{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3C4QWUMTYHNQ3IDLWRBP3A5TSK","short_pith_number":"pith:3C4QWUMT","canonical_record":{"source":{"id":"1212.0812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-04T18:13:28Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e4c53cc279d8d9eeaefb277d2db774ed83545da2f44dbbcad02672887586b1ee","abstract_canon_sha256":"04b03ad309d0daff74eec32634fbe36d2d1321a2eada10a977659cd133351e77"},"schema_version":"1.0"},"canonical_sha256":"d8b90b5193c1db0da06bb442fd83b3929ed92b157e6ef3b0ae1c711d0e0175ad","source":{"kind":"arxiv","id":"1212.0812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0812","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0812v2","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0812","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"3C4QWUMTYHNQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3C4QWUMTYHNQ3IDL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3C4QWUMT","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3C4QWUMTYHNQ3IDLWRBP3A5TSK","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-04T18:13:28Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e4c53cc279d8d9eeaefb277d2db774ed83545da2f44dbbcad02672887586b1ee","abstract_canon_sha256":"04b03ad309d0daff74eec32634fbe36d2d1321a2eada10a977659cd133351e77"},"schema_version":"1.0"},"canonical_sha256":"d8b90b5193c1db0da06bb442fd83b3929ed92b157e6ef3b0ae1c711d0e0175ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:35.944914Z","signature_b64":"GxclqYmD+vCZKHoBGQTrYGf01s0I1NJaKtLVW6xc0eXAPYf08DLkyUSqNGWjMXnY6YHyhiMftKfsVqpH6rA1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b90b5193c1db0da06bb442fd83b3929ed92b157e6ef3b0ae1c711d0e0175ad","last_reissued_at":"2026-05-17T23:53:35.944355Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:35.944355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0812","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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1gP2qAR4dgCUn3T64/KD+AfSFO1aIjARmtCgM+bTs+lXPX226AM/zom/3j9TIp5OhYyiR/VtjMxfdSGdKF6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:56:03.241671Z"},"content_sha256":"82845f02c6a39289cd75976d634155c23878af0f1d0f62b3a382423d2262b656","schema_version":"1.0","event_id":"sha256:82845f02c6a39289cd75976d634155c23878af0f1d0f62b3a382423d2262b656"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3C4QWUMTYHNQ3IDLWRBP3A5TSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Houman Owhadi, Lei Zhang, Leonid Berlyand","submitted_at":"2012-12-04T18:13:28Z","abstract_excerpt":"We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\\infty$) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution $H$) minimizing the $L^2$ norm of the source terms; its (pre-)computation involves minimizing $\\mathcal{O}(H^{-d})$ quadratic (ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0812","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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttpGhGuVJz7tzV/44OTL2bAh8L3Dod9jH+0VA+68GaL4HEp2IRpA5Eg1p2TjdAcyTdwUXVEzl3ZytFiR5JCHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:56:03.242064Z"},"content_sha256":"aed8085dd2c0884fcd66707d324d7924eb54c1c2c7e37ec6dd6015ad95ee2d1d","schema_version":"1.0","event_id":"sha256:aed8085dd2c0884fcd66707d324d7924eb54c1c2c7e37ec6dd6015ad95ee2d1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK/bundle.json","state_url":"https://pith.science/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK/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":"2026-05-29T17:56:03Z","links":{"resolver":"https://pith.science/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK","bundle":"https://pith.science/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK/bundle.json","state":"https://pith.science/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3C4QWUMTYHNQ3IDLWRBP3A5TSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3C4QWUMTYHNQ3IDLWRBP3A5TSK","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":"04b03ad309d0daff74eec32634fbe36d2d1321a2eada10a977659cd133351e77","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-04T18:13:28Z","title_canon_sha256":"e4c53cc279d8d9eeaefb277d2db774ed83545da2f44dbbcad02672887586b1ee"},"schema_version":"1.0","source":{"id":"1212.0812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0812","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0812v2","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0812","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"3C4QWUMTYHNQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3C4QWUMTYHNQ3IDL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3C4QWUMT","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:aed8085dd2c0884fcd66707d324d7924eb54c1c2c7e37ec6dd6015ad95ee2d1d","target":"graph","created_at":"2026-05-17T23:53:35Z","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 introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\\infty$) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution $H$) minimizing the $L^2$ norm of the source terms; its (pre-)computation involves minimizing $\\mathcal{O}(H^{-d})$ quadratic (ce","authors_text":"Houman Owhadi, Lei Zhang, Leonid Berlyand","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-04T18:13:28Z","title":"Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0812","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":"sha256:82845f02c6a39289cd75976d634155c23878af0f1d0f62b3a382423d2262b656","target":"record","created_at":"2026-05-17T23:53:35Z","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":"04b03ad309d0daff74eec32634fbe36d2d1321a2eada10a977659cd133351e77","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-04T18:13:28Z","title_canon_sha256":"e4c53cc279d8d9eeaefb277d2db774ed83545da2f44dbbcad02672887586b1ee"},"schema_version":"1.0","source":{"id":"1212.0812","kind":"arxiv","version":2}},"canonical_sha256":"d8b90b5193c1db0da06bb442fd83b3929ed92b157e6ef3b0ae1c711d0e0175ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b90b5193c1db0da06bb442fd83b3929ed92b157e6ef3b0ae1c711d0e0175ad","first_computed_at":"2026-05-17T23:53:35.944355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:35.944355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GxclqYmD+vCZKHoBGQTrYGf01s0I1NJaKtLVW6xc0eXAPYf08DLkyUSqNGWjMXnY6YHyhiMftKfsVqpH6rA1Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:35.944914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82845f02c6a39289cd75976d634155c23878af0f1d0f62b3a382423d2262b656","sha256:aed8085dd2c0884fcd66707d324d7924eb54c1c2c7e37ec6dd6015ad95ee2d1d"],"state_sha256":"cdf820901cb9250bdd4a6a32cfd84745f330d1574d2039a112d55eb78d66ef81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLmffa1RFINdhsr+kALPmnUqJIBMNi9xMRxSey1krkxBFyuT84AmHy/FjYOtRC+kpiseSrmEfQ+FhIXU2xiYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:56:03.245359Z","bundle_sha256":"d65d707796806b14950312c2f791878744df7cc82c06c0330e52f77a35b678ca"}}