{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4EYVWCQAXXUKL72WNCIYUY5LFA","short_pith_number":"pith:4EYVWCQA","canonical_record":{"source":{"id":"1606.04810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T15:16:58Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"d67fc6378e46c7e77708c2ed242f2623e5e09642c83bda672b346e5e881e1b0a","abstract_canon_sha256":"5be3e38d3e5e308d60249066c429040df7fb9fad1fd1c439b78a5a33d3cf4bda"},"schema_version":"1.0"},"canonical_sha256":"e1315b0a00bde8a5ff5668918a63ab280de2ca4814db062bb9ed35e8b0c48a84","source":{"kind":"arxiv","id":"1606.04810","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04810","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04810v1","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04810","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"4EYVWCQAXXUK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4EYVWCQAXXUKL72W","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4EYVWCQA","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4EYVWCQAXXUKL72WNCIYUY5LFA","target":"record","payload":{"canonical_record":{"source":{"id":"1606.04810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T15:16:58Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"d67fc6378e46c7e77708c2ed242f2623e5e09642c83bda672b346e5e881e1b0a","abstract_canon_sha256":"5be3e38d3e5e308d60249066c429040df7fb9fad1fd1c439b78a5a33d3cf4bda"},"schema_version":"1.0"},"canonical_sha256":"e1315b0a00bde8a5ff5668918a63ab280de2ca4814db062bb9ed35e8b0c48a84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:23.313423Z","signature_b64":"YjSJMkD90iWZwNZ0yqcpswESKpSz7BfnO0wkJvmbi54H/pJu+xu1XZpac7SxWzmpukYCzx6Ev0NJzVdHGIzkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1315b0a00bde8a5ff5668918a63ab280de2ca4814db062bb9ed35e8b0c48a84","last_reissued_at":"2026-05-18T01:12:23.313081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:23.313081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.04810","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":"2026-05-18T01:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYjQZ7DhIH1635QmoEw4q2flJoqQN9PZUPNt2aM1VL3vAwG4ASfNuCSqarFs85SgLept0hOHR5gIJkUT4g3VAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:06:26.625893Z"},"content_sha256":"6aa547059f6be8db60a2157364c19fe14738223c3e082591a073fd489b45fe7b","schema_version":"1.0","event_id":"sha256:6aa547059f6be8db60a2157364c19fe14738223c3e082591a073fd489b45fe7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4EYVWCQAXXUKL72WNCIYUY5LFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Analysis for Perturbed Operators on Carnot Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Marius Mantoiu","submitted_at":"2016-06-15T15:16:58Z","abstract_excerpt":"Let $\\G$ be a Carnot group of homogeneous dimension $M$ and $\\Delta$ its horizontal sublaplacian. For $\\alpha\\in(0,M)$ we show that operators of the form $H_\\alpha:=(-\\Delta)^\\alpha+V$ have no singular spectrum, under generous assumptions on the multiplication operator $V$. The proof is based on commutator methods and Hardy inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04810","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":"2026-05-18T01:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BjeBoBcy4V8D53Ohqmg7FMIlabwLilwQPNMtfEUbQXbyZT/AO8N2zSGQCof5zCMOc/SNeCFPyxM6uRJn1wqhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:06:26.626235Z"},"content_sha256":"0beb3223401003264f0dd5a28499e21f558a45f9c520293e8ff51680190ff5cd","schema_version":"1.0","event_id":"sha256:0beb3223401003264f0dd5a28499e21f558a45f9c520293e8ff51680190ff5cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EYVWCQAXXUKL72WNCIYUY5LFA/bundle.json","state_url":"https://pith.science/pith/4EYVWCQAXXUKL72WNCIYUY5LFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EYVWCQAXXUKL72WNCIYUY5LFA/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":"2026-06-26T02:06:26Z","links":{"resolver":"https://pith.science/pith/4EYVWCQAXXUKL72WNCIYUY5LFA","bundle":"https://pith.science/pith/4EYVWCQAXXUKL72WNCIYUY5LFA/bundle.json","state":"https://pith.science/pith/4EYVWCQAXXUKL72WNCIYUY5LFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EYVWCQAXXUKL72WNCIYUY5LFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4EYVWCQAXXUKL72WNCIYUY5LFA","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":"5be3e38d3e5e308d60249066c429040df7fb9fad1fd1c439b78a5a33d3cf4bda","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T15:16:58Z","title_canon_sha256":"d67fc6378e46c7e77708c2ed242f2623e5e09642c83bda672b346e5e881e1b0a"},"schema_version":"1.0","source":{"id":"1606.04810","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04810","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04810v1","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04810","created_at":"2026-05-18T01:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"4EYVWCQAXXUK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4EYVWCQAXXUKL72W","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4EYVWCQA","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:0beb3223401003264f0dd5a28499e21f558a45f9c520293e8ff51680190ff5cd","target":"graph","created_at":"2026-05-18T01:12:23Z","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":"Let $\\G$ be a Carnot group of homogeneous dimension $M$ and $\\Delta$ its horizontal sublaplacian. For $\\alpha\\in(0,M)$ we show that operators of the form $H_\\alpha:=(-\\Delta)^\\alpha+V$ have no singular spectrum, under generous assumptions on the multiplication operator $V$. The proof is based on commutator methods and Hardy inequalities.","authors_text":"Marius Mantoiu","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T15:16:58Z","title":"Spectral Analysis for Perturbed Operators on Carnot Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04810","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":"sha256:6aa547059f6be8db60a2157364c19fe14738223c3e082591a073fd489b45fe7b","target":"record","created_at":"2026-05-18T01:12:23Z","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":"5be3e38d3e5e308d60249066c429040df7fb9fad1fd1c439b78a5a33d3cf4bda","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T15:16:58Z","title_canon_sha256":"d67fc6378e46c7e77708c2ed242f2623e5e09642c83bda672b346e5e881e1b0a"},"schema_version":"1.0","source":{"id":"1606.04810","kind":"arxiv","version":1}},"canonical_sha256":"e1315b0a00bde8a5ff5668918a63ab280de2ca4814db062bb9ed35e8b0c48a84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1315b0a00bde8a5ff5668918a63ab280de2ca4814db062bb9ed35e8b0c48a84","first_computed_at":"2026-05-18T01:12:23.313081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:23.313081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YjSJMkD90iWZwNZ0yqcpswESKpSz7BfnO0wkJvmbi54H/pJu+xu1XZpac7SxWzmpukYCzx6Ev0NJzVdHGIzkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:23.313423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04810","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aa547059f6be8db60a2157364c19fe14738223c3e082591a073fd489b45fe7b","sha256:0beb3223401003264f0dd5a28499e21f558a45f9c520293e8ff51680190ff5cd"],"state_sha256":"453e31c6a577f8447df8586dc0af513c70d452a75d04d2d4738f0bc8f1d5bd97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upS8CG3gK71oo3haVMYwyBbmpT3jTNJhnBlVxMeoM/skT5jJsILnBsLfd7G8uyK/zsOcj6j8xqyZHWGp1djhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:06:26.628113Z","bundle_sha256":"d2cfb1d5e232da1fb405d6a9cd2f3926146a1d1a1d1c165e853ddef4b20f5693"}}