{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5GPLR3SCGARRVQHKYHBVGGIHUF","short_pith_number":"pith:5GPLR3SC","canonical_record":{"source":{"id":"2405.11516","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-19T10:57:13Z","cross_cats_sorted":[],"title_canon_sha256":"cbb3ea8be44eb9f8d88f1ad4fefd50cf3af60ba70ef4aa3dc87e3af1ddba51ef","abstract_canon_sha256":"152ee897774047abe570987cdad69c97690fa410303ed60f12d9d2074026ee87"},"schema_version":"1.0"},"canonical_sha256":"e99eb8ee4230231ac0eac1c3531907a153b02f6bd3922cd93a1954830a2279a8","source":{"kind":"arxiv","id":"2405.11516","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.11516","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"arxiv_version","alias_value":"2405.11516v4","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11516","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"pith_short_12","alias_value":"5GPLR3SCGARR","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"pith_short_16","alias_value":"5GPLR3SCGARRVQHK","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"pith_short_8","alias_value":"5GPLR3SC","created_at":"2026-07-05T09:52:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5GPLR3SCGARRVQHKYHBVGGIHUF","target":"record","payload":{"canonical_record":{"source":{"id":"2405.11516","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-19T10:57:13Z","cross_cats_sorted":[],"title_canon_sha256":"cbb3ea8be44eb9f8d88f1ad4fefd50cf3af60ba70ef4aa3dc87e3af1ddba51ef","abstract_canon_sha256":"152ee897774047abe570987cdad69c97690fa410303ed60f12d9d2074026ee87"},"schema_version":"1.0"},"canonical_sha256":"e99eb8ee4230231ac0eac1c3531907a153b02f6bd3922cd93a1954830a2279a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:11.710370Z","signature_b64":"mjng09Syqb4SH6Yq3m+nLpQvkpEI4Js8/Spa4GxP/jc2ob+D/U1zenK4ZyvetUuACckACKEKaELKxhhthewtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e99eb8ee4230231ac0eac1c3531907a153b02f6bd3922cd93a1954830a2279a8","last_reissued_at":"2026-07-05T09:52:11.709947Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:11.709947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.11516","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:52:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"emnA4LvxYcldPY2tafK9jB5//I/TAyg1fGh5toEx2//hhhh7wWCm739mtKggOg6IEZICCcC2Efy6axSzIP4KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T17:09:01.690022Z"},"content_sha256":"d601c42d9c0b8bc0d39c094bd45faf65dd55277b9a9861e4d01790c7c290b090","schema_version":"1.0","event_id":"sha256:d601c42d9c0b8bc0d39c094bd45faf65dd55277b9a9861e4d01790c7c290b090"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5GPLR3SCGARRVQHKYHBVGGIHUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bingyang Hu, Jianlu Zhang, Son N.T. Tu","submitted_at":"2024-05-19T10:57:13Z","abstract_excerpt":"In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the convergence rate of homogenization and the regularity of the effective Hamiltonian, by using a new quantitative ergodic estimate for bounded quasi-periodic functions with Diophantine frequencies. As an application, we also study the convergent rate for Birkhoff average of unbounded quasi-periodic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11516","kind":"arxiv","version":4},"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/2405.11516/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":"2026-07-05T09:52:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WNXwqVDekzCUbLv6DMrYYqNMDHMDHhyH0bySoY4VkmpcisAcaMaOkrhTH870GGsmkLnQWmEd/MzYB2YWVNqtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T17:09:01.690401Z"},"content_sha256":"6b5ae8cba96a067b1f069b09e5549272001f3b3cf4b22c504527fd6c9fe1fda9","schema_version":"1.0","event_id":"sha256:6b5ae8cba96a067b1f069b09e5549272001f3b3cf4b22c504527fd6c9fe1fda9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GPLR3SCGARRVQHKYHBVGGIHUF/bundle.json","state_url":"https://pith.science/pith/5GPLR3SCGARRVQHKYHBVGGIHUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GPLR3SCGARRVQHKYHBVGGIHUF/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":"2026-07-22T17:09:01Z","links":{"resolver":"https://pith.science/pith/5GPLR3SCGARRVQHKYHBVGGIHUF","bundle":"https://pith.science/pith/5GPLR3SCGARRVQHKYHBVGGIHUF/bundle.json","state":"https://pith.science/pith/5GPLR3SCGARRVQHKYHBVGGIHUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GPLR3SCGARRVQHKYHBVGGIHUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5GPLR3SCGARRVQHKYHBVGGIHUF","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":"152ee897774047abe570987cdad69c97690fa410303ed60f12d9d2074026ee87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-19T10:57:13Z","title_canon_sha256":"cbb3ea8be44eb9f8d88f1ad4fefd50cf3af60ba70ef4aa3dc87e3af1ddba51ef"},"schema_version":"1.0","source":{"id":"2405.11516","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.11516","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"arxiv_version","alias_value":"2405.11516v4","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11516","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"pith_short_12","alias_value":"5GPLR3SCGARR","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"pith_short_16","alias_value":"5GPLR3SCGARRVQHK","created_at":"2026-07-05T09:52:11Z"},{"alias_kind":"pith_short_8","alias_value":"5GPLR3SC","created_at":"2026-07-05T09:52:11Z"}],"graph_snapshots":[{"event_id":"sha256:6b5ae8cba96a067b1f069b09e5549272001f3b3cf4b22c504527fd6c9fe1fda9","target":"graph","created_at":"2026-07-05T09:52:11Z","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/2405.11516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the convergence rate of homogenization and the regularity of the effective Hamiltonian, by using a new quantitative ergodic estimate for bounded quasi-periodic functions with Diophantine frequencies. As an application, we also study the convergent rate for Birkhoff average of unbounded quasi-periodic functions.","authors_text":"Bingyang Hu, Jianlu Zhang, Son N.T. Tu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-19T10:57:13Z","title":"Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11516","kind":"arxiv","version":4},"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:d601c42d9c0b8bc0d39c094bd45faf65dd55277b9a9861e4d01790c7c290b090","target":"record","created_at":"2026-07-05T09:52:11Z","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":"152ee897774047abe570987cdad69c97690fa410303ed60f12d9d2074026ee87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-19T10:57:13Z","title_canon_sha256":"cbb3ea8be44eb9f8d88f1ad4fefd50cf3af60ba70ef4aa3dc87e3af1ddba51ef"},"schema_version":"1.0","source":{"id":"2405.11516","kind":"arxiv","version":4}},"canonical_sha256":"e99eb8ee4230231ac0eac1c3531907a153b02f6bd3922cd93a1954830a2279a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e99eb8ee4230231ac0eac1c3531907a153b02f6bd3922cd93a1954830a2279a8","first_computed_at":"2026-07-05T09:52:11.709947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:11.709947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mjng09Syqb4SH6Yq3m+nLpQvkpEI4Js8/Spa4GxP/jc2ob+D/U1zenK4ZyvetUuACckACKEKaELKxhhthewtDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:11.710370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.11516","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d601c42d9c0b8bc0d39c094bd45faf65dd55277b9a9861e4d01790c7c290b090","sha256:6b5ae8cba96a067b1f069b09e5549272001f3b3cf4b22c504527fd6c9fe1fda9"],"state_sha256":"979c682c87ccdac9b7973b8fefb48b2dee85aae972b3f914e1556b582399d3e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djOB5JJTjGw8j2aIi5idwoxMKeRJo04BYpTf43TNxH11Djl/8oeuNKePv4va9DRBKXV41buTPlFwti+tMmakCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T17:09:01.692527Z","bundle_sha256":"65bd006d6627ace94c643ccad8a461339642bc4e99549acde6677e16274994df"}}