{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5RMJGMRHT3O4ZPI7V5CYETG7G3","short_pith_number":"pith:5RMJGMRH","canonical_record":{"source":{"id":"1603.04201","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2016-03-14T10:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"afca8102de0520ce3f78d776fe8576d96a25e177b11fe9f82e598cba7e52b396","abstract_canon_sha256":"7f703bc773a2c6e5a3639fde562fb6256f63a74fb04c0733dd30ff3d67092593"},"schema_version":"1.0"},"canonical_sha256":"ec589332279eddccbd1faf45824cdf36fb5ee5144926c1384b26e4c761f550c0","source":{"kind":"arxiv","id":"1603.04201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04201","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04201v1","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04201","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"5RMJGMRHT3O4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RMJGMRHT3O4ZPI7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RMJGMRH","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5RMJGMRHT3O4ZPI7V5CYETG7G3","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04201","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2016-03-14T10:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"afca8102de0520ce3f78d776fe8576d96a25e177b11fe9f82e598cba7e52b396","abstract_canon_sha256":"7f703bc773a2c6e5a3639fde562fb6256f63a74fb04c0733dd30ff3d67092593"},"schema_version":"1.0"},"canonical_sha256":"ec589332279eddccbd1faf45824cdf36fb5ee5144926c1384b26e4c761f550c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:09.126721Z","signature_b64":"yys3IQiv68BOui7ZypefcpqavAIWyAn0IPSaegs1SoI6YARVO4/Vm4jUdGs7SpDzBzaQZIiRznZGTrRzUUW/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec589332279eddccbd1faf45824cdf36fb5ee5144926c1384b26e4c761f550c0","last_reissued_at":"2026-05-18T01:19:09.126115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:09.126115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04201","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":"2026-05-18T01:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2D7uMCC3aSNyTTQcPJKktCN6MJgGc1HRKlYvsYiU/rerx7mezYZAdTBbZf3kbEAr0DyL+bElaspmKhi8rPFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:24:28.710375Z"},"content_sha256":"b0c3979607231a03c19445d79f089eb7e99da5556352a850c7822e364c857424","schema_version":"1.0","event_id":"sha256:b0c3979607231a03c19445d79f089eb7e99da5556352a850c7822e364c857424"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5RMJGMRHT3O4ZPI7V5CYETG7G3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sufficient conditions for the existence of limiting Carleman weights","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Faraco, Luis Guijarro, Pablo Angulo-Ardoy","submitted_at":"2016-03-14T10:46:50Z","abstract_excerpt":"In https://arxiv.org/abs/1411.4887, we found some necessary conditions for a Riemannian manifold to admit a local limiting Carleman weight (LCW), based upon the Cotton-York tensor in dimension $3$ and the Weyl tensor in dimension $4$. In this paper, we find further necessary conditions for the existence of local LCWs that are often sufficient. For a manifold of dimension $3$ or $4$, we classify the possible Cotton-York, or Weyl tensors, and provide a mechanism to find out whether the manifold admits local LCW for each type of tensor. In particular, we show that a product of two surfaces admits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04201","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":"2026-05-18T01:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"loZqF3Ye8+KzKaeSl0PtOmvb8N6KQFdvn0MGne+l4ZoVpDkeTy/C7DihGyDyBm6DPJQJ1my66svxYmLMcRBdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:24:28.711044Z"},"content_sha256":"581f1dcecf954b5039866d096a6b015de37deaf4ffb4e4dc3a33fcb5e960b915","schema_version":"1.0","event_id":"sha256:581f1dcecf954b5039866d096a6b015de37deaf4ffb4e4dc3a33fcb5e960b915"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3/bundle.json","state_url":"https://pith.science/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3/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":"2026-05-27T13:24:28Z","links":{"resolver":"https://pith.science/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3","bundle":"https://pith.science/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3/bundle.json","state":"https://pith.science/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RMJGMRHT3O4ZPI7V5CYETG7G3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5RMJGMRHT3O4ZPI7V5CYETG7G3","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":"7f703bc773a2c6e5a3639fde562fb6256f63a74fb04c0733dd30ff3d67092593","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2016-03-14T10:46:50Z","title_canon_sha256":"afca8102de0520ce3f78d776fe8576d96a25e177b11fe9f82e598cba7e52b396"},"schema_version":"1.0","source":{"id":"1603.04201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04201","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04201v1","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04201","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"5RMJGMRHT3O4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RMJGMRHT3O4ZPI7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RMJGMRH","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:581f1dcecf954b5039866d096a6b015de37deaf4ffb4e4dc3a33fcb5e960b915","target":"graph","created_at":"2026-05-18T01:19:09Z","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 https://arxiv.org/abs/1411.4887, we found some necessary conditions for a Riemannian manifold to admit a local limiting Carleman weight (LCW), based upon the Cotton-York tensor in dimension $3$ and the Weyl tensor in dimension $4$. In this paper, we find further necessary conditions for the existence of local LCWs that are often sufficient. For a manifold of dimension $3$ or $4$, we classify the possible Cotton-York, or Weyl tensors, and provide a mechanism to find out whether the manifold admits local LCW for each type of tensor. In particular, we show that a product of two surfaces admits","authors_text":"Daniel Faraco, Luis Guijarro, Pablo Angulo-Ardoy","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2016-03-14T10:46:50Z","title":"Sufficient conditions for the existence of limiting Carleman weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04201","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:b0c3979607231a03c19445d79f089eb7e99da5556352a850c7822e364c857424","target":"record","created_at":"2026-05-18T01:19:09Z","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":"7f703bc773a2c6e5a3639fde562fb6256f63a74fb04c0733dd30ff3d67092593","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2016-03-14T10:46:50Z","title_canon_sha256":"afca8102de0520ce3f78d776fe8576d96a25e177b11fe9f82e598cba7e52b396"},"schema_version":"1.0","source":{"id":"1603.04201","kind":"arxiv","version":1}},"canonical_sha256":"ec589332279eddccbd1faf45824cdf36fb5ee5144926c1384b26e4c761f550c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec589332279eddccbd1faf45824cdf36fb5ee5144926c1384b26e4c761f550c0","first_computed_at":"2026-05-18T01:19:09.126115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:09.126115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yys3IQiv68BOui7ZypefcpqavAIWyAn0IPSaegs1SoI6YARVO4/Vm4jUdGs7SpDzBzaQZIiRznZGTrRzUUW/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:09.126721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0c3979607231a03c19445d79f089eb7e99da5556352a850c7822e364c857424","sha256:581f1dcecf954b5039866d096a6b015de37deaf4ffb4e4dc3a33fcb5e960b915"],"state_sha256":"ffe5aab31c91161eb6454f018f63440231decdc42f780499aba2ec2faa566324"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q2ymMzuuRINxyePnLql6RJjYSZQc2T1ibsKqRYiDh2eRALyGAUYwus1flJf0S8CNKSMd5u2GMv/pj0YDjwJQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:24:28.714764Z","bundle_sha256":"652cea25270b43b997255bb9dd80224cc2de82853177b45417244d8cbc9d6540"}}