{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RV44HZHKP3SKWJHOYHTSVZ43EL","short_pith_number":"pith:RV44HZHK","canonical_record":{"source":{"id":"2607.18160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-20T17:04:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f136b15f4e9c9b1b7aa085b08ba9b7a24c3d5cb94be40966b709356531f5e4f3","abstract_canon_sha256":"0064455454c2a54627e9eb195305c8ae8452071b091cc590176ef5a0e2a2120c"},"schema_version":"1.0"},"canonical_sha256":"8d79c3e4ea7ee4ab24eec1e72ae79b22dcecd4961608573d151afdf2359d6bba","source":{"kind":"arxiv","id":"2607.18160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18160","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18160v1","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18160","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"RV44HZHKP3SK","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"pith_short_16","alias_value":"RV44HZHKP3SKWJHO","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"pith_short_8","alias_value":"RV44HZHK","created_at":"2026-07-21T02:22:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RV44HZHKP3SKWJHOYHTSVZ43EL","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-20T17:04:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f136b15f4e9c9b1b7aa085b08ba9b7a24c3d5cb94be40966b709356531f5e4f3","abstract_canon_sha256":"0064455454c2a54627e9eb195305c8ae8452071b091cc590176ef5a0e2a2120c"},"schema_version":"1.0"},"canonical_sha256":"8d79c3e4ea7ee4ab24eec1e72ae79b22dcecd4961608573d151afdf2359d6bba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T02:22:19.664909Z","signature_b64":"qLZENmF1iqqeA/+hWo3Fhb1cLUaFBMiaJj9kv7gB7WcFxRO94tqtbDc22fCayggGzevrtGxLopGEnI7Uf5X9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d79c3e4ea7ee4ab24eec1e72ae79b22dcecd4961608573d151afdf2359d6bba","last_reissued_at":"2026-07-21T02:22:19.664159Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T02:22:19.664159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18160","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":"2026-07-21T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ht8B+3SHMc12WTF9d7xOOnj6dkeWBJGln2uCa31CV1+7OBPVhSV2ZZqq6Hf8HoZYBXtD3sNbttabCQF4Tne7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:21:39.066186Z"},"content_sha256":"d67a38ace15ce240b559d9cfbf283394c8d774e10c4148f92861fa37810f3719","schema_version":"1.0","event_id":"sha256:d67a38ace15ce240b559d9cfbf283394c8d774e10c4148f92861fa37810f3719"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RV44HZHKP3SKWJHOYHTSVZ43EL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete analogues in harmonic analysis: Multi-parameter Radon averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Agnieszka Hejna-{\\L}y\\.zwa, Bartosz Langowski, Hoyoung Song, James Wright, Joonil Kim, Mariusz Mirek","submitted_at":"2026-07-20T17:04:10Z","abstract_excerpt":"In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method within the framework of Discrete Analogues in Harmonic Analysis. In particular, this gives quantitative estimates for these averages and their underlying Fourier multipliers which reveals an interesting major-arcs rigidity phenomenon. As a consequence, we completely resolve in the affirmative the multi-parameter Bellow--Furstenberg problem in pointwise ergodic theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18160","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/2607.18160/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":"2026-07-21T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkJFaO9aRl6zBfScYRrxZnSf3uJZDNhsLCc6/qDohtn0ZsQD/Gs3lzeNm9EwSRqgS5aLljZmjwGPORDSzLyWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:21:39.067116Z"},"content_sha256":"df0efbfc194e67dde3a572e91d9d325bb5efd018336d27cc5ca26d6f1932d494","schema_version":"1.0","event_id":"sha256:df0efbfc194e67dde3a572e91d9d325bb5efd018336d27cc5ca26d6f1932d494"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RV44HZHKP3SKWJHOYHTSVZ43EL/bundle.json","state_url":"https://pith.science/pith/RV44HZHKP3SKWJHOYHTSVZ43EL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RV44HZHKP3SKWJHOYHTSVZ43EL/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":"2026-08-12T08:21:39Z","links":{"resolver":"https://pith.science/pith/RV44HZHKP3SKWJHOYHTSVZ43EL","bundle":"https://pith.science/pith/RV44HZHKP3SKWJHOYHTSVZ43EL/bundle.json","state":"https://pith.science/pith/RV44HZHKP3SKWJHOYHTSVZ43EL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RV44HZHKP3SKWJHOYHTSVZ43EL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RV44HZHKP3SKWJHOYHTSVZ43EL","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":"0064455454c2a54627e9eb195305c8ae8452071b091cc590176ef5a0e2a2120c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-20T17:04:10Z","title_canon_sha256":"f136b15f4e9c9b1b7aa085b08ba9b7a24c3d5cb94be40966b709356531f5e4f3"},"schema_version":"1.0","source":{"id":"2607.18160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18160","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18160v1","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18160","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"RV44HZHKP3SK","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"pith_short_16","alias_value":"RV44HZHKP3SKWJHO","created_at":"2026-07-21T02:22:19Z"},{"alias_kind":"pith_short_8","alias_value":"RV44HZHK","created_at":"2026-07-21T02:22:19Z"}],"graph_snapshots":[{"event_id":"sha256:df0efbfc194e67dde3a572e91d9d325bb5efd018336d27cc5ca26d6f1932d494","target":"graph","created_at":"2026-07-21T02:22:19Z","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/2607.18160/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method within the framework of Discrete Analogues in Harmonic Analysis. In particular, this gives quantitative estimates for these averages and their underlying Fourier multipliers which reveals an interesting major-arcs rigidity phenomenon. As a consequence, we completely resolve in the affirmative the multi-parameter Bellow--Furstenberg problem in pointwise ergodic theory.","authors_text":"Agnieszka Hejna-{\\L}y\\.zwa, Bartosz Langowski, Hoyoung Song, James Wright, Joonil Kim, Mariusz Mirek","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-20T17:04:10Z","title":"Discrete analogues in harmonic analysis: Multi-parameter Radon averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18160","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:d67a38ace15ce240b559d9cfbf283394c8d774e10c4148f92861fa37810f3719","target":"record","created_at":"2026-07-21T02:22:19Z","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":"0064455454c2a54627e9eb195305c8ae8452071b091cc590176ef5a0e2a2120c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-20T17:04:10Z","title_canon_sha256":"f136b15f4e9c9b1b7aa085b08ba9b7a24c3d5cb94be40966b709356531f5e4f3"},"schema_version":"1.0","source":{"id":"2607.18160","kind":"arxiv","version":1}},"canonical_sha256":"8d79c3e4ea7ee4ab24eec1e72ae79b22dcecd4961608573d151afdf2359d6bba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d79c3e4ea7ee4ab24eec1e72ae79b22dcecd4961608573d151afdf2359d6bba","first_computed_at":"2026-07-21T02:22:19.664159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T02:22:19.664159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qLZENmF1iqqeA/+hWo3Fhb1cLUaFBMiaJj9kv7gB7WcFxRO94tqtbDc22fCayggGzevrtGxLopGEnI7Uf5X9Bg==","signature_status":"signed_v1","signed_at":"2026-07-21T02:22:19.664909Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d67a38ace15ce240b559d9cfbf283394c8d774e10c4148f92861fa37810f3719","sha256:df0efbfc194e67dde3a572e91d9d325bb5efd018336d27cc5ca26d6f1932d494"],"state_sha256":"c6ab5e1a59f3bf2fba9f8c049b2e7ab3d9db1db8244276d022e763db120149d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VgzBFJEqH+mP9kx6HCErX4Fs85OalDzC5LP6HbSxVX6if6yVoB6Y2woQi94cTbKtHA3VSH+6YbyCxxrkwlboDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T08:21:39.094210Z","bundle_sha256":"c30994b2f5dd372834fddeebb33bb2567879e8cd1fe382fcee9249f16df6bbf9"}}