{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PCWRZHCBYDTGJS7BXFQQ4MKH2O","short_pith_number":"pith:PCWRZHCB","canonical_record":{"source":{"id":"2601.10162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-01-15T08:04:13Z","cross_cats_sorted":[],"title_canon_sha256":"b697ccc8e7f4ed98175f7f265e19fbb3aa4e67642d7e4c0969aa95b8115f6c01","abstract_canon_sha256":"7557b674b7beda49c31e4cf2b6f84f86b13f0d7d1a0945cab526a6c4740f6e35"},"schema_version":"1.0"},"canonical_sha256":"78ad1c9c41c0e664cbe1b9610e3147d3a0973bde3f4483db141a78b48485bc93","source":{"kind":"arxiv","id":"2601.10162","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.10162","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"arxiv_version","alias_value":"2601.10162v3","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.10162","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"pith_short_12","alias_value":"PCWRZHCBYDTG","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"pith_short_16","alias_value":"PCWRZHCBYDTGJS7B","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"pith_short_8","alias_value":"PCWRZHCB","created_at":"2026-06-05T01:15:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PCWRZHCBYDTGJS7BXFQQ4MKH2O","target":"record","payload":{"canonical_record":{"source":{"id":"2601.10162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-01-15T08:04:13Z","cross_cats_sorted":[],"title_canon_sha256":"b697ccc8e7f4ed98175f7f265e19fbb3aa4e67642d7e4c0969aa95b8115f6c01","abstract_canon_sha256":"7557b674b7beda49c31e4cf2b6f84f86b13f0d7d1a0945cab526a6c4740f6e35"},"schema_version":"1.0"},"canonical_sha256":"78ad1c9c41c0e664cbe1b9610e3147d3a0973bde3f4483db141a78b48485bc93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:18.990022Z","signature_b64":"qjs03xjUW2wBqfhX1MtASvEkxRCP9wrFGovRUackPPpqqVrTrIuZ5k1OFopnRGPwvYdD5KTkjkDTp4yFCXdPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78ad1c9c41c0e664cbe1b9610e3147d3a0973bde3f4483db141a78b48485bc93","last_reissued_at":"2026-06-05T01:15:18.989547Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:18.989547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.10162","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-05T01:15:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vr+ttGaFwpsOPPZY12snE2gDhbqZKDwXICazVqrHFxxNC11kRgXVGsD6I6h4z1Ju8iMUDmQmY/wUWKfAbhOcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:23:15.721082Z"},"content_sha256":"d95f4d928d476fc51f4a119aceb86d16e6ca1cf5bcf5a0bbf3d98edd6fec4887","schema_version":"1.0","event_id":"sha256:d95f4d928d476fc51f4a119aceb86d16e6ca1cf5bcf5a0bbf3d98edd6fec4887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PCWRZHCBYDTGJS7BXFQQ4MKH2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toeplitz Operators on Quaternionic Fock Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chao Zu, Yufeng Lu, Zhaopeng Lin","submitted_at":"2026-01-15T08:04:13Z","abstract_excerpt":"We characterize boundedness and compactness of Toeplitz operators on quaternionic Fock spaces with positive measure symbols and slice-function symbols in \\(\\mathrm{BMO}^1\\). For positive measure symbols, we derive criteria using normalized reproducing kernels and symmetric box averages, while for slice \\(\\mathrm{BMO}^1\\) symbols, the characterizations rely on the Berezin transform. We further introduce a global quaternionic Fock space \\(F_\\alpha^p\\) to define Toeplitz operators with real-valued measure symbols; this space is built by integrating slice regular functions over all complex slices "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.10162","kind":"arxiv","version":3},"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/2601.10162/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":"2026-06-05T01:15:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cWUagZRNbTNky8UVSatr88HnQ7NsqdmxHej1BWcMjFeZzg+hhTyQMo5SS02tGHIqgDHyVpJxLnQnHaoNzc06Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:23:15.721466Z"},"content_sha256":"fdf34643e30f0206f58bc212ceaef278eb5bc6d80ae34e977bc7850acb0e09e4","schema_version":"1.0","event_id":"sha256:fdf34643e30f0206f58bc212ceaef278eb5bc6d80ae34e977bc7850acb0e09e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O/bundle.json","state_url":"https://pith.science/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O/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":"2026-07-05T04:23:15Z","links":{"resolver":"https://pith.science/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O","bundle":"https://pith.science/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O/bundle.json","state":"https://pith.science/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCWRZHCBYDTGJS7BXFQQ4MKH2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PCWRZHCBYDTGJS7BXFQQ4MKH2O","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":"7557b674b7beda49c31e4cf2b6f84f86b13f0d7d1a0945cab526a6c4740f6e35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-01-15T08:04:13Z","title_canon_sha256":"b697ccc8e7f4ed98175f7f265e19fbb3aa4e67642d7e4c0969aa95b8115f6c01"},"schema_version":"1.0","source":{"id":"2601.10162","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.10162","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"arxiv_version","alias_value":"2601.10162v3","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.10162","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"pith_short_12","alias_value":"PCWRZHCBYDTG","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"pith_short_16","alias_value":"PCWRZHCBYDTGJS7B","created_at":"2026-06-05T01:15:18Z"},{"alias_kind":"pith_short_8","alias_value":"PCWRZHCB","created_at":"2026-06-05T01:15:18Z"}],"graph_snapshots":[{"event_id":"sha256:fdf34643e30f0206f58bc212ceaef278eb5bc6d80ae34e977bc7850acb0e09e4","target":"graph","created_at":"2026-06-05T01:15:18Z","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/2601.10162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We characterize boundedness and compactness of Toeplitz operators on quaternionic Fock spaces with positive measure symbols and slice-function symbols in \\(\\mathrm{BMO}^1\\). For positive measure symbols, we derive criteria using normalized reproducing kernels and symmetric box averages, while for slice \\(\\mathrm{BMO}^1\\) symbols, the characterizations rely on the Berezin transform. We further introduce a global quaternionic Fock space \\(F_\\alpha^p\\) to define Toeplitz operators with real-valued measure symbols; this space is built by integrating slice regular functions over all complex slices ","authors_text":"Chao Zu, Yufeng Lu, Zhaopeng Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-01-15T08:04:13Z","title":"Toeplitz Operators on Quaternionic Fock Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.10162","kind":"arxiv","version":3},"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:d95f4d928d476fc51f4a119aceb86d16e6ca1cf5bcf5a0bbf3d98edd6fec4887","target":"record","created_at":"2026-06-05T01:15:18Z","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":"7557b674b7beda49c31e4cf2b6f84f86b13f0d7d1a0945cab526a6c4740f6e35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-01-15T08:04:13Z","title_canon_sha256":"b697ccc8e7f4ed98175f7f265e19fbb3aa4e67642d7e4c0969aa95b8115f6c01"},"schema_version":"1.0","source":{"id":"2601.10162","kind":"arxiv","version":3}},"canonical_sha256":"78ad1c9c41c0e664cbe1b9610e3147d3a0973bde3f4483db141a78b48485bc93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78ad1c9c41c0e664cbe1b9610e3147d3a0973bde3f4483db141a78b48485bc93","first_computed_at":"2026-06-05T01:15:18.989547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:18.989547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qjs03xjUW2wBqfhX1MtASvEkxRCP9wrFGovRUackPPpqqVrTrIuZ5k1OFopnRGPwvYdD5KTkjkDTp4yFCXdPCg==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:18.990022Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.10162","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d95f4d928d476fc51f4a119aceb86d16e6ca1cf5bcf5a0bbf3d98edd6fec4887","sha256:fdf34643e30f0206f58bc212ceaef278eb5bc6d80ae34e977bc7850acb0e09e4"],"state_sha256":"3ae5dd833655fb5ac267e4a7dc39b066cd2f9eed191d68439b5b3c16b01dae52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2okh1U/8wYpxnbpz8L6g/Vp3Ulb+ESWMfngVvNIY5V2q6RG4AeWO/77/jHwMEgSpJfjt8Veo9OnpQJc8DNkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T04:23:15.723442Z","bundle_sha256":"b4e215c9439df84f16ce03c1e9cebc54f5ca175b2604e33d79df477e65551d87"}}