{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:P2P6T24MMQU6BSPD6AQYD2NTZB","short_pith_number":"pith:P2P6T24M","canonical_record":{"source":{"id":"1201.0222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-31T04:34:47Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"title_canon_sha256":"63ec1095829d295d4a6216d546acf567ed85c82a1d6cd6058d50697e71d0cc81","abstract_canon_sha256":"64409179b5b380cb705803ae506b86b3bcd1977cf87b211bbeb298a9b8a55a33"},"schema_version":"1.0"},"canonical_sha256":"7e9fe9eb8c6429e0c9e3f02181e9b3c8442b46cd2d733eef91d485130120ed0c","source":{"kind":"arxiv","id":"1201.0222","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0222","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0222v2","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0222","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"P2P6T24MMQU6","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P2P6T24MMQU6BSPD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P2P6T24M","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:P2P6T24MMQU6BSPD6AQYD2NTZB","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-31T04:34:47Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"title_canon_sha256":"63ec1095829d295d4a6216d546acf567ed85c82a1d6cd6058d50697e71d0cc81","abstract_canon_sha256":"64409179b5b380cb705803ae506b86b3bcd1977cf87b211bbeb298a9b8a55a33"},"schema_version":"1.0"},"canonical_sha256":"7e9fe9eb8c6429e0c9e3f02181e9b3c8442b46cd2d733eef91d485130120ed0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:46.626377Z","signature_b64":"RQgBX9ql5qGdU01KzmFcKx7fX7ao+tHaWqFT3kDLdGUggtl8XOtBCFTMeUEdTkm+IvRrbOXtlkrcOc/sXXgdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e9fe9eb8c6429e0c9e3f02181e9b3c8442b46cd2d733eef91d485130120ed0c","last_reissued_at":"2026-05-18T03:12:46.625758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:46.625758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0222","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":"2026-05-18T03:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbsS7UMJota6bXZvLExxJZ4iUPIasHuj8r+bOumCCZj2lk6hcfF7d0XicZWTVf/F5JTUUEWuKsJp9LXpXV2ABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:55:48.494521Z"},"content_sha256":"8b8a97fcc05b2cd450d837b75f5b2cb16eb2fa1d358f0073585b4479347f6421","schema_version":"1.0","event_id":"sha256:8b8a97fcc05b2cd450d837b75f5b2cb16eb2fa1d358f0073585b4479347f6421"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:P2P6T24MMQU6BSPD6AQYD2NTZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $\\mathbf \\Gamma$-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"primary_cat":"math-ph","authors_text":"Cyrill B. Muratov, Dorian Goldman, Sylvia Serfaty","submitted_at":"2011-12-31T04:34:47Z","abstract_excerpt":"This is the first in a series of two papers in which we derive a $\\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In that model, two phases appear, which interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating small \"droplets\" of the minority phase in a \"sea\" of the majority phase. In this paper we show that an appropriate setting for $\\Gamma$-convergence in the considered parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0222","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":"2026-05-18T03:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUZL1mY1gFFucoJMCm5BzYnSxiyGT/QQNpTMHwPEeJIyMXTQjY7SNQc7SW9y+Dbqnlov9APn9UhaZ/8rULMnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:55:48.495247Z"},"content_sha256":"c42b3e55cd4291b25baef8c624b126a54f41623902073cd03299e3c595a29884","schema_version":"1.0","event_id":"sha256:c42b3e55cd4291b25baef8c624b126a54f41623902073cd03299e3c595a29884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2P6T24MMQU6BSPD6AQYD2NTZB/bundle.json","state_url":"https://pith.science/pith/P2P6T24MMQU6BSPD6AQYD2NTZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2P6T24MMQU6BSPD6AQYD2NTZB/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":"2026-05-26T21:55:48Z","links":{"resolver":"https://pith.science/pith/P2P6T24MMQU6BSPD6AQYD2NTZB","bundle":"https://pith.science/pith/P2P6T24MMQU6BSPD6AQYD2NTZB/bundle.json","state":"https://pith.science/pith/P2P6T24MMQU6BSPD6AQYD2NTZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2P6T24MMQU6BSPD6AQYD2NTZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:P2P6T24MMQU6BSPD6AQYD2NTZB","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":"64409179b5b380cb705803ae506b86b3bcd1977cf87b211bbeb298a9b8a55a33","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-31T04:34:47Z","title_canon_sha256":"63ec1095829d295d4a6216d546acf567ed85c82a1d6cd6058d50697e71d0cc81"},"schema_version":"1.0","source":{"id":"1201.0222","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0222","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0222v2","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0222","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"P2P6T24MMQU6","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P2P6T24MMQU6BSPD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P2P6T24M","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:c42b3e55cd4291b25baef8c624b126a54f41623902073cd03299e3c595a29884","target":"graph","created_at":"2026-05-18T03:12:46Z","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 is the first in a series of two papers in which we derive a $\\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In that model, two phases appear, which interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating small \"droplets\" of the minority phase in a \"sea\" of the majority phase. In this paper we show that an appropriate setting for $\\Gamma$-convergence in the considered parameter","authors_text":"Cyrill B. Muratov, Dorian Goldman, Sylvia Serfaty","cross_cats":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-31T04:34:47Z","title":"The $\\mathbf \\Gamma$-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0222","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":"sha256:8b8a97fcc05b2cd450d837b75f5b2cb16eb2fa1d358f0073585b4479347f6421","target":"record","created_at":"2026-05-18T03:12:46Z","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":"64409179b5b380cb705803ae506b86b3bcd1977cf87b211bbeb298a9b8a55a33","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-31T04:34:47Z","title_canon_sha256":"63ec1095829d295d4a6216d546acf567ed85c82a1d6cd6058d50697e71d0cc81"},"schema_version":"1.0","source":{"id":"1201.0222","kind":"arxiv","version":2}},"canonical_sha256":"7e9fe9eb8c6429e0c9e3f02181e9b3c8442b46cd2d733eef91d485130120ed0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9fe9eb8c6429e0c9e3f02181e9b3c8442b46cd2d733eef91d485130120ed0c","first_computed_at":"2026-05-18T03:12:46.625758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:46.625758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQgBX9ql5qGdU01KzmFcKx7fX7ao+tHaWqFT3kDLdGUggtl8XOtBCFTMeUEdTkm+IvRrbOXtlkrcOc/sXXgdCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:46.626377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0222","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b8a97fcc05b2cd450d837b75f5b2cb16eb2fa1d358f0073585b4479347f6421","sha256:c42b3e55cd4291b25baef8c624b126a54f41623902073cd03299e3c595a29884"],"state_sha256":"8f7f289a49c9c6bc4cc98e74fe79f2311ddbaa6b99a0797b5fcd67b7ddecf4ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxVSI+LOlj2AyZwRBnSLGuavHv6bUZAfwajXv4t9fBtHgtatB29d6HTVIAg1XQmi1dpx744uWx83ESrpt/WhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:55:48.498766Z","bundle_sha256":"e83ac31af611cd2eb635920dea529185bb2bff6ea14cd5e375dfe14f2f41bb10"}}