{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:EHTFG4B335W35A5ZUXPXZK2SBG","short_pith_number":"pith:EHTFG4B3","canonical_record":{"source":{"id":"math/0611313","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-11-10T13:14:28Z","cross_cats_sorted":[],"title_canon_sha256":"2c0dc34bbae899ff87f5bcefffc41bcf7718e8bef77b0fb12442a672f9e5decd","abstract_canon_sha256":"ba6ea84517105945ffbdfb397a996e9d30d5a54688dd07b4447d08bd150a1471"},"schema_version":"1.0"},"canonical_sha256":"21e653703bdf6dbe83b9a5df7cab5209a1e6b874630522a9675e5697425d2c6c","source":{"kind":"arxiv","id":"math/0611313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611313","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611313v2","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611313","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"EHTFG4B335W3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EHTFG4B335W35A5Z","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EHTFG4B3","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:EHTFG4B335W35A5ZUXPXZK2SBG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611313","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-11-10T13:14:28Z","cross_cats_sorted":[],"title_canon_sha256":"2c0dc34bbae899ff87f5bcefffc41bcf7718e8bef77b0fb12442a672f9e5decd","abstract_canon_sha256":"ba6ea84517105945ffbdfb397a996e9d30d5a54688dd07b4447d08bd150a1471"},"schema_version":"1.0"},"canonical_sha256":"21e653703bdf6dbe83b9a5df7cab5209a1e6b874630522a9675e5697425d2c6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:25.496689Z","signature_b64":"GOkKQkx/OfGtOXiAEFoyEXUDJaAKQj1PFJHwunJzqPf3gp22Ex96KOst0ZE5r69BXeGi0eJVQADx+LN1NHjBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21e653703bdf6dbe83b9a5df7cab5209a1e6b874630522a9675e5697425d2c6c","last_reissued_at":"2026-05-18T03:08:25.495930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:25.495930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611313","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtRfucYWJ/g8uZg3g7CXl9srvJ4kwksUrYW4werRxskhJM+7t+6EIO56vce5Lwf1saKuOBxHEDG9XcxVTUY2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:07:00.664628Z"},"content_sha256":"09b89896ddaf55ec42536254e6d3ea61603027b4133ce9e94688f4ea661432e8","schema_version":"1.0","event_id":"sha256:09b89896ddaf55ec42536254e6d3ea61603027b4133ce9e94688f4ea661432e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:EHTFG4B335W35A5ZUXPXZK2SBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of two-scale gradient Young measures and application to homogenization","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean-Francois Babadjian, Margarida Baia, Pedro M. Santos","submitted_at":"2006-11-10T13:14:28Z","abstract_excerpt":"This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611313","kind":"arxiv","version":2},"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":"2026-05-18T03:08:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5g3Hr9HWXH/2daLU/sA3yqReW6ukIverwRiBDNjIHbKx30Xjp98gjyzHU8FWP7foi3Gx5CYuLVItVn7idS59CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:07:00.665277Z"},"content_sha256":"7f4d061db949cab2b779a15ea1875d39449fd96cfba95a243ef109ad105598d9","schema_version":"1.0","event_id":"sha256:7f4d061db949cab2b779a15ea1875d39449fd96cfba95a243ef109ad105598d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHTFG4B335W35A5ZUXPXZK2SBG/bundle.json","state_url":"https://pith.science/pith/EHTFG4B335W35A5ZUXPXZK2SBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHTFG4B335W35A5ZUXPXZK2SBG/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":"2026-06-06T10:07:00Z","links":{"resolver":"https://pith.science/pith/EHTFG4B335W35A5ZUXPXZK2SBG","bundle":"https://pith.science/pith/EHTFG4B335W35A5ZUXPXZK2SBG/bundle.json","state":"https://pith.science/pith/EHTFG4B335W35A5ZUXPXZK2SBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHTFG4B335W35A5ZUXPXZK2SBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:EHTFG4B335W35A5ZUXPXZK2SBG","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":"ba6ea84517105945ffbdfb397a996e9d30d5a54688dd07b4447d08bd150a1471","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-11-10T13:14:28Z","title_canon_sha256":"2c0dc34bbae899ff87f5bcefffc41bcf7718e8bef77b0fb12442a672f9e5decd"},"schema_version":"1.0","source":{"id":"math/0611313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611313","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611313v2","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611313","created_at":"2026-05-18T03:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"EHTFG4B335W3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EHTFG4B335W35A5Z","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EHTFG4B3","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7f4d061db949cab2b779a15ea1875d39449fd96cfba95a243ef109ad105598d9","target":"graph","created_at":"2026-05-18T03:08:25Z","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":"This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.","authors_text":"Jean-Francois Babadjian, Margarida Baia, Pedro M. Santos","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-11-10T13:14:28Z","title":"Characterization of two-scale gradient Young measures and application to homogenization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611313","kind":"arxiv","version":2},"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":"sha256:09b89896ddaf55ec42536254e6d3ea61603027b4133ce9e94688f4ea661432e8","target":"record","created_at":"2026-05-18T03:08:25Z","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":"ba6ea84517105945ffbdfb397a996e9d30d5a54688dd07b4447d08bd150a1471","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-11-10T13:14:28Z","title_canon_sha256":"2c0dc34bbae899ff87f5bcefffc41bcf7718e8bef77b0fb12442a672f9e5decd"},"schema_version":"1.0","source":{"id":"math/0611313","kind":"arxiv","version":2}},"canonical_sha256":"21e653703bdf6dbe83b9a5df7cab5209a1e6b874630522a9675e5697425d2c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21e653703bdf6dbe83b9a5df7cab5209a1e6b874630522a9675e5697425d2c6c","first_computed_at":"2026-05-18T03:08:25.495930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:25.495930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GOkKQkx/OfGtOXiAEFoyEXUDJaAKQj1PFJHwunJzqPf3gp22Ex96KOst0ZE5r69BXeGi0eJVQADx+LN1NHjBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:25.496689Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09b89896ddaf55ec42536254e6d3ea61603027b4133ce9e94688f4ea661432e8","sha256:7f4d061db949cab2b779a15ea1875d39449fd96cfba95a243ef109ad105598d9"],"state_sha256":"c1e911f0bda67e29f6b69d59775832b760456204eabdad40b323ce1a90667962"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1zDzWjd+bg6ZdJaBpv7Bl6WeymJDLVOh4qCntXxyBO7eS2WvDyZxrX2N3RvM407ENisMig4naEgpP0vzFzOdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T10:07:00.668921Z","bundle_sha256":"01dcccb723ea375287caa156220035b7dac72874dfe0f2f1813797566d4359cf"}}