{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U4DSWNPQPT6QTRSDOPOK5UQ6S7","short_pith_number":"pith:U4DSWNPQ","canonical_record":{"source":{"id":"1802.04597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-13T12:59:14Z","cross_cats_sorted":[],"title_canon_sha256":"fe958988a43801db5ba3d6de06e8ba51dcf7962afdf14422fa35a904a6321f89","abstract_canon_sha256":"14d1fd55d51bf6339fd0302eee3b08b81d7ebaa4a3d3c4abfa26ec0d51539925"},"schema_version":"1.0"},"canonical_sha256":"a7072b35f07cfd09c64373dcaed21e97f541b98895968d027ffa84b9de243b47","source":{"kind":"arxiv","id":"1802.04597","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04597","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04597v1","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04597","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"pith_short_12","alias_value":"U4DSWNPQPT6Q","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U4DSWNPQPT6QTRSD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U4DSWNPQ","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U4DSWNPQPT6QTRSDOPOK5UQ6S7","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-13T12:59:14Z","cross_cats_sorted":[],"title_canon_sha256":"fe958988a43801db5ba3d6de06e8ba51dcf7962afdf14422fa35a904a6321f89","abstract_canon_sha256":"14d1fd55d51bf6339fd0302eee3b08b81d7ebaa4a3d3c4abfa26ec0d51539925"},"schema_version":"1.0"},"canonical_sha256":"a7072b35f07cfd09c64373dcaed21e97f541b98895968d027ffa84b9de243b47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:42.003278Z","signature_b64":"ilysO/uTh0UfeZ9Y0H2BvZcpe0MHM4GUQfQoNzUVz4kQrenGXx+hreiegWTxO/6fGvP0D3UDOtw6wlsra4KyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7072b35f07cfd09c64373dcaed21e97f541b98895968d027ffa84b9de243b47","last_reissued_at":"2026-05-18T00:23:42.002610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:42.002610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04597","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":"2026-05-18T00:23:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/p/0k20xPbzazTZMt/IFG6HlhLWSvp0ORlncY7bPVg+b8hEXK5Ocbt7/tSSOYNWQ7+Zat6naP7mpAGQYZ4nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:42:34.353084Z"},"content_sha256":"4dd4410a311edcfcb225c9f3cf3a8d782402b3334586c9efa72fbc3612aedee3","schema_version":"1.0","event_id":"sha256:4dd4410a311edcfcb225c9f3cf3a8d782402b3334586c9efa72fbc3612aedee3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U4DSWNPQPT6QTRSDOPOK5UQ6S7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mimetic Spectral Element Method for Anisotropic Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Artur Palha, Marc Gerritsma, Varun Jain, Yi Zhang","submitted_at":"2018-02-13T12:59:14Z","abstract_excerpt":"This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulations are point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable and displays optimal convergence on orthogonal and non-affine grids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04597","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":"2026-05-18T00:23:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAS65dDx52rKqhj1lja32DEJlxUmxqfs7AWO9sR4sfXsEPT+O/6xxNeGv8+KfbQLfB4Is2XP7OVyBzCyRK7WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:42:34.353794Z"},"content_sha256":"d0007df829aafa4268dbcd7d4d398c8c90c60959a5b1fb6a4c8953175381fd90","schema_version":"1.0","event_id":"sha256:d0007df829aafa4268dbcd7d4d398c8c90c60959a5b1fb6a4c8953175381fd90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7/bundle.json","state_url":"https://pith.science/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7/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":"2026-06-08T20:42:34Z","links":{"resolver":"https://pith.science/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7","bundle":"https://pith.science/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7/bundle.json","state":"https://pith.science/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4DSWNPQPT6QTRSDOPOK5UQ6S7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U4DSWNPQPT6QTRSDOPOK5UQ6S7","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":"14d1fd55d51bf6339fd0302eee3b08b81d7ebaa4a3d3c4abfa26ec0d51539925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-13T12:59:14Z","title_canon_sha256":"fe958988a43801db5ba3d6de06e8ba51dcf7962afdf14422fa35a904a6321f89"},"schema_version":"1.0","source":{"id":"1802.04597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04597","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04597v1","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04597","created_at":"2026-05-18T00:23:42Z"},{"alias_kind":"pith_short_12","alias_value":"U4DSWNPQPT6Q","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U4DSWNPQPT6QTRSD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U4DSWNPQ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:d0007df829aafa4268dbcd7d4d398c8c90c60959a5b1fb6a4c8953175381fd90","target":"graph","created_at":"2026-05-18T00:23:42Z","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":"This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulations are point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable and displays optimal convergence on orthogonal and non-affine grids.","authors_text":"Artur Palha, Marc Gerritsma, Varun Jain, Yi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-13T12:59:14Z","title":"Mimetic Spectral Element Method for Anisotropic Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04597","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":"sha256:4dd4410a311edcfcb225c9f3cf3a8d782402b3334586c9efa72fbc3612aedee3","target":"record","created_at":"2026-05-18T00:23:42Z","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":"14d1fd55d51bf6339fd0302eee3b08b81d7ebaa4a3d3c4abfa26ec0d51539925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-13T12:59:14Z","title_canon_sha256":"fe958988a43801db5ba3d6de06e8ba51dcf7962afdf14422fa35a904a6321f89"},"schema_version":"1.0","source":{"id":"1802.04597","kind":"arxiv","version":1}},"canonical_sha256":"a7072b35f07cfd09c64373dcaed21e97f541b98895968d027ffa84b9de243b47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7072b35f07cfd09c64373dcaed21e97f541b98895968d027ffa84b9de243b47","first_computed_at":"2026-05-18T00:23:42.002610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:42.002610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ilysO/uTh0UfeZ9Y0H2BvZcpe0MHM4GUQfQoNzUVz4kQrenGXx+hreiegWTxO/6fGvP0D3UDOtw6wlsra4KyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:42.003278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dd4410a311edcfcb225c9f3cf3a8d782402b3334586c9efa72fbc3612aedee3","sha256:d0007df829aafa4268dbcd7d4d398c8c90c60959a5b1fb6a4c8953175381fd90"],"state_sha256":"4e8de3ec6d23f309289c17fc6e963effc0c050ac328001abb097a9ee677ba55e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mv5RVpSkAqOJ4N9rW5MHTt3Zhgnn61W3PWuhUNYEC7VMZmYx5qXKFVO75wl0M42+kw3Yt8zi0aXlzWey6rMeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:42:34.357643Z","bundle_sha256":"2aaa82afacf862bf92ddc0341f8de618f77f10f5b234584b00c4bb4626b46e48"}}