{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:7CASM2HBVVTKTX46P2HJLK3EOW","short_pith_number":"pith:7CASM2HB","canonical_record":{"source":{"id":"math/0611625","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-11-21T02:00:13Z","cross_cats_sorted":[],"title_canon_sha256":"f33fef3390e4d22dd6dedf9e0868f0c6e43636971b6ccafba832e22ae548dce3","abstract_canon_sha256":"697a6444b74c31647ce4f96782f5fc05e254488ed097cb6f677041fbdce1c323"},"schema_version":"1.0"},"canonical_sha256":"f8812668e1ad66a9df9e7e8e95ab64759dc44bed65afd2c1db5669b38f5a9962","source":{"kind":"arxiv","id":"math/0611625","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611625","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611625v1","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611625","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"7CASM2HBVVTK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7CASM2HBVVTKTX46","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7CASM2HB","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:7CASM2HBVVTKTX46P2HJLK3EOW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611625","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-11-21T02:00:13Z","cross_cats_sorted":[],"title_canon_sha256":"f33fef3390e4d22dd6dedf9e0868f0c6e43636971b6ccafba832e22ae548dce3","abstract_canon_sha256":"697a6444b74c31647ce4f96782f5fc05e254488ed097cb6f677041fbdce1c323"},"schema_version":"1.0"},"canonical_sha256":"f8812668e1ad66a9df9e7e8e95ab64759dc44bed65afd2c1db5669b38f5a9962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:05.178616Z","signature_b64":"XDOUQqc3jYJQdDx3FQq1aHGKwAdKmiTCpTxvxl7T1SiITjrX7iY/FqpSxd4wztqIbZSxhrO8tdxDV3e+k/h9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8812668e1ad66a9df9e7e8e95ab64759dc44bed65afd2c1db5669b38f5a9962","last_reissued_at":"2026-05-18T00:49:05.178173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:05.178173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611625","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":"2026-05-18T00:49:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4dZ7Fj7qSR4vCnaHDaU0czguueD4ecBFd/kkgq33pihIzTnZ72a+GxmIevLvh/rN6iHkQD/Tyjll8kvfJupCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:36:04.257777Z"},"content_sha256":"0ca022b852563478f141ec30b09f0389606bb0ec3dcb11766785dd46521a965e","schema_version":"1.0","event_id":"sha256:0ca022b852563478f141ec30b09f0389606bb0ec3dcb11766785dd46521a965e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:7CASM2HBVVTKTX46P2HJLK3EOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kinetic decomposition for periodic homogenization problems","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Athanasios E. Tzavaras, Pierre-Emmanuel Jabin","submitted_at":"2006-11-21T02:00:13Z","abstract_excerpt":"We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a kinetic equation. We establish conditions determining an effective equation and counterexamples for the case that such conditions fail. Second, when the kinetic decomposition is applied to the problem of enhanced "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611625","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":"2026-05-18T00:49:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9aj8La4O78Hq1nXBM8wUsXIkDuA4BudsniewNx7oDGFvSLhxA1psGWu0EL8hN5zZSNNh67Y5ffqWvzTT1WMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:36:04.258427Z"},"content_sha256":"f5f6ad02fbe6c21390197b8fc366c32b239bbbc858bd94f331edd294a2903565","schema_version":"1.0","event_id":"sha256:f5f6ad02fbe6c21390197b8fc366c32b239bbbc858bd94f331edd294a2903565"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CASM2HBVVTKTX46P2HJLK3EOW/bundle.json","state_url":"https://pith.science/pith/7CASM2HBVVTKTX46P2HJLK3EOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CASM2HBVVTKTX46P2HJLK3EOW/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":"2026-05-26T00:36:04Z","links":{"resolver":"https://pith.science/pith/7CASM2HBVVTKTX46P2HJLK3EOW","bundle":"https://pith.science/pith/7CASM2HBVVTKTX46P2HJLK3EOW/bundle.json","state":"https://pith.science/pith/7CASM2HBVVTKTX46P2HJLK3EOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CASM2HBVVTKTX46P2HJLK3EOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:7CASM2HBVVTKTX46P2HJLK3EOW","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":"697a6444b74c31647ce4f96782f5fc05e254488ed097cb6f677041fbdce1c323","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-11-21T02:00:13Z","title_canon_sha256":"f33fef3390e4d22dd6dedf9e0868f0c6e43636971b6ccafba832e22ae548dce3"},"schema_version":"1.0","source":{"id":"math/0611625","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611625","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611625v1","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611625","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"7CASM2HBVVTK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7CASM2HBVVTKTX46","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7CASM2HB","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f5f6ad02fbe6c21390197b8fc366c32b239bbbc858bd94f331edd294a2903565","target":"graph","created_at":"2026-05-18T00:49:05Z","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 develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a kinetic equation. We establish conditions determining an effective equation and counterexamples for the case that such conditions fail. Second, when the kinetic decomposition is applied to the problem of enhanced ","authors_text":"Athanasios E. Tzavaras, Pierre-Emmanuel Jabin","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-11-21T02:00:13Z","title":"Kinetic decomposition for periodic homogenization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611625","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":"sha256:0ca022b852563478f141ec30b09f0389606bb0ec3dcb11766785dd46521a965e","target":"record","created_at":"2026-05-18T00:49:05Z","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":"697a6444b74c31647ce4f96782f5fc05e254488ed097cb6f677041fbdce1c323","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-11-21T02:00:13Z","title_canon_sha256":"f33fef3390e4d22dd6dedf9e0868f0c6e43636971b6ccafba832e22ae548dce3"},"schema_version":"1.0","source":{"id":"math/0611625","kind":"arxiv","version":1}},"canonical_sha256":"f8812668e1ad66a9df9e7e8e95ab64759dc44bed65afd2c1db5669b38f5a9962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8812668e1ad66a9df9e7e8e95ab64759dc44bed65afd2c1db5669b38f5a9962","first_computed_at":"2026-05-18T00:49:05.178173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:05.178173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDOUQqc3jYJQdDx3FQq1aHGKwAdKmiTCpTxvxl7T1SiITjrX7iY/FqpSxd4wztqIbZSxhrO8tdxDV3e+k/h9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:05.178616Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611625","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ca022b852563478f141ec30b09f0389606bb0ec3dcb11766785dd46521a965e","sha256:f5f6ad02fbe6c21390197b8fc366c32b239bbbc858bd94f331edd294a2903565"],"state_sha256":"414eb93f7ea705cc5dec0a9dc3c9c4e9e75ec3d320061b9f8bec0eefa15edf3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pl4L0mCeFiM03e8ecJ8QejG7vxmNLKYrLfJVk/EH2WKYZv4m/Ix0Lfb6hqe4qYbj3GKsp/RJQcX35m/LSieoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:36:04.262173Z","bundle_sha256":"bde47ecda0ef596597ecefae33cf188b3e6cd272c31d62020c96d242a62ddc63"}}