{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SVXBHZ2MVQKF575QYRQDCM4WUI","short_pith_number":"pith:SVXBHZ2M","canonical_record":{"source":{"id":"2407.18860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-07-26T16:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"ce9b275dc3dd7d27b24328b1833617db0d80d3ea16ed34b0cb34522a9fffa654","abstract_canon_sha256":"9787a59c732db004d751ec0dec199b19ac4549f888a9f7d53cdd90823b79702c"},"schema_version":"1.0"},"canonical_sha256":"956e13e74cac145effb0c460313396a21c7594f609bdf2016e2e3b78fd9245c1","source":{"kind":"arxiv","id":"2407.18860","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.18860","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"2407.18860v1","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.18860","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"SVXBHZ2MVQKF","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_16","alias_value":"SVXBHZ2MVQKF575Q","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_8","alias_value":"SVXBHZ2M","created_at":"2026-07-05T08:48:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SVXBHZ2MVQKF575QYRQDCM4WUI","target":"record","payload":{"canonical_record":{"source":{"id":"2407.18860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-07-26T16:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"ce9b275dc3dd7d27b24328b1833617db0d80d3ea16ed34b0cb34522a9fffa654","abstract_canon_sha256":"9787a59c732db004d751ec0dec199b19ac4549f888a9f7d53cdd90823b79702c"},"schema_version":"1.0"},"canonical_sha256":"956e13e74cac145effb0c460313396a21c7594f609bdf2016e2e3b78fd9245c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:48:55.600648Z","signature_b64":"I9BxQhbStKPNixkdk/wctOKPNkcQkA5238ZibLO8JbonItqUmeVhTAmJUwhR/2TUE+Tg7jgN+7UVwYUWir8KDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"956e13e74cac145effb0c460313396a21c7594f609bdf2016e2e3b78fd9245c1","last_reissued_at":"2026-07-05T08:48:55.600176Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:48:55.600176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.18860","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":"2026-07-05T08:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wt29vnMXlkQaKqUQq1ZTdGZqCbj63XWpmb2qvNCmp8yWRYLK/89deghNC3apIUB96aX55MKsdy0qXMVJR+C+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:54:26.219568Z"},"content_sha256":"cce1a181ab5f656b2adc20c8f3f8896d2876551159e576ba22dda14fb4d966ec","schema_version":"1.0","event_id":"sha256:cce1a181ab5f656b2adc20c8f3f8896d2876551159e576ba22dda14fb4d966ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SVXBHZ2MVQKF575QYRQDCM4WUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Sublevel Estimates for Form-Valued Functions and Related Results for Radon-like Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Philip T. Gressman","submitted_at":"2024-07-26T16:48:36Z","abstract_excerpt":"Motivated by the testing condition for Radon-Brascamp-Lieb multilinear functionals established in arXiv:2201.12201, this paper is concerned with identifying local conditions on smooth maps $u(t)$ with values in the space of decomposable p-forms on some real vector space V which guarantee uniform integrability of $||u(t)||^{-\\tau}$ over a certain natural, noncompact family of norms. One can loosely regard this problem as a higher-dimensional analogue of establishing uniform bounds for the size of a sublevel set of a function in terms of the size of its derivatives. The resulting theorem relies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.18860","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/2407.18860/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":"2026-07-05T08:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0ETXnuByFokJRvmz6fb1NZmG7LEN13wqAehAS/rOvX+9NJuO+r6FAC+jyq/EyFi0YCIih1dVUNSgrE0UY2EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:54:26.220384Z"},"content_sha256":"581d63f7c1c000d070b1c2c34801ba0f6cf3a8080de01929abeb81e90d6ecc73","schema_version":"1.0","event_id":"sha256:581d63f7c1c000d070b1c2c34801ba0f6cf3a8080de01929abeb81e90d6ecc73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVXBHZ2MVQKF575QYRQDCM4WUI/bundle.json","state_url":"https://pith.science/pith/SVXBHZ2MVQKF575QYRQDCM4WUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVXBHZ2MVQKF575QYRQDCM4WUI/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":"2026-08-18T01:54:26Z","links":{"resolver":"https://pith.science/pith/SVXBHZ2MVQKF575QYRQDCM4WUI","bundle":"https://pith.science/pith/SVXBHZ2MVQKF575QYRQDCM4WUI/bundle.json","state":"https://pith.science/pith/SVXBHZ2MVQKF575QYRQDCM4WUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVXBHZ2MVQKF575QYRQDCM4WUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SVXBHZ2MVQKF575QYRQDCM4WUI","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":"9787a59c732db004d751ec0dec199b19ac4549f888a9f7d53cdd90823b79702c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-07-26T16:48:36Z","title_canon_sha256":"ce9b275dc3dd7d27b24328b1833617db0d80d3ea16ed34b0cb34522a9fffa654"},"schema_version":"1.0","source":{"id":"2407.18860","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.18860","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"2407.18860v1","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.18860","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"SVXBHZ2MVQKF","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_16","alias_value":"SVXBHZ2MVQKF575Q","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_8","alias_value":"SVXBHZ2M","created_at":"2026-07-05T08:48:55Z"}],"graph_snapshots":[{"event_id":"sha256:581d63f7c1c000d070b1c2c34801ba0f6cf3a8080de01929abeb81e90d6ecc73","target":"graph","created_at":"2026-07-05T08:48:55Z","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/2407.18860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the testing condition for Radon-Brascamp-Lieb multilinear functionals established in arXiv:2201.12201, this paper is concerned with identifying local conditions on smooth maps $u(t)$ with values in the space of decomposable p-forms on some real vector space V which guarantee uniform integrability of $||u(t)||^{-\\tau}$ over a certain natural, noncompact family of norms. One can loosely regard this problem as a higher-dimensional analogue of establishing uniform bounds for the size of a sublevel set of a function in terms of the size of its derivatives. The resulting theorem relies ","authors_text":"Philip T. Gressman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-07-26T16:48:36Z","title":"Generalized Sublevel Estimates for Form-Valued Functions and Related Results for Radon-like Transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.18860","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:cce1a181ab5f656b2adc20c8f3f8896d2876551159e576ba22dda14fb4d966ec","target":"record","created_at":"2026-07-05T08:48:55Z","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":"9787a59c732db004d751ec0dec199b19ac4549f888a9f7d53cdd90823b79702c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-07-26T16:48:36Z","title_canon_sha256":"ce9b275dc3dd7d27b24328b1833617db0d80d3ea16ed34b0cb34522a9fffa654"},"schema_version":"1.0","source":{"id":"2407.18860","kind":"arxiv","version":1}},"canonical_sha256":"956e13e74cac145effb0c460313396a21c7594f609bdf2016e2e3b78fd9245c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"956e13e74cac145effb0c460313396a21c7594f609bdf2016e2e3b78fd9245c1","first_computed_at":"2026-07-05T08:48:55.600176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:48:55.600176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I9BxQhbStKPNixkdk/wctOKPNkcQkA5238ZibLO8JbonItqUmeVhTAmJUwhR/2TUE+Tg7jgN+7UVwYUWir8KDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:48:55.600648Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.18860","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cce1a181ab5f656b2adc20c8f3f8896d2876551159e576ba22dda14fb4d966ec","sha256:581d63f7c1c000d070b1c2c34801ba0f6cf3a8080de01929abeb81e90d6ecc73"],"state_sha256":"5f5c5800c768cb8a30fe6728a34f70e1d15da598ff3642bd3dd8a58575a4adce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2qzHHNjKw+tEsIyQy9hAT3lIj3NDaiG4cSp6DyNshEXcONY2DoYy3BBLRnQrPA5AUXWVxbu/zi6DG5SpXeeCCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T01:54:26.225830Z","bundle_sha256":"8a65e96baf8a447100e438246997ec0baa48ef42d033b7e8c4898b7d43cbefda"}}