{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SFAYDKQRCLHAN7LX6PWUMFQ2UG","short_pith_number":"pith:SFAYDKQR","canonical_record":{"source":{"id":"2606.29154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-28T02:23:01Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"62ba55da33e7e44b26d960e68f816a00c1d6d8935a9a406a77adcc89c56db327","abstract_canon_sha256":"7dac546531cc349bcdca6d4c074df7917552e403ca86f5db571d89f5020e0d26"},"schema_version":"1.0"},"canonical_sha256":"914181aa1112ce06fd77f3ed46161aa194cd65195cccd1bc9ee4733cbf28b040","source":{"kind":"arxiv","id":"2606.29154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29154","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29154v1","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29154","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"SFAYDKQRCLHA","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"pith_short_16","alias_value":"SFAYDKQRCLHAN7LX","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"pith_short_8","alias_value":"SFAYDKQR","created_at":"2026-06-30T01:17:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SFAYDKQRCLHAN7LX6PWUMFQ2UG","target":"record","payload":{"canonical_record":{"source":{"id":"2606.29154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-28T02:23:01Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"62ba55da33e7e44b26d960e68f816a00c1d6d8935a9a406a77adcc89c56db327","abstract_canon_sha256":"7dac546531cc349bcdca6d4c074df7917552e403ca86f5db571d89f5020e0d26"},"schema_version":"1.0"},"canonical_sha256":"914181aa1112ce06fd77f3ed46161aa194cd65195cccd1bc9ee4733cbf28b040","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:54.841976Z","signature_b64":"bMItV+VPgexLY9ca2D65l+xyAaS1MxI36JVYECOoafIYE6/pKkrbsK4o15dF4j8sUsIp6kczxIZZ+c3DgPTJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"914181aa1112ce06fd77f3ed46161aa194cd65195cccd1bc9ee4733cbf28b040","last_reissued_at":"2026-06-30T01:17:54.841292Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:54.841292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.29154","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":"2026-06-30T01:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82XRo8u+d7XoJVfc0KHIpTDSmAkEAp0ah69lHG3k/fAmBGED6Wh905p1ZTOwwxCuvTBte5HFDNX8TDOhM6Y0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:03:13.946203Z"},"content_sha256":"85258f28574aef9b8bbeffceae9918bbe071f81fc64f53475213a3c9ef86628b","schema_version":"1.0","event_id":"sha256:85258f28574aef9b8bbeffceae9918bbe071f81fc64f53475213a3c9ef86628b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SFAYDKQRCLHAN7LX6PWUMFQ2UG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Jiangong You, Qi Zhou, Xianzhe Li, Zhenfu Wang","submitted_at":"2026-06-28T02:23:01Z","abstract_excerpt":"We introduce an operator-theoretic framework for long-range operators over general dynamical systems with analytic hopping and small potential. By establishing a partially hyperbolic splitting on the fibered solution bundle, we define the Canonical Center Bundle (CCB) as the center subbundle of this splitting, which is shown to be globally trivial. The center bundle admits a representation via Riesz spectral projections of the transfer operator. Furthermore, we show that, in the local regime, the center bundle arising in this framework essentially coincides, in the sense of gap convergence, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29154","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29154/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":"2026-06-30T01:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mj6+V1nN7JS220htDd2ZkR/86zhen0jtIyxrmlfhsQAfQZyW8XCnw2krk6Q3E2QqkfOow2VfxJAoN6M2eDEJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:03:13.946628Z"},"content_sha256":"7a6324941c738b3e2c8c5121a7dd0fed5cb4bdeffa9e91de92cfa2c063f2eac4","schema_version":"1.0","event_id":"sha256:7a6324941c738b3e2c8c5121a7dd0fed5cb4bdeffa9e91de92cfa2c063f2eac4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG/bundle.json","state_url":"https://pith.science/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG/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":"2026-06-30T17:03:13Z","links":{"resolver":"https://pith.science/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG","bundle":"https://pith.science/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG/bundle.json","state":"https://pith.science/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFAYDKQRCLHAN7LX6PWUMFQ2UG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SFAYDKQRCLHAN7LX6PWUMFQ2UG","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":"7dac546531cc349bcdca6d4c074df7917552e403ca86f5db571d89f5020e0d26","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-28T02:23:01Z","title_canon_sha256":"62ba55da33e7e44b26d960e68f816a00c1d6d8935a9a406a77adcc89c56db327"},"schema_version":"1.0","source":{"id":"2606.29154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29154","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29154v1","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29154","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"SFAYDKQRCLHA","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"pith_short_16","alias_value":"SFAYDKQRCLHAN7LX","created_at":"2026-06-30T01:17:54Z"},{"alias_kind":"pith_short_8","alias_value":"SFAYDKQR","created_at":"2026-06-30T01:17:54Z"}],"graph_snapshots":[{"event_id":"sha256:7a6324941c738b3e2c8c5121a7dd0fed5cb4bdeffa9e91de92cfa2c063f2eac4","target":"graph","created_at":"2026-06-30T01:17:54Z","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/2606.29154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce an operator-theoretic framework for long-range operators over general dynamical systems with analytic hopping and small potential. By establishing a partially hyperbolic splitting on the fibered solution bundle, we define the Canonical Center Bundle (CCB) as the center subbundle of this splitting, which is shown to be globally trivial. The center bundle admits a representation via Riesz spectral projections of the transfer operator. Furthermore, we show that, in the local regime, the center bundle arising in this framework essentially coincides, in the sense of gap convergence, wi","authors_text":"Jiangong You, Qi Zhou, Xianzhe Li, Zhenfu Wang","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-28T02:23:01Z","title":"Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29154","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":"sha256:85258f28574aef9b8bbeffceae9918bbe071f81fc64f53475213a3c9ef86628b","target":"record","created_at":"2026-06-30T01:17:54Z","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":"7dac546531cc349bcdca6d4c074df7917552e403ca86f5db571d89f5020e0d26","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-28T02:23:01Z","title_canon_sha256":"62ba55da33e7e44b26d960e68f816a00c1d6d8935a9a406a77adcc89c56db327"},"schema_version":"1.0","source":{"id":"2606.29154","kind":"arxiv","version":1}},"canonical_sha256":"914181aa1112ce06fd77f3ed46161aa194cd65195cccd1bc9ee4733cbf28b040","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"914181aa1112ce06fd77f3ed46161aa194cd65195cccd1bc9ee4733cbf28b040","first_computed_at":"2026-06-30T01:17:54.841292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:54.841292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bMItV+VPgexLY9ca2D65l+xyAaS1MxI36JVYECOoafIYE6/pKkrbsK4o15dF4j8sUsIp6kczxIZZ+c3DgPTJCA==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:54.841976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85258f28574aef9b8bbeffceae9918bbe071f81fc64f53475213a3c9ef86628b","sha256:7a6324941c738b3e2c8c5121a7dd0fed5cb4bdeffa9e91de92cfa2c063f2eac4"],"state_sha256":"607239e40d634a224e0f602e554f4ea0603ba2dabd11942673b837304599bc49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o10PuPuYrOKBDmeiewwxFKgVtWozNJgBTLsEPWggSO+G5D4bMfABmeg6YHeo4L66kxZpWbJSF1xICcOiI8a/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:03:13.948742Z","bundle_sha256":"6261943860b2ef90b78934a1044fec58064eb76b15927073361db4753f44f6e3"}}