{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:J76Z2MISRBDZWSTN6TKSNSERZ4","short_pith_number":"pith:J76Z2MIS","canonical_record":{"source":{"id":"2507.00998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-01T17:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"9bb09ff73417efb3e30db691103fc3768dc01660d9a278a6c3b3b72443dc5a9c","abstract_canon_sha256":"80c59224464ce225de4c39a4e848c1259675b805851eab9c1ad12875ee5f0258"},"schema_version":"1.0"},"canonical_sha256":"4ffd9d311288479b4a6df4d526c891cf0d197447fcca26a92135ca5bbd6f181b","source":{"kind":"arxiv","id":"2507.00998","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00998","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00998v1","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00998","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"pith_short_12","alias_value":"J76Z2MISRBDZ","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"J76Z2MISRBDZWSTN","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"J76Z2MIS","created_at":"2026-07-05T11:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:J76Z2MISRBDZWSTN6TKSNSERZ4","target":"record","payload":{"canonical_record":{"source":{"id":"2507.00998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-01T17:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"9bb09ff73417efb3e30db691103fc3768dc01660d9a278a6c3b3b72443dc5a9c","abstract_canon_sha256":"80c59224464ce225de4c39a4e848c1259675b805851eab9c1ad12875ee5f0258"},"schema_version":"1.0"},"canonical_sha256":"4ffd9d311288479b4a6df4d526c891cf0d197447fcca26a92135ca5bbd6f181b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:30:19.422082Z","signature_b64":"f9LgUB9wfRrLNpTYAW7KNQTnWatMPYhkoumRw0HXFIbdwmLTdnQi5DfIWus6qTenJSJQnNTdMuJoMxp1smb8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ffd9d311288479b4a6df4d526c891cf0d197447fcca26a92135ca5bbd6f181b","last_reissued_at":"2026-07-05T11:30:19.421480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:30:19.421480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.00998","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":"2026-07-05T11:30:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kh28rQvtp6xg5jDFjar1KxSNhQ8DEE8hb+IaPyfTfpe1OG9kRxPWZHorB2TwRzJeMFV3cxDOCpO+xb2g28uoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:37:43.046170Z"},"content_sha256":"b25894200b68b2603d47d431b0aab9e0af3117d4c14bd2c7df59d588c1e9827c","schema_version":"1.0","event_id":"sha256:b25894200b68b2603d47d431b0aab9e0af3117d4c14bd2c7df59d588c1e9827c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:J76Z2MISRBDZWSTN6TKSNSERZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brown-Halmos type characterization for the tetrablock","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Milan Kumar Mal, Paramita Pramanick, Shubham Jain, Surjit Kumar","submitted_at":"2025-07-01T17:50:10Z","abstract_excerpt":"In this note, we obtain a Brown-Halmos type characterization for Toeplitz operators on the Hardy space associated with the tetrablock. As an application, we show that the zero operator is the only compact Toeplitz operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00998","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/2507.00998/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":"2026-07-05T11:30:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xPoAj0b8lUGNHYtngio+VAxYPXd5NKUuojcMGchxTTKN7ateUJfjmmokMLPO/feNe1pFRBGD4DH2gLkLuQgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:37:43.046682Z"},"content_sha256":"f9dbaa6a2ff467c98323b4f24cc155a450aac7bb02693f36f54aa78dc18e228e","schema_version":"1.0","event_id":"sha256:f9dbaa6a2ff467c98323b4f24cc155a450aac7bb02693f36f54aa78dc18e228e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J76Z2MISRBDZWSTN6TKSNSERZ4/bundle.json","state_url":"https://pith.science/pith/J76Z2MISRBDZWSTN6TKSNSERZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J76Z2MISRBDZWSTN6TKSNSERZ4/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":"2026-08-08T23:37:43Z","links":{"resolver":"https://pith.science/pith/J76Z2MISRBDZWSTN6TKSNSERZ4","bundle":"https://pith.science/pith/J76Z2MISRBDZWSTN6TKSNSERZ4/bundle.json","state":"https://pith.science/pith/J76Z2MISRBDZWSTN6TKSNSERZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J76Z2MISRBDZWSTN6TKSNSERZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J76Z2MISRBDZWSTN6TKSNSERZ4","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":"80c59224464ce225de4c39a4e848c1259675b805851eab9c1ad12875ee5f0258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-01T17:50:10Z","title_canon_sha256":"9bb09ff73417efb3e30db691103fc3768dc01660d9a278a6c3b3b72443dc5a9c"},"schema_version":"1.0","source":{"id":"2507.00998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00998","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00998v1","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00998","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"pith_short_12","alias_value":"J76Z2MISRBDZ","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"J76Z2MISRBDZWSTN","created_at":"2026-07-05T11:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"J76Z2MIS","created_at":"2026-07-05T11:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:f9dbaa6a2ff467c98323b4f24cc155a450aac7bb02693f36f54aa78dc18e228e","target":"graph","created_at":"2026-07-05T11:30:19Z","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/2507.00998/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we obtain a Brown-Halmos type characterization for Toeplitz operators on the Hardy space associated with the tetrablock. As an application, we show that the zero operator is the only compact Toeplitz operator.","authors_text":"Milan Kumar Mal, Paramita Pramanick, Shubham Jain, Surjit Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-01T17:50:10Z","title":"Brown-Halmos type characterization for the tetrablock"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00998","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:b25894200b68b2603d47d431b0aab9e0af3117d4c14bd2c7df59d588c1e9827c","target":"record","created_at":"2026-07-05T11:30:19Z","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":"80c59224464ce225de4c39a4e848c1259675b805851eab9c1ad12875ee5f0258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-01T17:50:10Z","title_canon_sha256":"9bb09ff73417efb3e30db691103fc3768dc01660d9a278a6c3b3b72443dc5a9c"},"schema_version":"1.0","source":{"id":"2507.00998","kind":"arxiv","version":1}},"canonical_sha256":"4ffd9d311288479b4a6df4d526c891cf0d197447fcca26a92135ca5bbd6f181b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ffd9d311288479b4a6df4d526c891cf0d197447fcca26a92135ca5bbd6f181b","first_computed_at":"2026-07-05T11:30:19.421480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:30:19.421480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9LgUB9wfRrLNpTYAW7KNQTnWatMPYhkoumRw0HXFIbdwmLTdnQi5DfIWus6qTenJSJQnNTdMuJoMxp1smb8AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:30:19.422082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.00998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b25894200b68b2603d47d431b0aab9e0af3117d4c14bd2c7df59d588c1e9827c","sha256:f9dbaa6a2ff467c98323b4f24cc155a450aac7bb02693f36f54aa78dc18e228e"],"state_sha256":"df40d263ebf2251b6741e9c91414566b6744db0937cafec30d103f5b963ffad5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Na/MvVK7G161GG2BFiAgHM5ZzQYbVGwBI5fNkuggYhorr2PmBq9gASUP9AizUQwiM9szVYeC5Sos6/TllrnEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:37:43.050828Z","bundle_sha256":"e30f1c8743f1e08696c1c8ddc8288e99f68e371052812e39ea2448230a708510"}}