{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TFJCBFCCBEI77G3ZLJP7TDF7OP","short_pith_number":"pith:TFJCBFCC","canonical_record":{"source":{"id":"2511.02978","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-04T20:36:33Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"f5ece89c73e3e9442c5811a9d4c1c688cf970ec87f5b28f127f621c631d8fd75","abstract_canon_sha256":"b58a22edfafc0f751b0ca3b98bb95007bfc376382295a8f0417104af14cfb3fa"},"schema_version":"1.0"},"canonical_sha256":"99522094420911ff9b795a5ff98cbf73dd53dad21cd555294a97b7a6a74d9bcf","source":{"kind":"arxiv","id":"2511.02978","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.02978","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2511.02978v2","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.02978","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"TFJCBFCCBEI7","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"TFJCBFCCBEI77G3Z","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"TFJCBFCC","created_at":"2026-05-26T02:05:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TFJCBFCCBEI77G3ZLJP7TDF7OP","target":"record","payload":{"canonical_record":{"source":{"id":"2511.02978","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-04T20:36:33Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"f5ece89c73e3e9442c5811a9d4c1c688cf970ec87f5b28f127f621c631d8fd75","abstract_canon_sha256":"b58a22edfafc0f751b0ca3b98bb95007bfc376382295a8f0417104af14cfb3fa"},"schema_version":"1.0"},"canonical_sha256":"99522094420911ff9b795a5ff98cbf73dd53dad21cd555294a97b7a6a74d9bcf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:03.869729Z","signature_b64":"8YiOtqp/fxFIe3sJJhcTqQkjDh/7QDPMKpV46B1fXAiLTzM7PxzY53arnvojU3Sxfj9FxiWFtp5dwVYzCMJdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99522094420911ff9b795a5ff98cbf73dd53dad21cd555294a97b7a6a74d9bcf","last_reissued_at":"2026-05-26T02:05:03.868875Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:03.868875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2511.02978","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":"2026-05-26T02:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqgiP6Y3rsB9GcWImPGOn+hCgohgzZbeD4fnf4IlVYylWLNgPg6EeWugaRzKolR4m7wH4a0P00qxsmYWS9AIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:23:25.406463Z"},"content_sha256":"e6001f9eceedbece420fbbcf779996280630104425fff6bfd9c6f291f8ad8fa7","schema_version":"1.0","event_id":"sha256:e6001f9eceedbece420fbbcf779996280630104425fff6bfd9c6f291f8ad8fa7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TFJCBFCCBEI77G3ZLJP7TDF7OP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Sekhar Ghosh, Vishvesh Kumar, Yergen Aikyn","submitted_at":"2025-11-04T20:36:33Z","abstract_excerpt":"The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition operators\" defined as continuous superpositions of operators of mixed fractional order, modulated by a signed finite Borel measure on the unit interval. This framework encompasses, as particular cases, mixed local and nonlocal operators such as $-\\Delta_p+(-\\Delta_p)^s$, finite (possibly infinite) sums of fractional $p$-Laplacians with different orders, as well as operators involving fractional Laplacians with ``wrong\" si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.02978","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.02978/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-26T02:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qynjbs9iODnRxaSg4BPqazON0tlSWvQt9pV/G+Ah19gOA6BJavdmbSKMAMRCTQopfxj9Qel9r2800Ow46R6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:23:25.406835Z"},"content_sha256":"a62f6d639052f592900db4254b0e8fb96cec91a00bd4cb8130e0e17ae8b4ea47","schema_version":"1.0","event_id":"sha256:a62f6d639052f592900db4254b0e8fb96cec91a00bd4cb8130e0e17ae8b4ea47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP/bundle.json","state_url":"https://pith.science/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP/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":"2026-06-09T00:23:25Z","links":{"resolver":"https://pith.science/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP","bundle":"https://pith.science/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP/bundle.json","state":"https://pith.science/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TFJCBFCCBEI77G3ZLJP7TDF7OP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TFJCBFCCBEI77G3ZLJP7TDF7OP","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":"b58a22edfafc0f751b0ca3b98bb95007bfc376382295a8f0417104af14cfb3fa","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-04T20:36:33Z","title_canon_sha256":"f5ece89c73e3e9442c5811a9d4c1c688cf970ec87f5b28f127f621c631d8fd75"},"schema_version":"1.0","source":{"id":"2511.02978","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.02978","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2511.02978v2","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.02978","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"TFJCBFCCBEI7","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"TFJCBFCCBEI77G3Z","created_at":"2026-05-26T02:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"TFJCBFCC","created_at":"2026-05-26T02:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:a62f6d639052f592900db4254b0e8fb96cec91a00bd4cb8130e0e17ae8b4ea47","target":"graph","created_at":"2026-05-26T02:05:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.02978/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition operators\" defined as continuous superpositions of operators of mixed fractional order, modulated by a signed finite Borel measure on the unit interval. This framework encompasses, as particular cases, mixed local and nonlocal operators such as $-\\Delta_p+(-\\Delta_p)^s$, finite (possibly infinite) sums of fractional $p$-Laplacians with different orders, as well as operators involving fractional Laplacians with ``wrong\" si","authors_text":"Michael Ruzhansky, Sekhar Ghosh, Vishvesh Kumar, Yergen Aikyn","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-04T20:36:33Z","title":"Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.02978","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:e6001f9eceedbece420fbbcf779996280630104425fff6bfd9c6f291f8ad8fa7","target":"record","created_at":"2026-05-26T02:05:03Z","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":"b58a22edfafc0f751b0ca3b98bb95007bfc376382295a8f0417104af14cfb3fa","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-04T20:36:33Z","title_canon_sha256":"f5ece89c73e3e9442c5811a9d4c1c688cf970ec87f5b28f127f621c631d8fd75"},"schema_version":"1.0","source":{"id":"2511.02978","kind":"arxiv","version":2}},"canonical_sha256":"99522094420911ff9b795a5ff98cbf73dd53dad21cd555294a97b7a6a74d9bcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99522094420911ff9b795a5ff98cbf73dd53dad21cd555294a97b7a6a74d9bcf","first_computed_at":"2026-05-26T02:05:03.868875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:03.868875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8YiOtqp/fxFIe3sJJhcTqQkjDh/7QDPMKpV46B1fXAiLTzM7PxzY53arnvojU3Sxfj9FxiWFtp5dwVYzCMJdAg==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:03.869729Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.02978","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6001f9eceedbece420fbbcf779996280630104425fff6bfd9c6f291f8ad8fa7","sha256:a62f6d639052f592900db4254b0e8fb96cec91a00bd4cb8130e0e17ae8b4ea47"],"state_sha256":"7a16688e8c96f6b0935333fec8e07b10b05339ebd29a78356124793011131040"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsAxHI02VjWcsXgCHxjR2nmLOHv515wL3iSLACaU6+hWYi8plr6zN3nuYLHSZw4u3YigA5Zlkdj6FEFV1JQqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:23:25.408824Z","bundle_sha256":"301c288291888782e55b379b6a079d18cd756a574c3213748b451fde26a5da77"}}