{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LJ6UAZWYQUNQQLEGKBKY66L4BK","short_pith_number":"pith:LJ6UAZWY","canonical_record":{"source":{"id":"2607.07526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T15:20:47Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6bf6410421a45236a3d9a1b5688348c97b7afd449068be517ae864a5f3e01361","abstract_canon_sha256":"8be4dc5c1af1228b10a664a66afe9d52c2ed577ee1f1541639c63ca0770f9ea9"},"schema_version":"1.0"},"canonical_sha256":"5a7d4066d8851b082c8650558f797c0a848ee1293926cce89f883397ad7d53aa","source":{"kind":"arxiv","id":"2607.07526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07526","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07526v1","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07526","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"LJ6UAZWYQUNQ","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"pith_short_16","alias_value":"LJ6UAZWYQUNQQLEG","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"pith_short_8","alias_value":"LJ6UAZWY","created_at":"2026-07-09T01:20:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LJ6UAZWYQUNQQLEGKBKY66L4BK","target":"record","payload":{"canonical_record":{"source":{"id":"2607.07526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T15:20:47Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6bf6410421a45236a3d9a1b5688348c97b7afd449068be517ae864a5f3e01361","abstract_canon_sha256":"8be4dc5c1af1228b10a664a66afe9d52c2ed577ee1f1541639c63ca0770f9ea9"},"schema_version":"1.0"},"canonical_sha256":"5a7d4066d8851b082c8650558f797c0a848ee1293926cce89f883397ad7d53aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:28.016056Z","signature_b64":"+shph+DvlnldTFK7e/zgDJwQEl//BIPFnpJJFLLqyIoW/DvRoKDyXB1rh0+XyKBtcAMcXu5T+jlQVsw9nUboDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a7d4066d8851b082c8650558f797c0a848ee1293926cce89f883397ad7d53aa","last_reissued_at":"2026-07-09T01:20:28.015604Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:28.015604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.07526","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":"2026-07-09T01:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zv67oXk2Ed28780ACUfG5fTXcTz+k3Vbm+HB0+fAYxpld9AEsQyHfsNP3GmIn9w/Ri7Wm4XgL+ezHgIAP4QvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:50:10.235223Z"},"content_sha256":"7421fd593464d8ef49ad9a17f489a329eb825c5ec32b59fcd0f9cdee626c2110","schema_version":"1.0","event_id":"sha256:7421fd593464d8ef49ad9a17f489a329eb825c5ec32b59fcd0f9cdee626c2110"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LJ6UAZWYQUNQQLEGKBKY66L4BK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rate of the vanishing viscosity approximation for Mean Field Games with nonlocal coupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Alessandro Goffi, Gennaro Ciampa","submitted_at":"2026-07-08T15:20:47Z","abstract_excerpt":"We study quantitative convergence rates of the vanishing viscosity approximation of first-order time-dependent Mean Field Games with regularizing coupling acting in the Hamilton-Jacobi equation. Under standard structural assumptions on the Hamiltonian ensuring convergence of the vanishing viscosity approximation, previous results provide either qualitative convergence for the two unknown of the system or quantitative estimates merely for solutions of the Hamilton-Jacobi equation. In this work, we improve these convergence rates under the same assumptions and establish, in addition, quantitativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07526","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07526/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-09T01:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3YhbQD38m1tyHt8OBOoxn7GaoSsy0KGyNgtrWMs2BlRoFQcquKZ+GOkgJfzYyPfvIhLSOdyWl+CXsDyXpMXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:50:10.236115Z"},"content_sha256":"a1e649194a9b13dd6ad57a40959ee0554fb45620e0be4e53adc486dc6ddc3ac8","schema_version":"1.0","event_id":"sha256:a1e649194a9b13dd6ad57a40959ee0554fb45620e0be4e53adc486dc6ddc3ac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK/bundle.json","state_url":"https://pith.science/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK/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":"2026-08-09T22:50:10Z","links":{"resolver":"https://pith.science/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK","bundle":"https://pith.science/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK/bundle.json","state":"https://pith.science/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ6UAZWYQUNQQLEGKBKY66L4BK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LJ6UAZWYQUNQQLEGKBKY66L4BK","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":"8be4dc5c1af1228b10a664a66afe9d52c2ed577ee1f1541639c63ca0770f9ea9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T15:20:47Z","title_canon_sha256":"6bf6410421a45236a3d9a1b5688348c97b7afd449068be517ae864a5f3e01361"},"schema_version":"1.0","source":{"id":"2607.07526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07526","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07526v1","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07526","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"LJ6UAZWYQUNQ","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"pith_short_16","alias_value":"LJ6UAZWYQUNQQLEG","created_at":"2026-07-09T01:20:28Z"},{"alias_kind":"pith_short_8","alias_value":"LJ6UAZWY","created_at":"2026-07-09T01:20:28Z"}],"graph_snapshots":[{"event_id":"sha256:a1e649194a9b13dd6ad57a40959ee0554fb45620e0be4e53adc486dc6ddc3ac8","target":"graph","created_at":"2026-07-09T01:20:28Z","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/2607.07526/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study quantitative convergence rates of the vanishing viscosity approximation of first-order time-dependent Mean Field Games with regularizing coupling acting in the Hamilton-Jacobi equation. Under standard structural assumptions on the Hamiltonian ensuring convergence of the vanishing viscosity approximation, previous results provide either qualitative convergence for the two unknown of the system or quantitative estimates merely for solutions of the Hamilton-Jacobi equation. In this work, we improve these convergence rates under the same assumptions and establish, in addition, quantitativ","authors_text":"Alessandro Goffi, Gennaro Ciampa","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T15:20:47Z","title":"On the rate of the vanishing viscosity approximation for Mean Field Games with nonlocal coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07526","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":"sha256:7421fd593464d8ef49ad9a17f489a329eb825c5ec32b59fcd0f9cdee626c2110","target":"record","created_at":"2026-07-09T01:20:28Z","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":"8be4dc5c1af1228b10a664a66afe9d52c2ed577ee1f1541639c63ca0770f9ea9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T15:20:47Z","title_canon_sha256":"6bf6410421a45236a3d9a1b5688348c97b7afd449068be517ae864a5f3e01361"},"schema_version":"1.0","source":{"id":"2607.07526","kind":"arxiv","version":1}},"canonical_sha256":"5a7d4066d8851b082c8650558f797c0a848ee1293926cce89f883397ad7d53aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7d4066d8851b082c8650558f797c0a848ee1293926cce89f883397ad7d53aa","first_computed_at":"2026-07-09T01:20:28.015604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:28.015604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+shph+DvlnldTFK7e/zgDJwQEl//BIPFnpJJFLLqyIoW/DvRoKDyXB1rh0+XyKBtcAMcXu5T+jlQVsw9nUboDw==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:28.016056Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7421fd593464d8ef49ad9a17f489a329eb825c5ec32b59fcd0f9cdee626c2110","sha256:a1e649194a9b13dd6ad57a40959ee0554fb45620e0be4e53adc486dc6ddc3ac8"],"state_sha256":"65235ecc27f57d633467f3fff07c0fa4051dd41afe16eea828fd206670565dfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6apsPN+KuByK9aGWR8elLX0AZ9TAzgRHOjsaPGW4oiyshT3pc7AkaD1wdMoHLg5MgllvbXYCvCa0kT3Y9PwCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T22:50:10.242037Z","bundle_sha256":"9373fed50768bdc79d2d57a17933a1856fe48e01a4ec446b75eb05ca90d350a2"}}