{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YK37EGON7OUJS2ZHF5LXJY5AVX","short_pith_number":"pith:YK37EGON","canonical_record":{"source":{"id":"1509.08791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T15:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"bb73fc05b5eddaaef40407295c1bfc5e1cd4d8171adda1eadebef7e5a339272f","abstract_canon_sha256":"a701af7ab4190605105525eb3fd0fe9c35f8511f0886312a92e9ec6c69da4bb2"},"schema_version":"1.0"},"canonical_sha256":"c2b7f219cdfba8996b272f5774e3a0adfc7966b3fc01feaeaccfd98e83042a55","source":{"kind":"arxiv","id":"1509.08791","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08791","created_at":"2026-05-18T01:31:47Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08791v1","created_at":"2026-05-18T01:31:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08791","created_at":"2026-05-18T01:31:47Z"},{"alias_kind":"pith_short_12","alias_value":"YK37EGON7OUJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YK37EGON7OUJS2ZH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YK37EGON","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YK37EGON7OUJS2ZHF5LXJY5AVX","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T15:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"bb73fc05b5eddaaef40407295c1bfc5e1cd4d8171adda1eadebef7e5a339272f","abstract_canon_sha256":"a701af7ab4190605105525eb3fd0fe9c35f8511f0886312a92e9ec6c69da4bb2"},"schema_version":"1.0"},"canonical_sha256":"c2b7f219cdfba8996b272f5774e3a0adfc7966b3fc01feaeaccfd98e83042a55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:47.091504Z","signature_b64":"aU1xvuzg7uXG0aX52IfNsDbVoS3dq4l1+X9TMnzyTg4rwb96rhGFOjae/L4ysUQAurvW9ooWGb+lFxUIqgWjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2b7f219cdfba8996b272f5774e3a0adfc7966b3fc01feaeaccfd98e83042a55","last_reissued_at":"2026-05-18T01:31:47.091057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:47.091057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08791","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":"2026-05-18T01:31:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpHXrX68KJ+OAF/PbZNPvaHWZ7vy84pMB+xQhM6WZi48B2si0PQ/roM4rj40Q6lk2/CcY2/1u/zS1ayhinUUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:37:36.283075Z"},"content_sha256":"b379cbcfc2f32b111bfcfb544d4a8e3fefdb8a04f8d6662076bd56abf81d62c6","schema_version":"1.0","event_id":"sha256:b379cbcfc2f32b111bfcfb544d4a8e3fefdb8a04f8d6662076bd56abf81d62c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YK37EGON7OUJS2ZHF5LXJY5AVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Div-Curl for Higher Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew S. Raich, Loredana Lanzani","submitted_at":"2015-09-29T15:04:44Z","abstract_excerpt":"We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08791","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":"2026-05-18T01:31:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XDMGWDdFe0qE7m6wtxRlMBcvplfa8R/Sg9yh3rZ1+tmfEWYOeXFwrIBtg4SMPHySYcK0WP4z65/vdnk1486DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:37:36.283726Z"},"content_sha256":"cd422653f7b69126e16703cf720c632ec99d31457819a1130d7f72a06396574b","schema_version":"1.0","event_id":"sha256:cd422653f7b69126e16703cf720c632ec99d31457819a1130d7f72a06396574b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YK37EGON7OUJS2ZHF5LXJY5AVX/bundle.json","state_url":"https://pith.science/pith/YK37EGON7OUJS2ZHF5LXJY5AVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YK37EGON7OUJS2ZHF5LXJY5AVX/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":"2026-05-31T08:37:36Z","links":{"resolver":"https://pith.science/pith/YK37EGON7OUJS2ZHF5LXJY5AVX","bundle":"https://pith.science/pith/YK37EGON7OUJS2ZHF5LXJY5AVX/bundle.json","state":"https://pith.science/pith/YK37EGON7OUJS2ZHF5LXJY5AVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YK37EGON7OUJS2ZHF5LXJY5AVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YK37EGON7OUJS2ZHF5LXJY5AVX","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":"a701af7ab4190605105525eb3fd0fe9c35f8511f0886312a92e9ec6c69da4bb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T15:04:44Z","title_canon_sha256":"bb73fc05b5eddaaef40407295c1bfc5e1cd4d8171adda1eadebef7e5a339272f"},"schema_version":"1.0","source":{"id":"1509.08791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08791","created_at":"2026-05-18T01:31:47Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08791v1","created_at":"2026-05-18T01:31:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08791","created_at":"2026-05-18T01:31:47Z"},{"alias_kind":"pith_short_12","alias_value":"YK37EGON7OUJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YK37EGON7OUJS2ZH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YK37EGON","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:cd422653f7b69126e16703cf720c632ec99d31457819a1130d7f72a06396574b","target":"graph","created_at":"2026-05-18T01:31:47Z","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 present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.","authors_text":"Andrew S. Raich, Loredana Lanzani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T15:04:44Z","title":"On Div-Curl for Higher Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08791","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:b379cbcfc2f32b111bfcfb544d4a8e3fefdb8a04f8d6662076bd56abf81d62c6","target":"record","created_at":"2026-05-18T01:31:47Z","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":"a701af7ab4190605105525eb3fd0fe9c35f8511f0886312a92e9ec6c69da4bb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T15:04:44Z","title_canon_sha256":"bb73fc05b5eddaaef40407295c1bfc5e1cd4d8171adda1eadebef7e5a339272f"},"schema_version":"1.0","source":{"id":"1509.08791","kind":"arxiv","version":1}},"canonical_sha256":"c2b7f219cdfba8996b272f5774e3a0adfc7966b3fc01feaeaccfd98e83042a55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2b7f219cdfba8996b272f5774e3a0adfc7966b3fc01feaeaccfd98e83042a55","first_computed_at":"2026-05-18T01:31:47.091057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:47.091057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aU1xvuzg7uXG0aX52IfNsDbVoS3dq4l1+X9TMnzyTg4rwb96rhGFOjae/L4ysUQAurvW9ooWGb+lFxUIqgWjBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:47.091504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b379cbcfc2f32b111bfcfb544d4a8e3fefdb8a04f8d6662076bd56abf81d62c6","sha256:cd422653f7b69126e16703cf720c632ec99d31457819a1130d7f72a06396574b"],"state_sha256":"2fa4b5989d06e6367aca4f5c572f7b8669647988ae4e134bf369cb1fec2efbbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gpmd/m2GenWJD6iumHTarusoc/mY7vLJ1px54F0QvqLU/+JqluOM3kv5BgdtcB8XKZ129IAs9Qy7UQdUbqUzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:37:36.287087Z","bundle_sha256":"af63dacec2c6e216b3ad750f8427b7c2b1556c2a49616ed5b63f3849e72389bd"}}