f574f09f78fa7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T16:40:37Z","title_canon_sha256":"73fab3b65c6c87eae41fabfa25fdb0833a7c337ce617428a7c557b8af5bad8ef"},"schema_version":"1.0","source":{"id":"1202.3083","kind":"arxiv","version":2}},"canonical_sha256":"132647051541541c54d7d5ed2459668a38ef786c05672efffdba22b4cae00ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"132647051541541c54d7d5ed2459668a38ef786c05672efffdba22b4cae00ccc","first_computed_at":"2026-05-18T01:30:26.214294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:26.214294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIQfWOnu0hXao6Phd5KkpsXc3KCd4/9hNajQUaphogAnj796Yti+rEqF2ulQ2LCSGHQFLytW9FUT7pNGOEjxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:26.215118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f5346ff9cfaf3515cdb0a6af4ca7fa291bbdbe66b28196b70c4ae72d4d05fd8","sha256:f81b55dddef1673449fd7f02dd7e81c6c9bae7255f2917d6e54b8e55b7bdd57f"],"state_sha256":"2205746b9ab55f378a1e8091e9b82d73aad96ca646aefd233d6d986fd2e8b3ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HsmCm143zz0C67z5gaPyyV4kfoIKNcFGubNmZu3lBNWbCHGxfbXqBkBvpMIkwmQjmzNHCivMpAN0ht2ZxiUwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:20:12.538038Z","bundle_sha256":"23e91358d1ea8b10659c1f02f957a3692d6ba8777288bdaf670cb50ad7fdf35d"}}