{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2DJYUMQUVI4E6OV2G2YHFVV5CV","short_pith_number":"pith:2DJYUMQU","canonical_record":{"source":{"id":"1612.08013","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-23T15:49:12Z","cross_cats_sorted":[],"title_canon_sha256":"c210b9b450627f7615a4751d4ab5c3194194215602a6bbf717c2939dfdd6f1ed","abstract_canon_sha256":"e567065a00f2306a11f6f2dffd1051735308df337d31938f3fab5b50ebe5af94"},"schema_version":"1.0"},"canonical_sha256":"d0d38a3214aa384f3aba36b072d6bd15662d38d478bb52960e34534601c34487","source":{"kind":"arxiv","id":"1612.08013","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08013","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08013v3","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08013","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"pith_short_12","alias_value":"2DJYUMQUVI4E","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2DJYUMQUVI4E6OV2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2DJYUMQU","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2DJYUMQUVI4E6OV2G2YHFVV5CV","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08013","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-23T15:49:12Z","cross_cats_sorted":[],"title_canon_sha256":"c210b9b450627f7615a4751d4ab5c3194194215602a6bbf717c2939dfdd6f1ed","abstract_canon_sha256":"e567065a00f2306a11f6f2dffd1051735308df337d31938f3fab5b50ebe5af94"},"schema_version":"1.0"},"canonical_sha256":"d0d38a3214aa384f3aba36b072d6bd15662d38d478bb52960e34534601c34487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:59.272245Z","signature_b64":"DenqkYY5Ff24BY5SClBL9vuzn2RHEDaCUaQt6+yTPPOnAWZMWjGQfqWB4wWg4xdlL0Q0ziE9pnhixMmPIJzjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0d38a3214aa384f3aba36b072d6bd15662d38d478bb52960e34534601c34487","last_reissued_at":"2026-05-18T00:19:59.271811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:59.271811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08013","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"byKR0dHQW6FkPMBLGXErAb1aazLQBo+T+YThiQJAV5mQ5XID9cSov+x3wYh1Sysh2kCp/7P5bFiaT3dMfX4sDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:03:43.239347Z"},"content_sha256":"94bb56817f48eacee028c7e753d9c11416727c4cfc139adbe126826266020639","schema_version":"1.0","event_id":"sha256:94bb56817f48eacee028c7e753d9c11416727c4cfc139adbe126826266020639"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2DJYUMQUVI4E6OV2G2YHFVV5CV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of spectral discretizations of the Vlasov-Poisson system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Daniele Funaro, Gian Luca Delzanno, Gianmarco Manzini","submitted_at":"2016-12-23T15:49:12Z","abstract_excerpt":"We prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term, that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08013","kind":"arxiv","version":3},"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":"2026-05-18T00:19:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wtv8RDxTu/7zdZmr7E8Ee28/22UF2sZThxEzJpspPiWTV1ZlyXO4xS9ervhDBJ8Ad+svNMVf5eUkO9RdSsKVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:03:43.239704Z"},"content_sha256":"da8fcde4de7953a937b218eb1fabc613c0039917aae736ddda53be3e663ba493","schema_version":"1.0","event_id":"sha256:da8fcde4de7953a937b218eb1fabc613c0039917aae736ddda53be3e663ba493"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV/bundle.json","state_url":"https://pith.science/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV/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":"2026-06-01T18:03:43Z","links":{"resolver":"https://pith.science/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV","bundle":"https://pith.science/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV/bundle.json","state":"https://pith.science/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DJYUMQUVI4E6OV2G2YHFVV5CV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2DJYUMQUVI4E6OV2G2YHFVV5CV","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":"e567065a00f2306a11f6f2dffd1051735308df337d31938f3fab5b50ebe5af94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-23T15:49:12Z","title_canon_sha256":"c210b9b450627f7615a4751d4ab5c3194194215602a6bbf717c2939dfdd6f1ed"},"schema_version":"1.0","source":{"id":"1612.08013","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08013","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08013v3","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08013","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"pith_short_12","alias_value":"2DJYUMQUVI4E","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2DJYUMQUVI4E6OV2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2DJYUMQU","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:da8fcde4de7953a937b218eb1fabc613c0039917aae736ddda53be3e663ba493","target":"graph","created_at":"2026-05-18T00:19:59Z","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 prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term, that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out","authors_text":"Daniele Funaro, Gian Luca Delzanno, Gianmarco Manzini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-23T15:49:12Z","title":"Convergence of spectral discretizations of the Vlasov-Poisson system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08013","kind":"arxiv","version":3},"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":"sha256:94bb56817f48eacee028c7e753d9c11416727c4cfc139adbe126826266020639","target":"record","created_at":"2026-05-18T00:19:59Z","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":"e567065a00f2306a11f6f2dffd1051735308df337d31938f3fab5b50ebe5af94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-23T15:49:12Z","title_canon_sha256":"c210b9b450627f7615a4751d4ab5c3194194215602a6bbf717c2939dfdd6f1ed"},"schema_version":"1.0","source":{"id":"1612.08013","kind":"arxiv","version":3}},"canonical_sha256":"d0d38a3214aa384f3aba36b072d6bd15662d38d478bb52960e34534601c34487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0d38a3214aa384f3aba36b072d6bd15662d38d478bb52960e34534601c34487","first_computed_at":"2026-05-18T00:19:59.271811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:59.271811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DenqkYY5Ff24BY5SClBL9vuzn2RHEDaCUaQt6+yTPPOnAWZMWjGQfqWB4wWg4xdlL0Q0ziE9pnhixMmPIJzjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:59.272245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08013","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94bb56817f48eacee028c7e753d9c11416727c4cfc139adbe126826266020639","sha256:da8fcde4de7953a937b218eb1fabc613c0039917aae736ddda53be3e663ba493"],"state_sha256":"be1c50da4745e15c6074aa61b35a26e52723f6cb6c163c9ebc0ba370bbba2a28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lO3QmQ8EREqYzIcj/TbqicOeUGcRKC8+vvMiTx/msilo9JQ8yQusY/IOD9Tldw09KVY880OqbkkXnSR3GnDCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:03:43.241764Z","bundle_sha256":"99c96190e6251fa1efb8cd200c42bde97aa028549a3e8eda9a35703fa035c48c"}}