{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3N7XNEL6PWJ2OH3QHA7XSJPG6X","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":"1a5614b4e11f9ca8a63f8a550774105fc1c624297d6ab1ad207c5f957a41e808","cross_cats_sorted":["cs.NA","math.AP","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-25T10:39:05Z","title_canon_sha256":"0ecd8e397daf82d57d24c06ac297bbd061dbc8c82e4e68abd84e0b596fb90cf5"},"schema_version":"1.0","source":{"id":"2606.26853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26853","created_at":"2026-06-26T01:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26853v1","created_at":"2026-06-26T01:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26853","created_at":"2026-06-26T01:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"3N7XNEL6PWJ2","created_at":"2026-06-26T01:16:01Z"},{"alias_kind":"pith_short_16","alias_value":"3N7XNEL6PWJ2OH3Q","created_at":"2026-06-26T01:16:01Z"},{"alias_kind":"pith_short_8","alias_value":"3N7XNEL6","created_at":"2026-06-26T01:16:01Z"}],"graph_snapshots":[{"event_id":"sha256:5b3b251b2955b722ffc4f8f87874dbd551495c7d78909e00ca1184c524169f87","target":"graph","created_at":"2026-06-26T01:16:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.26853/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a particle method for the numerical approximation of time-dependent first-order Mean Field Games (MFGs) systems with non-separable, displacement monotone Hamiltonians and terminal costs, for arbitrary time-horizons and (possibly) singular initial player distributions in $\\mathcal{P}_2(\\mathbb{R}^d)$. The numerical scheme is based on an implicit Euler discretization in time and sampling in space of the characteristic Hamiltonian/Pontryagin system associated with the continuous MFGs system. We prove convergence of the approximations of the player distribution in the $L^{\\infty}(\\mat","authors_text":"Alp\\'ar R. M\\'esz\\'aros, Yohance A. P. Osborne","cross_cats":["cs.NA","math.AP","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-25T10:39:05Z","title":"Numerical analysis of first-order mean field games under displacement monotonicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26853","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":"sha256:49bdd10ddbab8e3df7108233d890a22e1e976f3d345c4d69e95550b900e2b218","target":"record","created_at":"2026-06-26T01:16:01Z","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":"1a5614b4e11f9ca8a63f8a550774105fc1c624297d6ab1ad207c5f957a41e808","cross_cats_sorted":["cs.NA","math.AP","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-25T10:39:05Z","title_canon_sha256":"0ecd8e397daf82d57d24c06ac297bbd061dbc8c82e4e68abd84e0b596fb90cf5"},"schema_version":"1.0","source":{"id":"2606.26853","kind":"arxiv","version":1}},"canonical_sha256":"db7f76917e7d93a71f70383f7925e6f5d8017217ec5b94e5858de9aa3406b5df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db7f76917e7d93a71f70383f7925e6f5d8017217ec5b94e5858de9aa3406b5df","first_computed_at":"2026-06-26T01:16:01.723491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:01.723491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pJ6y6AjsAi16hg93DPEgNcaO826c3K57mELMeLOadZF6YgM8Ixwu/wKH8NMWHWoLzSbtEaKaqBDiiGWxIoFKDQ==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:01.723900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49bdd10ddbab8e3df7108233d890a22e1e976f3d345c4d69e95550b900e2b218","sha256:5b3b251b2955b722ffc4f8f87874dbd551495c7d78909e00ca1184c524169f87"],"state_sha256":"0e640ad02da3e254a70640e8e72ddd838dac635b5f88842398bed0dbec3f33c4"}