{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YYHM6JTTLAFJHY3J62B7RO6RBF","short_pith_number":"pith:YYHM6JTT","canonical_record":{"source":{"id":"1009.5569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-28T13:50:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"e8648c63be62aa832a31d652ddb582f3c3379c2bcb23d905ff6f2f5cb0022f8d","abstract_canon_sha256":"f67fa01d2d4303adb9f4a4d514fd436f6ef3597d468800c453cb1238f719fada"},"schema_version":"1.0"},"canonical_sha256":"c60ecf2673580a93e369f683f8bbd10958a5ca1583968a15bf68951e86dc6b80","source":{"kind":"arxiv","id":"1009.5569","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5569","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5569v2","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5569","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"YYHM6JTTLAFJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YYHM6JTTLAFJHY3J","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YYHM6JTT","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YYHM6JTTLAFJHY3J62B7RO6RBF","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-28T13:50:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"e8648c63be62aa832a31d652ddb582f3c3379c2bcb23d905ff6f2f5cb0022f8d","abstract_canon_sha256":"f67fa01d2d4303adb9f4a4d514fd436f6ef3597d468800c453cb1238f719fada"},"schema_version":"1.0"},"canonical_sha256":"c60ecf2673580a93e369f683f8bbd10958a5ca1583968a15bf68951e86dc6b80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:55.486994Z","signature_b64":"qW/v9pSMrkIJuHOs/Jzhq/7nc+C36CrdziEBGcE8n9L4g0ZIDFiuJFoBZkyUt8bRpk8yTWMnxjB5OLli9U3gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c60ecf2673580a93e369f683f8bbd10958a5ca1583968a15bf68951e86dc6b80","last_reissued_at":"2026-05-18T04:29:55.486479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:55.486479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5569","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f3XB6MXq9m8VuftlpRER2MTygl6Wxsoz1kZXsffgIKKJq7/JuLYffw52rOcp0oI17YuqxnGAJEYhlOgJApgmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:13:29.696150Z"},"content_sha256":"a872736b9f33c5e7cbe55f452dd4cb607c47e0bccead2c621710c5aeb9b5596d","schema_version":"1.0","event_id":"sha256:a872736b9f33c5e7cbe55f452dd4cb607c47e0bccead2c621710c5aeb9b5596d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YYHM6JTTLAFJHY3J62B7RO6RBF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Square functions associated to Schrodinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"I. Abu-Falahah, J. L. Torrea, P. R. Stinga","submitted_at":"2010-09-28T13:50:04Z","abstract_excerpt":"We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrodinger operators of the form $L=-\\Delta+V$, where the nonnegative potential $V$ satisfies a reverse Holder inequality. The main idea is to sharpen the well known localization method introduced by Z. Shen. Our results can be regarded as alternative proofs of the boundedness in $H^1$, $L^p$ and $BMO$ of classical $L$-square functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5569","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T04:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Fje8wuMo7GOB+IM+fnZGtqGZ4dIE8r2F+KtN03Cc+cRxL27xhnSS93+YTjY+G/1YvLg9br7IEW/u7iCMqPVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:13:29.696493Z"},"content_sha256":"a66d120ae6cd84a5d447dec7843be63795f4c71fd29b96619cfee2901ba1408f","schema_version":"1.0","event_id":"sha256:a66d120ae6cd84a5d447dec7843be63795f4c71fd29b96619cfee2901ba1408f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYHM6JTTLAFJHY3J62B7RO6RBF/bundle.json","state_url":"https://pith.science/pith/YYHM6JTTLAFJHY3J62B7RO6RBF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYHM6JTTLAFJHY3J62B7RO6RBF/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":"2026-06-26T17:13:29Z","links":{"resolver":"https://pith.science/pith/YYHM6JTTLAFJHY3J62B7RO6RBF","bundle":"https://pith.science/pith/YYHM6JTTLAFJHY3J62B7RO6RBF/bundle.json","state":"https://pith.science/pith/YYHM6JTTLAFJHY3J62B7RO6RBF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYHM6JTTLAFJHY3J62B7RO6RBF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YYHM6JTTLAFJHY3J62B7RO6RBF","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":"f67fa01d2d4303adb9f4a4d514fd436f6ef3597d468800c453cb1238f719fada","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-28T13:50:04Z","title_canon_sha256":"e8648c63be62aa832a31d652ddb582f3c3379c2bcb23d905ff6f2f5cb0022f8d"},"schema_version":"1.0","source":{"id":"1009.5569","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5569","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5569v2","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5569","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"YYHM6JTTLAFJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YYHM6JTTLAFJHY3J","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YYHM6JTT","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:a66d120ae6cd84a5d447dec7843be63795f4c71fd29b96619cfee2901ba1408f","target":"graph","created_at":"2026-05-18T04:29:55Z","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"},"paper":{"abstract_excerpt":"We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrodinger operators of the form $L=-\\Delta+V$, where the nonnegative potential $V$ satisfies a reverse Holder inequality. The main idea is to sharpen the well known localization method introduced by Z. Shen. Our results can be regarded as alternative proofs of the boundedness in $H^1$, $L^p$ and $BMO$ of classical $L$-square functions.","authors_text":"I. Abu-Falahah, J. L. Torrea, P. R. Stinga","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-28T13:50:04Z","title":"Square functions associated to Schrodinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5569","kind":"arxiv","version":2},"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:a872736b9f33c5e7cbe55f452dd4cb607c47e0bccead2c621710c5aeb9b5596d","target":"record","created_at":"2026-05-18T04:29:55Z","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":"f67fa01d2d4303adb9f4a4d514fd436f6ef3597d468800c453cb1238f719fada","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-28T13:50:04Z","title_canon_sha256":"e8648c63be62aa832a31d652ddb582f3c3379c2bcb23d905ff6f2f5cb0022f8d"},"schema_version":"1.0","source":{"id":"1009.5569","kind":"arxiv","version":2}},"canonical_sha256":"c60ecf2673580a93e369f683f8bbd10958a5ca1583968a15bf68951e86dc6b80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c60ecf2673580a93e369f683f8bbd10958a5ca1583968a15bf68951e86dc6b80","first_computed_at":"2026-05-18T04:29:55.486479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:55.486479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qW/v9pSMrkIJuHOs/Jzhq/7nc+C36CrdziEBGcE8n9L4g0ZIDFiuJFoBZkyUt8bRpk8yTWMnxjB5OLli9U3gAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:55.486994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5569","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a872736b9f33c5e7cbe55f452dd4cb607c47e0bccead2c621710c5aeb9b5596d","sha256:a66d120ae6cd84a5d447dec7843be63795f4c71fd29b96619cfee2901ba1408f"],"state_sha256":"095473c4ca24958c93f15fc53f966dd02914cb62f99e18998d8be5348ee7d388"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MeGcBBb4aO8y56HvEsFplD2foY3CWa1m5Bl1usH4xgm2pvVBvTK6+DYJvqpL+W2T8lKwsWtMGmjEF9p6ilYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:13:29.698419Z","bundle_sha256":"edf807e60a2d7be6061f1d01b805116d3d9ac389de21a3d71a2d2c78a3abfa63"}}