{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JIJZDJURFX433RFTSWKDVICX23","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":"813b3538650be12a88e5e95524f7cd3726f7c67cea9e8e50aa312f363062f87a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T13:08:49Z","title_canon_sha256":"4a1ea1a4d3075cce9d497c8c93b190025b85b904c537762bba3fc400fe547b7c"},"schema_version":"1.0","source":{"id":"1411.4463","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4463","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4463v2","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4463","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"JIJZDJURFX43","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JIJZDJURFX433RFT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JIJZDJUR","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a81e7e657521463f930e356825d8ca05cb0c37d45141685c8ff49618904c15e0","target":"graph","created_at":"2026-05-18T00:10:04Z","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 study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter $\\varepsilon$ and the magnets as classical $\\pm 1$ spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of $\\Gamma$-convergence that, up to subsequences, the (continuum) $\\Gamma$-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it","authors_text":"M. Cicalese, M. Ruf, R. Alicandro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T13:08:49Z","title":"Domain formation in magnetic polymer composites: an approach via stochastic homogenization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4463","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":"sha256:76f05c746b43ecb83182aa91a892fa19e8730f7eeb63defcf8272d68f02fec51","target":"record","created_at":"2026-05-18T00:10:04Z","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":"813b3538650be12a88e5e95524f7cd3726f7c67cea9e8e50aa312f363062f87a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T13:08:49Z","title_canon_sha256":"4a1ea1a4d3075cce9d497c8c93b190025b85b904c537762bba3fc400fe547b7c"},"schema_version":"1.0","source":{"id":"1411.4463","kind":"arxiv","version":2}},"canonical_sha256":"4a1391a6912df9bdc4b395943aa057d6c145bc1255e237c2824e4371a197b27c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a1391a6912df9bdc4b395943aa057d6c145bc1255e237c2824e4371a197b27c","first_computed_at":"2026-05-18T00:10:04.628300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:04.628300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lkgr1OHLlAEKc5Dm/LX4sO42WOfnhWCLwOy5CnGfhxICcvBwJjIXjnO8gzRqs6OyJA5PSKPeFHzilwZoV4PYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:04.629041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4463","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76f05c746b43ecb83182aa91a892fa19e8730f7eeb63defcf8272d68f02fec51","sha256:a81e7e657521463f930e356825d8ca05cb0c37d45141685c8ff49618904c15e0"],"state_sha256":"4d7d0fb45b93b51beeaf9ed6545545cd2698c49abbddd9234de3a654ca13595f"}