{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HLKFWWVVGJZKHKQPF4NS6G352Q","short_pith_number":"pith:HLKFWWVV","canonical_record":{"source":{"id":"1012.4184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-19T16:46:27Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"19c07afb69c5acf1c57bb5a7ce1e0b99e22a070a19d65096802ae0ad7484cdff","abstract_canon_sha256":"a437ebcc168e6e1a30effed9ee2a276a0124dc2aa35e1bf3d022b402452da994"},"schema_version":"1.0"},"canonical_sha256":"3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da","source":{"kind":"arxiv","id":"1012.4184","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4184","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4184v1","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4184","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"HLKFWWVVGJZK","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HLKFWWVVGJZKHKQP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HLKFWWVV","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HLKFWWVVGJZKHKQPF4NS6G352Q","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-19T16:46:27Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"19c07afb69c5acf1c57bb5a7ce1e0b99e22a070a19d65096802ae0ad7484cdff","abstract_canon_sha256":"a437ebcc168e6e1a30effed9ee2a276a0124dc2aa35e1bf3d022b402452da994"},"schema_version":"1.0"},"canonical_sha256":"3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:04.472279Z","signature_b64":"Humu9IEiYk8xxiUBdJ9L0WgrCiCtuwOv+7hX5QfTmr6Dc1bXPYGvtxePaMTA7MI6OogzW6vYc4//1hj0O0/mBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da","last_reissued_at":"2026-05-18T02:52:04.471852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:04.471852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4184","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":"2026-05-18T02:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFct+T9xOPkSYgENUDQFS62SPhZYS0BXgmNOCY2bZaJ+2n+8ObyWAQKvGalulBeh3xFA/4qB6DwKl0RT/De/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:04:13.624427Z"},"content_sha256":"cdea7a01f7f01467c3d1c680be44c9995ce4829d4d264b75ce7c6db3e47204c0","schema_version":"1.0","event_id":"sha256:cdea7a01f7f01467c3d1c680be44c9995ce4829d4d264b75ce7c6db3e47204c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HLKFWWVVGJZKHKQPF4NS6G352Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertical versus conical square functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jos\\'e Maria Martell, Pascal Auscher (LM-Orsay), Steve Hofmann","submitted_at":"2010-12-19T16:46:27Z","abstract_excerpt":"We study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4184","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":""},"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":"2026-05-18T02:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2Sf/6RbJD7RqR/vKKuaUgxd9A53VBgm/WiKOQOzhsywXBR4IWQeTbU+UKFBY8aBsfj2gH5f7N+P6KyYapOlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:04:13.624766Z"},"content_sha256":"a6e9d93469e2dc1aee616e09c42366b41d57821f5b8f9f4d997c4a0c6d3becb5","schema_version":"1.0","event_id":"sha256:a6e9d93469e2dc1aee616e09c42366b41d57821f5b8f9f4d997c4a0c6d3becb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLKFWWVVGJZKHKQPF4NS6G352Q/bundle.json","state_url":"https://pith.science/pith/HLKFWWVVGJZKHKQPF4NS6G352Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLKFWWVVGJZKHKQPF4NS6G352Q/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":"2026-06-07T05:04:13Z","links":{"resolver":"https://pith.science/pith/HLKFWWVVGJZKHKQPF4NS6G352Q","bundle":"https://pith.science/pith/HLKFWWVVGJZKHKQPF4NS6G352Q/bundle.json","state":"https://pith.science/pith/HLKFWWVVGJZKHKQPF4NS6G352Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLKFWWVVGJZKHKQPF4NS6G352Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HLKFWWVVGJZKHKQPF4NS6G352Q","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":"a437ebcc168e6e1a30effed9ee2a276a0124dc2aa35e1bf3d022b402452da994","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-19T16:46:27Z","title_canon_sha256":"19c07afb69c5acf1c57bb5a7ce1e0b99e22a070a19d65096802ae0ad7484cdff"},"schema_version":"1.0","source":{"id":"1012.4184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4184","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4184v1","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4184","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"HLKFWWVVGJZK","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HLKFWWVVGJZKHKQP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HLKFWWVV","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:a6e9d93469e2dc1aee616e09c42366b41d57821f5b8f9f4d997c4a0c6d3becb5","target":"graph","created_at":"2026-05-18T02:52:04Z","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 study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator.","authors_text":"Jos\\'e Maria Martell, Pascal Auscher (LM-Orsay), Steve Hofmann","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-19T16:46:27Z","title":"Vertical versus conical square functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4184","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:cdea7a01f7f01467c3d1c680be44c9995ce4829d4d264b75ce7c6db3e47204c0","target":"record","created_at":"2026-05-18T02:52:04Z","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":"a437ebcc168e6e1a30effed9ee2a276a0124dc2aa35e1bf3d022b402452da994","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-19T16:46:27Z","title_canon_sha256":"19c07afb69c5acf1c57bb5a7ce1e0b99e22a070a19d65096802ae0ad7484cdff"},"schema_version":"1.0","source":{"id":"1012.4184","kind":"arxiv","version":1}},"canonical_sha256":"3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da","first_computed_at":"2026-05-18T02:52:04.471852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:04.471852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Humu9IEiYk8xxiUBdJ9L0WgrCiCtuwOv+7hX5QfTmr6Dc1bXPYGvtxePaMTA7MI6OogzW6vYc4//1hj0O0/mBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:04.472279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdea7a01f7f01467c3d1c680be44c9995ce4829d4d264b75ce7c6db3e47204c0","sha256:a6e9d93469e2dc1aee616e09c42366b41d57821f5b8f9f4d997c4a0c6d3becb5"],"state_sha256":"d77ff11602227c209dd51c72981b7727e2f69a978c32c26a6cb4d9aace180323"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cc/SwZObihrnAQILu6yU5GtBcTdg2ulN6YLtOqZeXIYFcFLbGv0UgHm+UMhoQVu8f/f9zdXIFtt/vO4mchzjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:04:13.626612Z","bundle_sha256":"1335ffb71beed9af5ca8a42976e472cac8186e8302248cab37b767ae27e93595"}}