{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GAD5GDTB6HTCS55CNE2FDCFJHX","short_pith_number":"pith:GAD5GDTB","canonical_record":{"source":{"id":"1112.2971","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-13T17:32:38Z","cross_cats_sorted":[],"title_canon_sha256":"7db7188653bd34e254f5b0618a87e09f86e4d84bcc8d432525b2837b567ab3b8","abstract_canon_sha256":"c8855b2a3099ad1b10f09e7abea71c128a7a4c4329f0b754d78cf8e5191e527c"},"schema_version":"1.0"},"canonical_sha256":"3007d30e61f1e62977a269345188a93defc2814d367be1095ccd36fea309a9c8","source":{"kind":"arxiv","id":"1112.2971","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2971","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2971v6","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2971","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"GAD5GDTB6HTC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GAD5GDTB6HTCS55C","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GAD5GDTB","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GAD5GDTB6HTCS55CNE2FDCFJHX","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2971","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-13T17:32:38Z","cross_cats_sorted":[],"title_canon_sha256":"7db7188653bd34e254f5b0618a87e09f86e4d84bcc8d432525b2837b567ab3b8","abstract_canon_sha256":"c8855b2a3099ad1b10f09e7abea71c128a7a4c4329f0b754d78cf8e5191e527c"},"schema_version":"1.0"},"canonical_sha256":"3007d30e61f1e62977a269345188a93defc2814d367be1095ccd36fea309a9c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:50.176886Z","signature_b64":"gWcKpXXH9IK4DEfG5JIS9hzAPizzFWmG18fVQb3V803ZHPpBVNBh4iN5NMMlXzrBiNHvQK114MPmLb7waQY1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3007d30e61f1e62977a269345188a93defc2814d367be1095ccd36fea309a9c8","last_reissued_at":"2026-05-18T02:27:50.176410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:50.176410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2971","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"egF3JNN/OLvc22yAAgi1Y2HkhZA9h46KgiaU/rtGsaJz7MaGZt0AV9KW+aYd4azTxUHDgYrzR/+RpiZ8DlAFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:38:03.674435Z"},"content_sha256":"6dc8eb3be7a6ed6e11f5e2ca1935cb321324d3f73735ff430ae3dd4537b8eaec","schema_version":"1.0","event_id":"sha256:6dc8eb3be7a6ed6e11f5e2ca1935cb321324d3f73735ff430ae3dd4537b8eaec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GAD5GDTB6HTCS55CNE2FDCFJHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $\\Gamma$-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part III: The energies with non local terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arkady Poliakovsky","submitted_at":"2011-12-13T17:32:38Z","abstract_excerpt":"We use the technique developed in [32]-[33] to construct the upper and the lower bounds for classes of problems containing non-local terms, including problems in micromagnetics and problems arising in the variational study of the Method of Vanishing Viscosity for systems of conservation laws. We reduced these problems to the problems considered in [32]-[33], with the appropriate prescribed differential constraint."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2971","kind":"arxiv","version":6},"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":"2026-05-18T02:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9Yl7jqk0Fxsi5g3W9lnhHqX1ITLCOik0Rue5a5Oi0TKtVkQ+l4qdnkNTphB8SLwdSQvvTRjgynBEN6mt1reDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:38:03.674784Z"},"content_sha256":"a9656d513ea07bd1820e93188c6741507fe11bfe3ba46737f75e51a99edbe7e8","schema_version":"1.0","event_id":"sha256:a9656d513ea07bd1820e93188c6741507fe11bfe3ba46737f75e51a99edbe7e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAD5GDTB6HTCS55CNE2FDCFJHX/bundle.json","state_url":"https://pith.science/pith/GAD5GDTB6HTCS55CNE2FDCFJHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAD5GDTB6HTCS55CNE2FDCFJHX/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":"2026-06-23T15:38:03Z","links":{"resolver":"https://pith.science/pith/GAD5GDTB6HTCS55CNE2FDCFJHX","bundle":"https://pith.science/pith/GAD5GDTB6HTCS55CNE2FDCFJHX/bundle.json","state":"https://pith.science/pith/GAD5GDTB6HTCS55CNE2FDCFJHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAD5GDTB6HTCS55CNE2FDCFJHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GAD5GDTB6HTCS55CNE2FDCFJHX","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":"c8855b2a3099ad1b10f09e7abea71c128a7a4c4329f0b754d78cf8e5191e527c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-13T17:32:38Z","title_canon_sha256":"7db7188653bd34e254f5b0618a87e09f86e4d84bcc8d432525b2837b567ab3b8"},"schema_version":"1.0","source":{"id":"1112.2971","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2971","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2971v6","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2971","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"GAD5GDTB6HTC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GAD5GDTB6HTCS55C","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GAD5GDTB","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:a9656d513ea07bd1820e93188c6741507fe11bfe3ba46737f75e51a99edbe7e8","target":"graph","created_at":"2026-05-18T02:27:50Z","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 use the technique developed in [32]-[33] to construct the upper and the lower bounds for classes of problems containing non-local terms, including problems in micromagnetics and problems arising in the variational study of the Method of Vanishing Viscosity for systems of conservation laws. We reduced these problems to the problems considered in [32]-[33], with the appropriate prescribed differential constraint.","authors_text":"Arkady Poliakovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-13T17:32:38Z","title":"On the $\\Gamma$-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part III: The energies with non local terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2971","kind":"arxiv","version":6},"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":"sha256:6dc8eb3be7a6ed6e11f5e2ca1935cb321324d3f73735ff430ae3dd4537b8eaec","target":"record","created_at":"2026-05-18T02:27:50Z","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":"c8855b2a3099ad1b10f09e7abea71c128a7a4c4329f0b754d78cf8e5191e527c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-13T17:32:38Z","title_canon_sha256":"7db7188653bd34e254f5b0618a87e09f86e4d84bcc8d432525b2837b567ab3b8"},"schema_version":"1.0","source":{"id":"1112.2971","kind":"arxiv","version":6}},"canonical_sha256":"3007d30e61f1e62977a269345188a93defc2814d367be1095ccd36fea309a9c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3007d30e61f1e62977a269345188a93defc2814d367be1095ccd36fea309a9c8","first_computed_at":"2026-05-18T02:27:50.176410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:50.176410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gWcKpXXH9IK4DEfG5JIS9hzAPizzFWmG18fVQb3V803ZHPpBVNBh4iN5NMMlXzrBiNHvQK114MPmLb7waQY1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:50.176886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2971","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dc8eb3be7a6ed6e11f5e2ca1935cb321324d3f73735ff430ae3dd4537b8eaec","sha256:a9656d513ea07bd1820e93188c6741507fe11bfe3ba46737f75e51a99edbe7e8"],"state_sha256":"f80051743e2ba56efe32c609302982c10ce1369f248ece568158949a2cb16dba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCH8PpohxxhF8MB7LdkMA4GKkYhJXP2u0tOA3sIdbqc1SRjUuG7TdhF6zW35nlu/Syu0iMr7viD7foJb6pTbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:38:03.676662Z","bundle_sha256":"96283b128eb1cd4507ff5ca5fac0f1d1093753352211c067cd5e8f52178f7904"}}